Unit 2

Knowledge-Based Agent in Artificial intelligence

o An intelligent agent needs knowledge about the real world for taking decisions
and reasoning to act efficiently.
o Knowledge-based agents are those agents who have the capability of maintaining an
internal state of knowledge, reason over that knowledge, update their knowledge
after observations and take actions. These agents can represent the world with some
formal representation and act intelligently.
o Knowledge-based agents are composed of two main parts:
o Knowledge-base and
o Inference system.

A knowledge-based agent must able to do the following:

o An agent should be able to represent states, actions, etc.

o An agent Should be able to incorporate new percepts
o An agent can update the internal representation of the world
o An agent can deduce the internal representation of the world
o An agent can deduce appropriate actions.

The architecture of knowledge-based agent:

The above diagram is representing a generalized architecture for a knowledge-based agent. The
knowledge-based agent (KBA) takes input from the environment by perceiving the environment.
The input is taken by the inference engine of the agent and which also communicate with KB to
decide as per the knowledge store in KB. The learning element of KBA regularly updates the KB
by learning new knowledge.

Knowledge base: Knowledge-base is a central component of a knowledge-based agent, it is also

known as KB. It is a collection of sentences (here 'sentence' is a technical term and it is not
identical to sentence in English). These sentences are expressed in a language which is called a
knowledge representation language. The Knowledge-base of KBA stores fact about the world.

Why use a knowledge base?

Knowledge-base is required for updating knowledge for an agent to learn with experiences and
take action as per the knowledge.

Inference system
Inference means deriving new sentences from old. Inference system allows us to add a new
sentence to the knowledge base. A sentence is a proposition about the world. Inference system
applies logical rules to the KB to deduce new information.

Inference system generates new facts so that an agent can update the KB. An inference system
works mainly in two rules which are given as:

o Forward chaining
o Backward chaining

Operations Performed by KBA

Following are three operations which are performed by KBA in order to show the
intelligent behavior:

1. TELL: This operation tells the knowledge base what it perceives from the environment.
2. ASK: This operation asks the knowledge base what action it should perform.
3. Perform: It performs the selected action.
 A generic knowledge-based agent:
Following is the structure outline of a generic knowledge-based agents program:

1. function KB-AGENT(percept):
2. persistent: KB, a knowledge base
3. t, a counter, initially 0, indicating time
4. TELL(KB, MAKE-PERCEPT-SENTENCE(percept, t))
5. Action = ASK(KB, MAKE-ACTION-QUERY(t))
6. TELL(KB, MAKE-ACTION-SENTENCE(action, t))
7. t=t+1
8. return action

The knowledge-based agent takes percept as input and returns an action as output. The agent
maintains the knowledge base, KB, and it initially has some background knowledge of the real
world. It also has a counter to indicate the time for the whole process, and this counter is
initialized with zero.

Each time when the function is called, it performs its three operations:

o Firstly it TELLs the KB what it perceives.

o Secondly, it asks KB what action it should take
o Third agent program TELLS the KB that which action was chosen.

The MAKE-PERCEPT-SENTENCE generates a sentence as setting that the agent perceived the
given percept at the given time.

The MAKE-ACTION-QUERY generates a sentence to ask which action should be done at the
current time.

MAKE-ACTION-SENTENCE generates a sentence which asserts that the chosen action was
executed.
Various levels of knowledge-based agent:
A knowledge-based agent can be viewed at different levels which are given below:

1. Knowledge level
Knowledge level is the first level of knowledge-based agent, and in this level, we need to specify
what the agent knows, and what the agent goals are. With these specifications, we can fix its
behavior. For example, suppose an automated taxi agent needs to go from a station A to station
B, and he knows the way from A to B, so this comes at the knowledge level.

2. Logical level:
At this level, we understand that how the knowledge representation of knowledge is stored. At
this level, sentences are encoded into different logics. At the logical level, an encoding of
knowledge into logical sentences occurs. At the logical level we can expect to the automated taxi
agent to reach to the destination B.

3. Implementation level:
This is the physical representation of logic and knowledge. At the implementation level agent
perform actions as per logical and knowledge level. At this level, an automated taxi agent
actually implements his knowledge and logic so that he can reach to the destination.

Approaches to designing a knowledge-based agent:

There are mainly two approaches to build a knowledge-based agent:

1. 1. Declarative approach: We can create a knowledge-based agent by initializing

with an empty knowledge base and telling the agent all the sentences with which
we want to start with. This approach is called Declarative approach.
2. 2. Procedural approach: In the procedural approach, we directly encode desired
behavior as a program code. Which means we just need to write a program that
already encodes the desired behavior or agent.

However, in the real world, a successful agent can be built by combining both
declarative and procedural approaches, and declarative knowledge can often be
compiled into more efficient procedural code.
What is knowledge representation?
Humans are best at understanding, reasoning, and interpreting knowledge. Human
knows things, which is knowledge and as per their knowledge they perform various
actions in the real world. But how machines do all these things comes under
knowledge representation and reasoning. Hence we can describe Knowledge
representation as following:

o Knowledge representation and reasoning (KR, KRR) is the part of Artificial

intelligence which concerned with AI agents thinking and how thinking
contributes to intelligent behavior of agents.
o It is responsible for representing information about the real world so that a
computer can understand and can utilize this knowledge to solve the complex
real world problems such as diagnosis a medical condition or communicating
with humans in natural language.
o It is also a way which describes how we can represent knowledge in artificial
intelligence. Knowledge representation is not just storing data into some
database, but it also enables an intelligent machine to learn from that knowledge
and experiences so that it can behave intelligently like a human.

What to Represent:
Following are the kind of knowledge which needs to be represented in AI systems:

o Object: All the facts about objects in our world domain. E.g., Guitars contains
strings, trumpets are brass instruments.
o Events: Events are the actions which occur in our world.
o Performance: It describe behavior which involves knowledge about how to do
things.
o Meta-knowledge: It is knowledge about what we know.
o Facts: Facts are the truths about the real world and what we represent.
o Knowledge-Base: The central component of the knowledge-based agents is the
knowledge base. It is represented as KB. The Knowledgebase is a group of the
Sentences (Here, sentences are used as a technical term and not identical with
the English language).
Knowledge: Knowledge is awareness or familiarity gained by experiences of facts, data,
and situations. Following are the types of knowledge in artificial intelligence:

Types of knowledge
Following are the various types of knowledge:

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1. Declarative Knowledge:

o Declarative knowledge is to know about something.

o It includes concepts, facts, and objects.
o It is also called descriptive knowledge and expressed in declarativesentences.
o It is simpler than procedural language.

2. Procedural Knowledge

o It is also known as imperative knowledge.

 o Procedural knowledge is a type of knowledge which is responsible for knowing
how to do something.
o It can be directly applied to any task.
o It includes rules, strategies, procedures, agendas, etc.
o Procedural knowledge depends on the task on which it can be applied.

3. Meta-knowledge:

o Knowledge about the other types of knowledge is called Meta-knowledge.

4. Heuristic knowledge:

o Heuristic knowledge is representing knowledge of some experts in a filed or

subject.
o Heuristic knowledge is rules of thumb based on previous experiences, awareness
of approaches, and which are good to work but not guaranteed.

5. Structural knowledge:

o Structural knowledge is basic knowledge to problem-solving.

o It describes relationships between various concepts such as kind of, part of, and
grouping of something.
o It describes the relationship that exists between concepts or objects.

The relation between knowledge and intelligence:

Knowledge of real-worlds plays a vital role in intelligence and same for creating artificial
intelligence. Knowledge plays an important role in demonstrating intelligent behavior in
AI agents. An agent is only able to accurately act on some input when he has some
knowledge or experience about that input.

Let's suppose if you met some person who is speaking in a language which you don't
know, then how you will able to act on that. The same thing applies to the intelligent
behavior of the agents.
As we can see in below diagram, there is one decision maker which act by sensing the
environment and using knowledge. But if the knowledge part will not present then, it
cannot display intelligent behavior.

AI knowledge cycle:
An Artificial intelligence system has the following components for displaying intelligent
behavior:

o Perception
o Learning
o Knowledge Representation and Reasoning
o Planning
o Execution
The above diagram is showing how an AI system can interact with the real world and
what components help it to show intelligence. AI system has Perception component by
which it retrieves information from its environment. It can be visual, audio or another
form of sensory input. The learning component is responsible for learning from data
captured by Perception comportment. In the complete cycle, the main components are
knowledge representation and Reasoning. These two components are involved in
showing the intelligence in machine-like humans. These two components are
independent with each other but also coupled together. The planning and execution
depend on analysis of Knowledge representation and reasoning.

Approaches to knowledge representation:

There are mainly four approaches to knowledge representation, which are givenbelow:

1. Simple relational knowledge:

o It is the simplest way of storing facts which uses the relational method, and each
fact about a set of the object is set out systematically in columns.
o This approach of knowledge representation is famous in database systems where
the relationship between different entities is represented.
o This approach has little opportunity for inference.

Example: The following is the simple relational knowledge representation.

 Player Weight Age

Player1 65 23

Player2 58 18

Player3 75 24

2. Inheritable knowledge:

o In the inheritable knowledge approach, all data must be stored into a hierarchy of
classes.
o All classes should be arranged in a generalized form or a hierarchal manner.
o In this approach, we apply inheritance property.
o Elements inherit values from other members of a class.
o This approach contains inheritable knowledge which shows a relation between
instance and class, and it is called instance relation.
o Every individual frame can represent the collection of attributes and its value.
o In this approach, objects and values are represented in Boxed nodes.
o We use Arrows which point from objects to their values.
o Example:
3. Inferential knowledge:

o Inferential knowledge approach represents knowledge in the form of formal

logics.
o This approach can be used to derive more facts.
o It guaranteed correctness.
o Example: Let's suppose there are two statements:
a. Marcus is a man
b. All men are mortal
Then it can represent as;

man(Marcus)
∀x = man (x) ----------> mortal (x)s

4. Procedural knowledge:

o Procedural knowledge approach uses small programs and codes which describes
how to do specific things, and how to proceed.
o In this approach, one important rule is used which is If-Then rule.
o In this knowledge, we can use various coding languages such as LISP
language and Prolog language.
o We can easily represent heuristic or domain-specific knowledge using this
approach.
o But it is not necessary that we can represent all cases in this approach.

Requirements for knowledge Representation system:

A good knowledge representation system must possess the following properties.

1. Representational Accuracy:
KR system should have the ability to represent all kind of required knowledge.
 2. Inferential Adequacy:
KR system should have ability to manipulate the representational structures to
produce new knowledge corresponding to existing structure.

3. Inferential Efficiency:
The ability to direct the inferential knowledge mechanism into the most
productive directions by storing appropriate guides.

4. Acquisitional efficiency- The ability to acquire the new knowledge easily

using automatic methods.

Techniques of knowledge representation

There are mainly four ways of knowledge representation which are given as follows:

1. Logical Representation
2. Semantic Network Representation
3. Frame Representation
4. Production Rules

1. Logical Representation
Logical representation is a language with some concrete rules which deals with
propositions and has no ambiguity in representation. Logical representation means
drawing a conclusion based on various conditions. This representation lays down some
important communication rules. It consists of precisely defined syntax and semantics
which supports the sound inference. Each sentence can be translated into logics using
syntax and semantics.

Syntax:

o Syntaxes are the rules which decide how we can construct legal sentences in the
logic.
 o It determines which symbol we can use in knowledge representation.
o How to write those symbols.

Semantics:

o Semantics are the rules by which we can interpret the sentence in the logic.
o Semantic also involves assigning a meaning to each sentence.

Logical representation can be categorised into mainly two logics:

a. Propositional Logics
b. Predicate logics

Note: We will discuss Prepositional Logics and Predicate logics in later chapters.

Advantages of logical representation:

1. Logical representation enables us to do logical reasoning.

2. Logical representation is the basis for the programming languages.

Disadvantages of logical Representation:

1. Logical representations have some restrictions and are challenging to work with.
2. Logical representation technique may not be very natural, and inference may not
be so efficient.

Note: Do not be confused with logical representation and logical reasoning as logical
representation is a representation language and reasoning is a process of thinking logically.

2. Semantic Network Representation

Semantic networks are alternative of predicate logic for knowledge representation. In
Semantic networks, we can represent our knowledge in the form of graphical networks.
This network consists of nodes representing objects and arcs which describe the
relationship between those objects. Semantic networks can categorize the object in
different forms and can also link those objects. Semantic networks are easy to
understand and can be easily extended.
This representation consist of mainly two types of relations:

a. IS-A relation (Inheritance)

b. Kind-of-relation

Example: Following are some statements which we need to represent in the form of
nodes and arcs.

Statements:

a. Jerry is a cat.
b. Jerry is a mammal
c. Jerry is owned by Priya.
d. Jerry is brown colored.
e. All Mammals are animal.

In the above diagram, we have represented the different type of knowledge in the form
of nodes and arcs. Each object is connected with another object by some relation.

Drawbacks in Semantic representation:

1. Semantic networks take more computational time at runtime as we need to

traverse the complete network tree to answer some questions. It might be
possible in the worst case scenario that after traversing the entire tree, we find
that the solution does not exist in this network.
2. Semantic networks try to model human-like memory (Which has 1015 neurons
and links) to store the information, but in practice, it is not possible to build such
a vast semantic network.
3. These types of representations are inadequate as they do not have any
equivalent quantifier, e.g., for all, for some, none, etc.
4. Semantic networks do not have any standard definition for the link names.
5. These networks are not intelligent and depend on the creator of the system.
Advantages of Semantic network:

1. Semantic networks are a natural representation of knowledge.

2. Semantic networks convey meaning in a transparent manner.
3. These networks are simple and easily understandable.

3. Frame Representation
A frame is a record like structure which consists of a collection of attributes and its
values to describe an entity in the world. Frames are the AI data structure which divides
knowledge into substructures by representing stereotypes situations. It consists of a
collection of slots and slot values. These slots may be of any type and sizes. Slots have
names and values which are called facets.

Facets: The various aspects of a slot is known as Facets. Facets are features of frames
which enable us to put constraints on the frames. Example: IF-NEEDED facts are called
when data of any particular slot is needed. A frame may consist of any number of slots,
and a slot may include any number of facets and facets may have any number of values.
A frame is also known as slot-filter knowledge representation in artificial intelligence.

Frames are derived from semantic networks and later evolved into our modern-day
classes and objects. A single frame is not much useful. Frames system consist of a
collection of frames which are connected. In the frame, knowledge about an object or
event can be stored together in the knowledge base. The frame is a type of technology
which is widely used in various applications including Natural language processing and
machine visions.

Example: 1
Let's take an example of a frame for a book

Slots Filters

Title Artificial Intelligence

Genre Computer Science

Author Peter Norvig

Edition Third Edition

Year 1996

Page 1152

Example 2:
Let's suppose we are taking an entity, Peter. Peter is an engineer as a profession, and his
age is 25, he lives in city London, and the country is England. So following is the frame
representation for this:

Slots Filter

Name Peter

Profession Doctor

Age 25

Marital status Single

Weight 78

Advantages of frame representation:

1. The frame knowledge representation makes the programming easier by grouping

the related data.
2. The frame representation is comparably flexible and used by many applications in
AI.
3. It is very easy to add slots for new attribute and relations.
4. It is easy to include default data and to search for missing values.
5. Frame representation is easy to understand and visualize.

Disadvantages of frame representation:

1. In frame system inference mechanism is not be easily processed.

 2. Inference mechanism cannot be smoothly proceeded by frame representation.
3. Frame representation has a much generalized approach.

4. Production Rules
Production rules system consist of (condition, action) pairs which mean, "If condition
then action". It has mainly three parts:

o The set of production rules

o Working Memory
o The recognize-act-cycle

In production rules agent checks for the condition and if the condition exists then
production rule fires and corresponding action is carried out. The condition part of the
rule determines which rule may be applied to a problem. And the action part carries out
the associated problem-solving steps. This complete process is called a recognize-act
cycle.

The working memory contains the description of the current state of problems-solving
and rule can write knowledge to the working memory. This knowledge match and may
fire other rules.

If there is a new situation (state) generates, then multiple production rules will be fired
together, this is called conflict set. In this situation, the agent needs to select a rule from
these sets, and it is called a conflict resolution.

Example:

o IF (at bus stop AND bus arrives) THEN action (get into the bus)
o IF (on the bus AND paid AND empty seat) THEN action (sit down).
o IF (on bus AND unpaid) THEN action (pay charges).
o IF (bus arrives at destination) THEN action (get down from the bus).

Advantages of Production rule:

1. The production rules are expressed in natural language.

 2. The production rules are highly modular, so we can easily remove, add or modify
an individual rule.

Disadvantages of Production rule:

1. Production rule system does not exhibit any learning capabilities, as it does not
store the result of the problem for the future uses.
2. During the execution of the program, many rules may be active hence rule-based
production systems are inefficient.

Propositional logic in Artificial intelligence

Propositional logic (PL) is the simplest form of logic where all the statements are made
by propositions. A proposition is a declarative statement which is either true or false. It is
a technique of knowledge representation in logical and mathematical form.

Example:

1. a) It is Sunday.
2. b) The Sun rises from West (False proposition)
3. c) 3+3= 7(False proposition)
4. d) 5 is a prime number.

Following are some basic facts about propositional logic:

o Propositional logic is also called Boolean logic as it works on 0 and 1.

o In propositional logic, we use symbolic variables to represent the logic, and we
can use any symbol for a representing a proposition, such A, B, C, P, Q, R, etc.
o Propositions can be either true or false, but it cannot be both.
o Propositional logic consists of an object, relations or function, and logical
connectives.
o These connectives are also called logical operators.
o The propositions and connectives are the basic elements of the propositional
logic.
 o Connectives can be said as a logical operator which connects two sentences.
o A proposition formula which is always true is called tautology, and it is also
called a valid sentence.
o A proposition formula which is always false is called Contradiction.
o A proposition formula which has both true and false values is called
o Statements which are questions, commands, or opinions are not propositions
such as "Where is Rohini", "How are you", "What is your name", are not
propositions.

Syntax of propositional logic:

The syntax of propositional logic defines the allowable sentences for the knowledge
representation. There are two types of Propositions:

a. Atomic Propositions
b. Compound propositions

o Atomic Proposition: Atomic propositions are the simple propositions. It consists

of a single proposition symbol. These are the sentences which must be either true
or false.

Example:

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1. a) 2+2 is 4, it is an atomic proposition as it is a true fact.

2. b) "The Sun is cold" is also a proposition as it is a false fact.

o Compound proposition: Compound propositions are constructed by combining

simpler or atomic propositions, using parenthesis and logical connectives.

Example:

1. a) "It is raining today, and street is wet."

2. b) "Ankit is a doctor, and his clinic is in Mumbai."
Logical Connectives:
Logical connectives are used to connect two simpler propositions or representing a
sentence logically. We can create compound propositions with the help of logical
connectives. There are mainly five connectives, which are given as follows:

1. Negation: A sentence such as ¬ P is called negation of P. A literal can be either

Positive literal or negative literal.
2. Conjunction: A sentence which has ∧ connective such as, P ∧ Q is called a
conjunction.
Example: Rohan is intelligent and hardworking. It can be written as,
P= Rohan is intelligent,
Q= Rohan is hardworking. → P∧ Q.
3. Disjunction: A sentence which has ∨ connective, such as P ∨ Q. is called
disjunction, where P and Q are the propositions.
Example: "Ritika is a doctor or Engineer",
Here P= Ritika is Doctor. Q= Ritika is Doctor, so we can write it as P ∨ Q.
4. Implication: A sentence such as P → Q, is called an implication. Implications are
also known as if-then rules. It can be represented as
If it is raining, then the street is wet.
Let P= It is raining, and Q= Street is wet, so it is represented as P → Q
5. Biconditional: A sentence such as P⇔ Q is a Biconditional sentence, example
If I am breathing, then I am alive
P= I am breathing, Q= I am alive, it can be represented as P ⇔ Q.

Following is the summarized table for Propositional Logic

Connectives:
Truth Table:
In propositional logic, we need to know the truth values of propositions in all possible
scenarios. We can combine all the possible combination with logical connectives, and
the representation of these combinations in a tabular format is called Truth table.
Following are the truth table for all logical connectives:
Truth table with three propositions:
We can build a proposition composing three propositions P, Q, and R. This truth table is
made-up of 8n Tuples as we have taken three proposition symbols.

Precedence of connectives:
Just like arithmetic operators, there is a precedence order for propositional connectors
or logical operators. This order should be followed while evaluating a propositional
problem. Following is the list of the precedence order for operators:

Precedence Operators

First Precedence Parenthesis

Second Precedence Negation

Third Precedence Conjunction(AND)

Fourth Precedence Disjunction(OR)

Fifth Precedence Implication

Six Precedence Biconditional

Note: For better understanding use parenthesis to make sure of the correct interpretations.
Such as ¬R∨ Q, It can be interpreted as (¬R) ∨ Q.

Logical equivalence:
Logical equivalence is one of the features of propositional logic. Two propositions are
said to be logically equivalent if and only if the columns in the truth table are identical
to each other.
Let's take two propositions A and B, so for logical equivalence, we can write it as A⇔B.
In below truth table we can see that column for ¬A∨ B and A→B, are identical hence A is
Equivalent to B

Properties of Operators:

o Commutativity:
o P∧ Q= Q ∧ P, or
o P ∨ Q = Q ∨ P.
o Associativity:
o (P ∧ Q) ∧ R= P ∧ (Q ∧ R),
o (P ∨ Q) ∨ R= P ∨ (Q ∨ R)
o Identity element:
o P ∧ True = P,
o P ∨ True= True.
o Distributive:
o P∧ (Q ∨ R) = (P ∧ Q) ∨ (P ∧ R).
o P ∨ (Q ∧ R) = (P ∨ Q) ∧ (P ∨ R).
o DE Morgan's Law:
o ¬ (P ∧ Q) = (¬P) ∨ (¬Q)
o ¬ (P ∨ Q) = (¬ P) ∧ (¬Q).
o Double-negation elimination:
o ¬ (¬P) = P.

Limitations of Propositional logic:

o We cannot represent relations like ALL, some, or none with propositional logic.
Example:
 a. All the girls are intelligent.
b. Some apples are sweet.
o Propositional logic has limited expressive power.
o In propositional logic, we cannot describe statements in terms of their properties
or logical relationships.

Rules of Inference in Artificial intelligence

Inference:
In artificial intelligence, we need intelligent computers which can create new logic from
old logic or by evidence, so generating the conclusions from evidence and facts is
termed as Inference.

Inference rules:
Inference rules are the templates for generating valid arguments. Inference rules are
applied to derive proofs in artificial intelligence, and the proof is a sequence of the
conclusion that leads to the desired goal.

In inference rules, the implication among all the connectives plays an important role.
Following are some terminologies related to inference rules:

o Implication: It is one of the logical connectives which can be represented as P →

Q. It is a Boolean expression.
o Converse: The converse of implication, which means the right-hand side
proposition goes to the left-hand side and vice-versa. It can be written as Q → P.
o Contrapositive: The negation of converse is termed as contrapositive, and it can
be represented as ¬ Q → ¬ P.
o Inverse: The negation of implication is called inverse. It can be represented as ¬
P → ¬ Q.

From the above term some of the compound statements are equivalent to each other,
which we can prove using truth table:
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x

Hence from the above truth table, we can prove that P → Q is equivalent to ¬ Q → ¬ P,
and Q→ P is equivalent to ¬ P → ¬ Q.

Types of Inference rules:

1. Modus Ponens:
The Modus Ponens rule is one of the most important rules of inference, and it states
that if P and P → Q is true, then we can infer that Q will be true. It can be represented as:

Example:

Statement-1: "If I am sleepy then I go to bed" ==> P→ Q

Statement-2: "I am sleepy" ==> P
Conclusion: "I go to bed." ==> Q.
Hence, we can say that, if P→ Q is true and P is true then Q will be true.

Proof by Truth table:

2. Modus Tollens:
The Modus Tollens rule state that if P→ Q is true and ¬ Q is true, then ¬ P will also
true. It can be represented as:

Statement-1: "If I am sleepy then I go to bed" ==> P→ Q

Statement-2: "I do not go to the bed."==> ~Q
Statement-3: Which infers that "I am not sleepy" => ~P

Proof by Truth table:

3. Hypothetical Syllogism:
The Hypothetical Syllogism rule state that if P→R is true whenever P→Q is true, and
Q→R is true. It can be represented as the following notation:

Example:

Statement-1: If you have my home key then you can unlock my home. P→Q
Statement-2: If you can unlock my home then you can take my money. Q→R
Conclusion: If you have my home key then you can take my money. P→R

Proof by truth table:

4. Disjunctive Syllogism:
The Disjunctive syllogism rule state that if P∨Q is true, and ¬P is true, then Q will be true.
It can be represented as:

Example:

Statement-1: Today is Sunday or Monday. ==>P∨Q

Statement-2: Today is not Sunday. ==> ¬P
Conclusion: Today is Monday. ==> Q

Proof by truth-table:

5. Addition:
The Addition rule is one the common inference rule, and it states that If P is true, then
P∨Q will be true.
Example:

Statement: I have a vanilla ice-cream. ==> P

Statement-2: I have Chocolate ice-cream.
Conclusion: I have vanilla or chocolate ice-cream. ==> (P∨Q)

Proof by Truth-Table:

6. Simplification:
The simplification rule state that if P∧ Q is true, then Q or P will also be true. It can be
represented as:

Proof by Truth-Table:

7. Resolution:
The Resolution rule state that if P∨Q and ¬ P∧R is true, then Q∨R will also be true. It can
be represented as

Proof by Truth-Table:
The Wumpus World in Artificial intelligence
Wumpus world:
The Wumpus world is a simple world example to illustrate the worth of a knowledge-
based agent and to represent knowledge representation. It was inspired by a video
game Hunt the Wumpus by Gregory Yob in 1973.

The Wumpus world is a cave which has 4/4 rooms connected with passageways. So
there are total 16 rooms which are connected with each other. We have a knowledge-
based agent who will go forward in this world. The cave has a room with a beast which
is called Wumpus, who eats anyone who enters the room. The Wumpus can be shot by
the agent, but the agent has a single arrow. In the Wumpus world, there are some Pits
rooms which are bottomless, and if agent falls in Pits, then he will be stuck there forever.
The exciting thing with this cave is that in one room there is a possibility of finding a
heap of gold. So the agent goal is to find the gold and climb out the cave without fallen
into Pits or eaten by Wumpus. The agent will get a reward if he comes out with gold,
and he will get a penalty if eaten by Wumpus or falls in the pit.

Note: Here Wumpus is static and cannot move.

Following is a sample diagram for representing the Wumpus world. It is showing some
rooms with Pits, one room with Wumpus and one agent at (1, 1) square location of the
world.
There are also some components which can help the agent to navigate the cave.
These components are given as follows:

a. The rooms adjacent to the Wumpus room are smelly, so that it would have some
stench.
b. The room adjacent to PITs has a breeze, so if the agent reaches near to PIT, then
he will perceive the breeze.
c. There will be glitter in the room if and only if the room has gold.
d. The Wumpus can be killed by the agent if the agent is facing to it, and Wumpus
will emit a horrible scream which can be heard anywhere in the cave.

PEAS description of Wumpus world:

To explain the Wumpus world we have given PEAS description as below:

Performance measure:

o +1000 reward points if the agent comes out of the cave with the gold.
o -1000 points penalty for being eaten by the Wumpus or falling into the pit.
 o -1 for each action, and -10 for using an arrow.
o The game ends if either agent dies or came out of the cave.

Environment:

o A 4*4 grid of rooms.

o The agent initially in room square [1, 1], facing toward the right.
o Location of Wumpus and gold are chosen randomly except the first square [1,1].
o Each square of the cave can be a pit with probability 0.2 except the first square.

Actuators:

o Left turn,
o Right turn
o Move forward
o Grab
o Release
o Shoot.

Sensors:

o The agent will perceive the stench if he is in the room adjacent to the Wumpus.
(Not diagonally).
o The agent will perceive breeze if he is in the room directly adjacent to the Pit.
o The agent will perceive the glitter in the room where the gold is present.
o The agent will perceive the bump if he walks into a wall.
o When the Wumpus is shot, it emits a horrible scream which can be perceived
anywhere in the cave.
o These percepts can be represented as five element list, in which we will have
different indicators for each sensor.
o Example if agent perceives stench, breeze, but no glitter, no bump, and no
scream then it can be represented as:
[Stench, Breeze, None, None, None].
The Wumpus world Properties:
o Partially observable: The Wumpus world is partially observable because the
agent can only perceive the close environment such as an adjacent room.
o Deterministic: It is deterministic, as the result and outcome of the world are
already known.
o Sequential: The order is important, so it is sequential.
o Static: It is static as Wumpus and Pits are not moving.
o Discrete: The environment is discrete.
o One agent: The environment is a single agent as we have one agent only and
Wumpus is not considered as an agent.

Exploring the Wumpus world:

Now we will explore the Wumpus world and will determine how the agent will find its
goal by applying logical reasoning.

Agent's First step:

Initially, the agent is in the first room or on the square [1,1], and we already know that
this room is safe for the agent, so to represent on the below diagram (a) that room is
safe we will add symbol OK. Symbol A is used to represent agent, symbol B for the
breeze, G for Glitter or gold, V for the visited room, P for pits, W for Wumpus.

At Room [1,1] agent does not feel any breeze or any Stench which means the adjacent
squares are also OK.
Agent's second Step:

Now agent needs to move forward, so it will either move to [1, 2], or [2,1]. Let's suppose
agent moves to the room [2, 1], at this room agent perceives some breeze which means
Pit is around this room. The pit can be in [3, 1], or [2,2], so we will add symbol P? to say
that, is this Pit room?

Now agent will stop and think and will not make any harmful move. The agent will go
back to the [1, 1] room. The room [1,1], and [2,1] are visited by the agent, so we will use
symbol V to represent the visited squares.

Agent's third step:

At the third step, now agent will move to the room [1,2] which is OK. In the room [1,2]
agent perceives a stench which means there must be a Wumpus nearby. But Wumpus
cannot be in the room [1,1] as by rules of the game, and also not in [2,2] (Agent had not
detected any stench when he was at [2,1]). Therefore agent infers that Wumpus is in the
room [1,3], and in current state, there is no breeze which means in [2,2] there is no Pit
and no Wumpus. So it is safe, and we will mark it OK, and the agent moves further in
[2,2].
Agent's fourth step:

At room [2,2], here no stench and no breezes present so let's suppose agent decides to
move to [2,3]. At room [2,3] agent perceives glitter, so it should grab the gold and climb
out of the cave.

Knowledge-base for Wumpus world

As in the previous topic we have learned about the wumpus world and how a
knowledge-based agent evolves the world. Now in this topic, we will create a knowledge
base for the wumpus world, and will derive some proves for the Wumpus-world using
propositional logic.

The agent starts visiting from first square [1, 1], and we already know that this room is
safe for the agent. To build a knowledge base for wumpus world, we will use some rules
and atomic propositions. We need symbol [i, j] for each location in the wumpus world,
where i is for the location of rows, and j for column location.
Atomic proposition variable for Wumpus world:

o Let Pi,j be true if there is a Pit in the room [i, j].

o Let Bi,j be true if agent perceives breeze in [i, j], (dead or alive).
o Let Wi,j be true if there is wumpus in the square[i, j].
o Let Si,j be true if agent perceives stench in the square [i, j].
o Let Vi,j be true if that square[i, j] is visited.
o Let Gi,j be true if there is gold (and glitter) in the square [i, j].
o Let OKi,j be true if the room is safe.

Note: For a 4 * 4 square board, there will be 7*4*4= 122 propositional variables.

Some Propositional Rules for the wumpus world:

Note: lack of variables gives us similar rules for each cell.

Representation of Knowledgebase for Wumpus world:

Following is the Simple KB for wumpus world when an agent moves from room [1, 1], to
room [2,1]:

Here in the first row, we have mentioned propositional variables for room[1,1], which is
showing that room does not have wumpus(¬ W11), no stench (¬S11), no Pit(¬P11), no
breeze(¬B11), no gold (¬G11), visited (V11), and the room is Safe(OK11).

In the second row, we have mentioned propositional variables for room [1,2], which is
showing that there is no wumpus, stench and breeze are unknown as an agent has not
visited room [1,2], no Pit, not visited yet, and the room is safe.

In the third row we have mentioned propositional variable for room[2,1], which is
showing that there is no wumpus(¬ W21), no stench (¬S21), no Pit (¬P21), Perceives
breeze(B21), no glitter(¬G21), visited (V21), and room is safe (OK21).

Prove that Wumpus is in the room (1, 3)

We can prove that wumpus is in the room (1, 3) using propositional rules which we have
derived for the wumpus world and using inference rule.

o Apply Modus Ponens with ¬S11 and R1:

We will firstly apply MP rule with R1 which is ¬S11 → ¬ W11 ^ ¬ W12 ^ ¬ W21,
and ¬S11 which will give the output ¬ W11 ^ W12 ^ W12.
 o Apply And-Elimination Rule:

After applying And-elimination rule to ¬ W11 ∧ ¬ W12 ∧ ¬ W21, we will get three
statements:
¬ W11, ¬ W12, and ¬W21.

o Apply Modus Ponens to ¬S21, and R2:

Now we will apply Modus Ponens to ¬S21 and R2 which is ¬S21 → ¬ W21 ∧¬ W22 ∧ ¬
W31, which will give the Output as ¬ W21 ∧ ¬ W22 ∧¬ W31

o Apply And -Elimination rule:

Now again apply And-elimination rule to ¬ W21 ∧ ¬ W22 ∧¬ W31, We will get three
statements:
¬ W21, ¬ W22, and ¬ W31.

o Apply MP to S12 and R4:

Apply Modus Ponens to S12 and R4 which is S12 → W13 ∨. W12 ∨. W22 ∨.W11, we will get
the output as W13∨ W12 ∨ W22 ∨.W11.
 o Apply Unit resolution on W13 ∨ W12 ∨ W22 ∨W11 and ¬ W11 :

After applying Unit resolution formula on W13 ∨ W12 ∨ W22 ∨W11 and ¬ W11 we will get
W13 ∨ W12 ∨ W22.

o Apply Unit resolution on W13 ∨ W12 ∨ W22 and ¬ W22 :

After applying Unit resolution on W13 ∨ W12 ∨ W22, and ¬W22, we will get W13 ∨ W12 as
output.

o Apply Unit Resolution on W13 ∨ W12 and ¬ W12 :

After Applying Unit resolution on W13 ∨ W12 and ¬ W12, we will get W13 as an output,
hence it is proved that the Wumpus is in the room [1, 3].
First-Order Logic in Artificial intelligence
In the topic of Propositional logic, we have seen that how to represent statements using
propositional logic. But unfortunately, in propositional logic, we can only represent the
facts, which are either true or false. PL is not sufficient to represent the complex
sentences or natural language statements. The propositional logic has very limited
expressive power. Consider the following sentence, which we cannot represent using PL
logic.

o "Some humans are intelligent", or

o "Sachin likes cricket."

To represent the above statements, PL logic is not sufficient, so we required some more
powerful logic, such as first-order logic.

First-Order logic:
o First-order logic is another way of knowledge representation in artificial
intelligence. It is an extension to propositional logic.
o FOL is sufficiently expressive to represent the natural language statements in a
concise way.
o First-order logic is also known as Predicate logic or First-order predicate logic.
First-order logic is a powerful language that develops information about the
objects in a more easy way and can also express the relationship between those
objects.
o First-order logic (like natural language) does not only assume that the world
contains facts like propositional logic but also assumes the following things in the
world:
 o Objects: A, B, people, numbers, colors, wars, theories, squares, pits,
wumpus, ......
o Relations: It can be unary relation such as: red, round, is adjacent, or n-
any relation such as: the sister of, brother of, has color, comes between
o Function: Father of, best friend, third inning of, end of, ......
o As a natural language, first-order logic also has two main parts:
a. Syntax
b. Semantics

Syntax of First-Order logic:

The syntax of FOL determines which collection of symbols is a logical expression in first-
order logic. The basic syntactic elements of first-order logic are symbols. We write
statements in short-hand notation in FOL.

Basic Elements of First-order logic:

Following are the basic elements of FOL syntax:

Play Video
x

Constant 1, 2, A, John, Mumbai, cat,....

Variables x, y, z, a, b,....

Predicates Brother, Father, >,....

Function sqrt, LeftLegOf, ....

Connectives ∧, ∨, ¬, ⇒, ⇔

Equality ==

Quantifier ∀, ∃

Atomic sentences:
 o Atomic sentences are the most basic sentences of first-order logic. These
sentences are formed from a predicate symbol followed by a parenthesis with a
sequence of terms.
o We can represent atomic sentences as Predicate (term1, term2, ......, term n).

Example: Ravi and Ajay are brothers: => Brothers(Ravi, Ajay).

Chinky is a cat: => cat (Chinky).

Complex Sentences:

o Complex sentences are made by combining atomic sentences using connectives.

First-order logic statements can be divided into two parts:

o Subject: Subject is the main part of the statement.

o Predicate: A predicate can be defined as a relation, which binds two atoms
together in a statement.

Consider the statement: "x is an integer.", it consists of two parts, the first part x is
the subject of the statement and second part "is an integer," is known as a predicate.

Quantifiers in First-order logic:

o A quantifier is a language element which generates quantification, and
quantification specifies the quantity of specimen in the universe of discourse.
o These are the symbols that permit to determine or identify the range and scope
of the variable in the logical expression. There are two types of quantifier:
a. Universal Quantifier, (for all, everyone, everything)
b. Existential quantifier, (for some, at least one).

Universal Quantifier:
Universal quantifier is a symbol of logical representation, which specifies that the
statement within its range is true for everything or every instance of a particular thing.

The Universal quantifier is represented by a symbol ∀, which resembles an inverted A.

Note: In universal quantifier we use implication "→".

If x is a variable, then ∀x is read as:

o For all x
o For each x
o For every x.

Example:
All man drink coffee.

Let a variable x which refers to a cat so all x can be represented in UOD as below:

∀x man(x) → drink (x, coffee).

It will be read as: There are all x where x is a man who drink coffee.
Existential Quantifier:
Existential quantifiers are the type of quantifiers, which express that the statement within
its scope is true for at least one instance of something.

It is denoted by the logical operator ∃, which resembles as inverted E. When it is used

with a predicate variable then it is called as an existential quantifier.

Note: In Existential quantifier we always use AND or Conjunction symbol (∧).

If x is a variable, then existential quantifier will be ∃x or ∃(x). And it will be read as:

o There exists a 'x.'

o For some 'x.'
o For at least one 'x.'

Example:
Some boys are intelligent.

∃x: boys(x) ∧ intelligent(x)

It will be read as: There are some x where x is a boy who is intelligent.
Points to remember:
o The main connective for universal quantifier ∀ is implication →.
o The main connective for existential quantifier ∃ is and ∧.

Properties of Quantifiers:
o In universal quantifier, ∀x∀y is similar to ∀y∀x.
o In Existential quantifier, ∃x∃y is similar to ∃y∃x.
o ∃x∀y is not similar to ∀y∃x.

Some Examples of FOL using quantifier:

1. All birds fly.

In this question the predicate is "fly(bird)."
And since there are all birds who fly so it will be represented as follows.
∀x bird(x) →fly(x).

2. Every man respects his parent.

In this question, the predicate is "respect(x, y)," where x=man, and y= parent.
Since there is every man so will use ∀, and it will be represented as follows:
∀x man(x) → respects (x, parent).

3. Some boys play cricket.

In this question, the predicate is "play(x, y)," where x= boys, and y= game. Since there
are some boys so we will use ∃, and it will be represented as:
∃x boys(x) → play(x, cricket).

4. Not all students like both Mathematics and Science.

In this question, the predicate is "like(x, y)," where x= student, and y= subject.
Since there are not all students, so we will use ∀ with negation, so following
representation for this:
¬∀ (x) [ student(x) → like(x, Mathematics) ∧ like(x, Science)].

5. Only one student failed in Mathematics.

In this question, the predicate is "failed(x, y)," where x= student, and y= subject.
Since there is only one student who failed in Mathematics, so we will use following
representation for this:
 ∃(x) [ student(x) → failed (x, Mathematics) ∧∀ (y) [¬(x==y) ∧ student(y) →
¬failed (x, Mathematics)].

Free and Bound Variables:

The quantifiers interact with variables which appear in a suitable way. There are two
types of variables in First-order logic which are given below:

Free Variable: A variable is said to be a free variable in a formula if it occurs outside the
scope of the quantifier.

Example: ∀x ∃(y)[P (x, y, z)], where z is a free variable.

Bound Variable: A variable is said to be a bound variable in a formula if it occurs within

the scope of the quantifier.

Example: ∀x [A (x) B( y)], here x and y are the bound variables.

Forward Chaining and backward chaining in AI

In artificial intelligence, forward and backward chaining is one of the important topics,
but before understanding forward and backward chaining lets first understand that from
where these two terms came.

Inference engine:
The inference engine is the component of the intelligent system in artificial intelligence,
which applies logical rules to the knowledge base to infer new information from known
facts. The first inference engine was part of the expert system. Inference engine
commonly proceeds in two modes, which are:

a. Forward chaining
b. Backward chaining

Horn Clause and Definite clause:

Horn clause and definite clause are the forms of sentences, which enables knowledge
base to use a more restricted and efficient inference algorithm. Logical inference
algorithms use forward and backward chaining approaches, which require KB in the
form of the first-order definite clause.

Definite clause: A clause which is a disjunction of literals with exactly one positive
literal is known as a definite clause or strict horn clause.

Horn clause: A clause which is a disjunction of literals with at most one positive
literal is known as horn clause. Hence all the definite clauses are horn clauses.

Example: (¬ p V ¬ q V k). It has only one positive literal k.

It is equivalent to p ∧ q → k.

A. Forward Chaining
Forward chaining is also known as a forward deduction or forward reasoning method
when using an inference engine. Forward chaining is a form of reasoning which start
with atomic sentences in the knowledge base and applies inference rules (Modus
Ponens) in the forward direction to extract more data until a goal is reached.

The Forward-chaining algorithm starts from known facts, triggers all rules whose
premises are satisfied, and add their conclusion to the known facts. This process repeats
until the problem is solved.

Properties of Forward-Chaining:

o It is a down-up approach, as it moves from bottom to top.

o It is a process of making a conclusion based on known facts or data, by starting
from the initial state and reaches the goal state.
o Forward-chaining approach is also called as data-driven as we reach to the goal
using available data.
o Forward -chaining approach is commonly used in the expert system, such as
CLIPS, business, and production rule systems.

Consider the following famous example which we will use in both approaches:
Example:
"As per the law, it is a crime for an American to sell weapons to hostile nations.
Country A, an enemy of America, has some missiles, and all the missiles were sold
to it by Robert, who is an American citizen."

Prove that "Robert is criminal."

To solve the above problem, first, we will convert all the above facts into first-order
definite clauses, and then we will use a forward-chaining algorithm to reach the goal.

Facts Conversion into FOL:

o It is a crime for an American to sell weapons to hostile nations. (Let's say p, q, and
r are variables)
American (p) ∧ weapon(q) ∧ sells (p, q, r) ∧ hostile(r) → Criminal(p) ...(1)
o Country A has some missiles. ?p Owns(A, p) ∧ Missile(p). It can be written in two
definite clauses by using Existential Instantiation, introducing new Constant T1.
Owns(A, T1) ......(2)
Missile(T1) .......(3)
o All of the missiles were sold to country A by Robert.
?p Missiles(p) ∧ Owns (A, p) → Sells (Robert, p, A) ......(4)
o Missiles are weapons.
Missile(p) → Weapons (p) .......(5)
o Enemy of America is known as hostile.
Enemy(p, America) →Hostile(p) ........(6)
o Country A is an enemy of America.
Enemy (A, America) .........(7)
o Robert is American
American(Robert). ..........(8)

Forward chaining proof:

Step-1:
In the first step we will start with the known facts and will choose the sentences which
do not have implications, such as: American(Robert), Enemy(A, America), Owns(A,
T1), and Missile(T1). All these facts will be represented as below.

Step-2:

At the second step, we will see those facts which infer from available facts and with
satisfied premises.

Rule-(1) does not satisfy premises, so it will not be added in the first iteration.

Rule-(2) and (3) are already added.

Rule-(4) satisfy with the substitution {p/T1}, so Sells (Robert, T1, A) is added, which
infers from the conjunction of Rule (2) and (3).

Rule-(6) is satisfied with the substitution(p/A), so Hostile(A) is added and which infers
from Rule-(7).

Step-3:

At step-3, as we can check Rule-(1) is satisfied with the substitution {p/Robert, q/T1,
r/A}, so we can add Criminal(Robert) which infers all the available facts. And hence we
reached our goal statement.
Hence it is proved that Robert is Criminal using forward chaining approach.

B. Backward Chaining:
Backward-chaining is also known as a backward deduction or backward reasoning
method when using an inference engine. A backward chaining algorithm is a form of
reasoning, which starts with the goal and works backward, chaining through rules to
find known facts that support the goal.

Properties of backward chaining:

o It is known as a top-down approach.

o Backward-chaining is based on modus ponens inference rule.
o In backward chaining, the goal is broken into sub-goal or sub-goals to prove the
facts true.
o It is called a goal-driven approach, as a list of goals decides which rules are
selected and used.
o Backward -chaining algorithm is used in game theory, automated theorem
proving tools, inference engines, proof assistants, and various AI applications.
o The backward-chaining method mostly used a depth-first search strategy for
proof.
Example:
In backward-chaining, we will use the same above example, and will rewrite all the rules.

o American (p) ∧ weapon(q) ∧ sells (p, q, r) ∧ hostile(r) → Criminal(p) ...(1)

Owns(A, T1) ........(2)
o Missile(T1)
o ?p Missiles(p) ∧ Owns (A, p) → Sells (Robert, p, A) ......(4)
o Missile(p) → Weapons (p) .......(5)
o Enemy(p, America) →Hostile(p) ........(6)
o Enemy (A, America) .........(7)
o American (Robert). ..........(8)

Backward-Chaining proof:
In Backward chaining, we will start with our goal predicate, which is Criminal (Robert),
and then infer further rules.

Step-1:

At the first step, we will take the goal fact. And from the goal fact, we will infer other
facts, and at last, we will prove those facts true. So our goal fact is "Robert is Criminal,"
so following is the predicate of it.

Step-2:

At the second step, we will infer other facts form goal fact which satisfies the rules. So as
we can see in Rule-1, the goal predicate Criminal (Robert) is present with substitution
{Robert/P}. So we will add all the conjunctive facts below the first level and will replace p
with Robert.

Here we can see American (Robert) is a fact, so it is proved here.

Step-3:t At step-3, we will extract further fact Missile(q) which infer from Weapon(q), as
it satisfies Rule-(5). Weapon (q) is also true with the substitution of a constant T1 at q.

Step-4:

At step-4, we can infer facts Missile(T1) and Owns(A, T1) form Sells(Robert, T1, r) which
satisfies the Rule- 4, with the substitution of A in place of r. So these two statements are
proved here.
Step-5:

At step-5, we can infer the fact Enemy(A, America) from Hostile(A) which satisfies
Rule- 6. And hence all the statements are proved true using backward chaining.
Difference between backward chaining and
forward chaining
Following is the difference between the forward chaining and backward chaining:

o Forward chaining as the name suggests, start from the known facts and move
forward by applying inference rules to extract more data, and it continues until it
reaches to the goal, whereas backward chaining starts from the goal, move
backward by using inference rules to determine the facts that satisfy the goal.
o Forward chaining is called a data-driven inference technique, whereas backward
chaining is called a goal-driven inference technique.
o Forward chaining is known as the down-up approach, whereas backward
chaining is known as a top-down approach.
o Forward chaining uses breadth-first search strategy, whereas backward chaining
uses depth-first search strategy.
o Forward and backward chaining both applies Modus ponens inference rule.
o Forward chaining can be used for tasks such as planning, design process
monitoring, diagnosis, and classification, whereas backward chaining can be
used for classification and diagnosis tasks.
o Forward chaining can be like an exhaustive search, whereas backward chaining
tries to avoid the unnecessary path of reasoning.
o In forward-chaining there can be various ASK questions from the knowledge
base, whereas in backward chaining there can be fewer ASK questions.
o Forward chaining is slow as it checks for all the rules, whereas backward chaining
is fast as it checks few required rules only.

S. Forward Chaining Backward Chaining

No.

1. Forward chaining starts from known facts Backward chaining starts from the goal
and applies inference rule to extract more and works backward through inference
data unit it reaches to the goal. rules to find the required facts that
support the goal.
2. It is a bottom-up approach It is a top-down approach

3. Forward chaining is known as data-driven Backward chaining is known as goal-

inference technique as we reach to the goal driven technique as we start from the
using the available data. goal and divide into sub-goal to extract
the facts.

4. Forward chaining reasoning applies a Backward chaining reasoning applies a

breadth-first search strategy. depth-first search strategy.

5. Forward chaining tests for all the available Backward chaining only tests for few
rules required rules.

6. Forward chaining is suitable for the Backward chaining is suitable for

planning, monitoring, control, and diagnostic, prescription, and debugging
interpretation application. application.

7. Forward chaining can generate an infinite Backward chaining generates a finite

number of possible conclusions. number of possible conclusions.

8. It operates in the forward direction. It operates in the backward direction.

9. Forward chaining is aimed for any Backward chaining is only aimed for the
conclusion. required data.

Reasoning in Artificial intelligence

In previous topics, we have learned various ways of knowledge representation in
artificial intelligence. Now we will learn the various ways to reason on this knowledge
using different logical schemes.

Reasoning:
The reasoning is the mental process of deriving logical conclusion and making
predictions from available knowledge, facts, and beliefs. Or we can say, "Reasoning is a
way to infer facts from existing data." It is a general process of thinking rationally, to
find valid conclusions.
In artificial intelligence, the reasoning is essential so that the machine can also think
rationally as a human brain, and can perform like a human.

Types of Reasoning
In artificial intelligence, reasoning can be divided into the following categories:

o Deductive reasoning
o Inductive reasoning
o Abductive reasoning
o Common Sense Reasoning
o Monotonic Reasoning
o Non-monotonic Reasoning

Note: Inductive and deductive reasoning are the forms of propositional logic.

1. Deductive reasoning:
Deductive reasoning is deducing new information from logically related known
information. It is the form of valid reasoning, which means the argument's conclusion
must be true when the premises are true.

Deductive reasoning is a type of propositional logic in AI, and it requires various rules
and facts. It is sometimes referred to as top-down reasoning, and contradictory to
inductive reasoning.

In deductive reasoning, the truth of the premises guarantees the truth of the conclusion.

Deductive reasoning mostly starts from the general premises to the specific conclusion,
which can be explained as below example.

Example:

Premise-1: All the human eats veggies

Premise-2: Suresh is human.

Conclusion: Suresh eats veggies.

The general process of deductive reasoning is given below:

2. Inductive Reasoning:
Inductive reasoning is a form of reasoning to arrive at a conclusion using limited sets of
facts by the process of generalization. It starts with the series of specific facts or data
and reaches to a general statement or conclusion.

Inductive reasoning is a type of propositional logic, which is also known as cause-effect

reasoning or bottom-up reasoning.

In inductive reasoning, we use historical data or various premises to generate a generic

rule, for which premises support the conclusion.

In inductive reasoning, premises provide probable supports to the conclusion, so the

truth of premises does not guarantee the truth of the conclusion.

Example:

Premise: All of the pigeons we have seen in the zoo are white.

Conclusion: Therefore, we can expect all the pigeons to be white.

3. Abductive reasoning:
Abductive reasoning is a form of logical reasoning which starts with single or multiple
observations then seeks to find the most likely explanation or conclusion for the
observation.

Abductive reasoning is an extension of deductive reasoning, but in abductive reasoning,

the premises do not guarantee the conclusion.
Example:

Implication: Cricket ground is wet if it is raining

Axiom: Cricket ground is wet.

Conclusion It is raining.

4. Common Sense Reasoning

Common sense reasoning is an informal form of reasoning, which can be gained
through experiences.

Common Sense reasoning simulates the human ability to make presumptions about
events which occurs on every day.

It relies on good judgment rather than exact logic and operates on heuristic
knowledge and heuristic rules.

Example:

1. One person can be at one place at a time.

2. If I put my hand in a fire, then it will burn.

The above two statements are the examples of common sense reasoning which a
human mind can easily understand and assume.

5. Monotonic Reasoning:
In monotonic reasoning, once the conclusion is taken, then it will remain the same even
if we add some other information to existing information in our knowledge base. In
monotonic reasoning, adding knowledge does not decrease the set of prepositions that
can be derived.

To solve monotonic problems, we can derive the valid conclusion from the available
facts only, and it will not be affected by new facts.

Monotonic reasoning is not useful for the real-time systems, as in real time, facts get
changed, so we cannot use monotonic reasoning.
Monotonic reasoning is used in conventional reasoning systems, and a logic-based
system is monotonic.

Any theorem proving is an example of monotonic reasoning.

Example:

o Earth revolves around the Sun.

It is a true fact, and it cannot be changed even if we add another sentence in knowledge
base like, "The moon revolves around the earth" Or "Earth is not round," etc.

Advantages of Monotonic Reasoning:

o In monotonic reasoning, each old proof will always remain valid.

o If we deduce some facts from available facts, then it will remain valid for always.

Disadvantages of Monotonic Reasoning:

o We cannot represent the real world scenarios using Monotonic reasoning.

o Hypothesis knowledge cannot be expressed with monotonic reasoning, which
means facts should be true.
o Since we can only derive conclusions from the old proofs, so new knowledge
from the real world cannot be added.

6. Non-monotonic Reasoning
In Non-monotonic reasoning, some conclusions may be invalidated if we add some
more information to our knowledge base.

Logic will be said as non-monotonic if some conclusions can be invalidated by adding

more knowledge into our knowledge base.

Non-monotonic reasoning deals with incomplete and uncertain models.

"Human perceptions for various things in daily life, "is a general example of non-
monotonic reasoning.

Example: Let suppose the knowledge base contains the following knowledge:
 o Birds can fly
o Penguins cannot fly
o Pitty is a bird

So from the above sentences, we can conclude that Pitty can fly.

However, if we add one another sentence into knowledge base "Pitty is a penguin",
which concludes "Pitty cannot fly", so it invalidates the above conclusion.

Advantages of Non-monotonic reasoning:

o For real-world systems such as Robot navigation, we can use non-monotonic

reasoning.
o In Non-monotonic reasoning, we can choose probabilistic facts or can make
assumptions.

Disadvantages of Non-monotonic Reasoning:

o In non-monotonic reasoning, the old facts may be invalidated by adding new

sentences.
o It cannot be used for theorem proving.
Issues of knowledge representation
There are some common issues of knowledge representation in AI. They are:

 Relationship Issue
 Granularity Issue
 Attribute Issue

All the issues of knowledge representation in AI are discussed in short below.

Relationship Issue
When we represent some knowledge in a specific way some relationship issue arrives.
For example, inverses, existence, techniques for reasoning about values and single valued
attributes.

Consider the below two representation for same facts:

language(Danny, Javascript)
This tells Danny is Javascript Developer or Danny’s language is Javascript.

This can be also represented in the way below:

language = Javascript
developers = Danny, ........
There is a little bit difference in relationship representation in above two case.
Granularity Issue
While representing any knowledge we should care at what level should the knowledge be
represented and what are the primitives. Granularity of Representation Primitives are
fundamental concepts such as holding, seeing, playing.

For example, English is a popular language with over half a million words.

It needs to ensure we will find difficulty in deciding upon which words to choose as our
primitives in a series of situations. See the below statements:

If Harry feeds a dog then it could become:

feeds(harry, dog)
If Harry gives the dog a bone that could be:

gives(harry, dog, bone)

These two statements are not same. So, we should choose primitives carefully.

In this condition we may need an additional statement which will relate the giving as
feeding.

give(x, food) → feed(x)

So, we may need to add some inferential rules in this case.

Attribute Issue
There are some attributes which may occur in many different types of problem.

Consider, there are two instance and isa and each is important because each supports
property inheritance.

So, this may be an attribute issue.

INTRODUCTION TO RULE BASED SYSTEMS:
In the past few years, technology has experienced a drastic change. Be it in the field
of computer science (CS) or artificial intelligence (AI), new, more advanced research and
inventions have given way machines that deliver excellence and help us imitate human
knowledge. However, these new inventions are a result of numerous technologies that work
behind the scenes and enable them to deliver services that are on par with us humans. Rule-
Based Expert System is one such technology, which is being used extensively across sectors to
develop artificial intelligence applications and systems.

Therefore, today, we will explore the concept of the rule-based system (RBS) and try to
understand its role in research and development.
WHAT ARE RULE-BASED SYSTEMS (RBS)?
Present in the heart of automated processes, Rule-Based System technology helps
develop knowledge-based systems and applications, that is, intelligent programs and software
capable of providing specialized problem-solving expertise in a specific subject by utilizing
domain-specific knowledge. In rule-based systems, knowledge is encoded in the form of facts,
goals, and rules and is used to evaluate and manipulate data.
These are, in short, computer systems that use rules to perform a variety of tasks like diagnoses,
solve a problem, interpretation, or to determine a course of action in a particular situation.
Moreover, these are applied to systems involving human-crafted or curated rule nodes and can
be used to perform lexical analysis to compile or interpret computer programs, or in natural
language processing.

The rule-based expert systems consist of three important elements:

 Set of Facts: These are assertions or anything relevant to the beginning state of the
system.
 Set of Rules: It contains all actions that should be taken within the scope of a
problem and specify how to act on the assertion set. Here, facts are represented in
an IF-THEN form.
 Termination Criteria or Interpreter: Determines whether a solution exists or
not, as well as when to terminate the process.
RULE-BASED SYSTEM EXAMPLE:
A domain-specific expert system that uses rules to make deductions or narrow down choices is
one of the most popular as well as the classic example of rule-based systems. Furthermore,
recent advancement in technology has given way to the development of modern machines and
systems like:
 IKEA Virtual Assistant.
 Diagnostics Oriented Rockwell Intelligence System (DORIS).
 Machine for Intelligent Diagnosis (MIND).
FEATURES OF RULE-BASED SYSTEMS:
Widely used in Artificial Intelligence, Rule-Based Expert System is not just only responsible
for modeling intelligent behavior in machines and building expert system that
outperform human expert(s) but also helps:

 Composed of combined knowledge of human experts in the problem domain.

 Represent knowledge in a highly declarative way.
 Enables the use of several different knowledge representations paradigms.
 Supports implementation of non-deterministic search and control strategies.
 It helps describe fragmentary, ill-structured, heuristic, judgemental knowledge.
 It is robust and can operate with uncertain or incomplete knowledge.
 Helps with rule-based decision making examples monitoring, control,
diagnostics, service, etc.

COMPONENTS OF RULE-BASED SYSTEMS:

The rule-based expert system architecture is an amalgamation of four (4) important
components that are focused on different aspects of the problem in hand. From assessing the
information to helping machines reach the goal state, these components are integral for the
smooth functioning of rule-based systems. These are:

 Rule Base: This is a list of rules that is specific to a type of knowledge base, which
can be rule-based vs. model-based, etc.
 Semantic Reasoner: Also known as the inference engine, it infers information or
takes necessary actions based on input and the rule base in the knowledge base.
Semantic reasoner involves a match-resolve-act cycle, wherein:
o Match: A section of the production rule system is matched with the contents of
the working memory to obtain a conflict, which consists of various instances of
the satisfied productions.
o Conflict-Resolution: When the production system is matched, one of the
production instances in the conflict is chosen for execution, to determine the
progress of the process.
o Act: Finally, the production instance executed in the above phase is executed,
which impacts the contents of the working memory.
 Working Memory: Stores temporary information or data.
 User Interface: It is the connection to the outside world, input and output signals
are sent and received.
Now that we have covered the basics of Rule-Based systems, let us try and answer “What is
rule-based approach?”.

CONSTRUCTION OF RULE-BASED SYSTEMS:

Before we move on to discuss the types of rule-based systems, we need to understand its
construction, as it plays a crucial role in how the system evaluated the information. The
construction of rule-based systems is based on a specific type of logic, such as Boolean logic,
fuzzy logic, and probabilistic logic and is categorized into:

 Knowledge-Based Approach: It is a knowledge-based construction that follows a

traditional engineering approach, which is domain-independent. Here, it is
important to acquire requirements as well as necessary knowledge before
identifying the relationships between attributes.
 Data-Based Approach: This data-based construction follows a machine learning
approach, which, like the earlier approach, is domain-independent. This rule-based
approach is subdivided into:
o Supervised Learning.
o Unsupervised Learning.

TYPES OF RULE-BASED SYSTEMS:

Like expert systems, rule-based systems can also be categorized into:

 Forward Chaining: Also known as data-driven reasoning, forward chaining is a

data-driven technique that follows a deductive approach to reach a conclusion.
 Backward Chaining: Often used in formulating plans, backward chaining is an
alternative to forward chaining. It is a goal-driven technique that follows an
inductive approach or associative reasoning.

ADVANTAGES OF RULE-BASED SYSTEMS:

Being one of the core technologies responsible for making machines capable of rule-based
learning, rule-based systems offer a range of advantages like:

 Rule-based programming is easy to understand.

 It can be built to represent expert judgment in simple or complicated subjects.
 The cause-and-effect in Rule-Based Systems is transparent.
 It offers flexibility and an adequate mechanism to model several basic mental
processes into machines.
 Mechanizes the reasoning process.

DISADVANTAGES OF RULE-BASED SYSTEMS:

Though exceptionally beneficial, rule-based systems have certain drawbacks associated with
them, such as:

 They require deep domain knowledge and manual work.

 Generating rules for a complex system is quite challenging and time-consuming.
 It has less learning capacity, as it generates results based on the rules.

DIFFERENCE BETWEEN RULE BASED SYSTEM AND MACHINE

LEARNING:
Machine learning is among the few techniques of artificial intelligence that is time and again
compared with Rule-Based Systems to comprehend their uniqueness. Hence, a discussion on the
latter cannot be complete without a comparison between Rule-Based Systems and Machine
Learning:
RULE-BASED SYSTEMS

 It is a simplified form of Artificial Intelligence.

 It is based on Facts and Rules.
 Labor intensive and hard to implement.
 Deliver excellent performance within a narrow domain.
 Limited to human coded information.
MACHINE LEARNING

 Machine Learning is an application of Artificial Intelligence.

 It is based on models.
 Easy to implement and use.
 It helps deliver more accurate results.
 It effortlessly deals with complex and excessive data.