Curry is a declarative multi-paradigm programming language which combines in a seamless way features from functional programming (nested expressions, higher-order functions, strong typing, lazy evaluation) and logic programming (non-determinism, built-in search, free variables, partial data structures). Compared to the single programming paradigms, Curry provides additional features, like optimal evaluation for logic-oriented computations and flexible, non-deterministic pattern matching with user-defined functions.

If you take a bunch of high tech math, modeling dependent types becomes surprisingly simple.

via: https://buttondown.com/hillelwayne/archive/the-angels-and-demons-of-nondeterminism/

Do we care about the best case or the worst case?

More techniques from the math mines

The paper (arXiv 2020, also AI review 2023) opens up with discussing recent high-profile AI debates: the Montréal AI Debate and the AAAI 2020 fireside chat with Kahneman, Hinton, LeCun, and Bengio. A consensus seems to be emerging: for AI to be robust and trustworthy, it must combine learning with reasoning. Kahneman’s “System 1 vs. System 2” dual framing of cognition maps well to deep learning and symbolic reasoning. And AI needs both.

Paper (and post) introduced to me the idea of the logic tensor network, which genuinely looks quite different interesting. I hope to see adoption of the architecture in the future.

The paper (2023) argues for integrating two historically divergent traditions in artificial intelligence (neural networks and symbolic reasoning) into a unified paradigm called Neurosymbolic AI. It argues that the path to capable, explainable, and trustworthy artificial intelligence lies in marrying perception-driven neural systems with structure-aware symbolic models.

In this reference guide, we provide basic definitions, intuitive explanations, and theoretical underpinnings of various consistency models for engineers and academics alike.

via: https://www.youtube.com/watch?v=d9cM8f_qSLQ

see also: https://www.hillelwayne.com/talks/informal-specification/

So when you see a no-go theorem that’s being given a very broad interpretation, you may do well to ask whether there is, after all, a way to get around the theorem, by achieving what the theorem is informally understood to preclude without doing what the theorem formally precludes.

An extensive collection of notes on picat that cover nearly all corners of the language

Gödel’s Incompleteness Theorem explained with Pen, Paper & Lean (the proof assistant)

How we can think about pushouts as applying rules via substitution, featuring examples in categorical databases and Datalog.

Substitution of a term into a predicate is pullback, but substitution of a term into a term is composition.

An extensive collection of notes on picat that cover nearly all corners of the language

A now classic talk that links propositions, types and categories together.

Today we’re excited to announce the first pre-alpha release of our new software CatColab 0.1: Hummingbird. CatColab is software for making models of the world together.

A peculiar book list for the adventurous and free-spirited on which to build a solid base for their future software adventures.