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The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…
State-of-the-art pretrained language models tend to perform below their capabilities when applied out-of-the-box on tasks that require understanding and working with numbers. Recent work suggests two main reasons for this: (1) popular…
We introduce a problem set-up we call the Iterated Matching Pennies (IMP) game and show that it is a powerful framework for the study of three problems: adversarial learnability, conventional (i.e., non-adversarial) learnability and…
Game semantics aim at describing the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. In this article, we introduce a game semantics for a fragment of first order propositional logic. One…
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…
Continual learning enables incremental learning of new tasks without forgetting those previously learned, resulting in positive knowledge transfer that can enhance performance on both new and old tasks. However, continual learning poses new…
"Clarithmetic" is a generic name for formal number theories similar to Peano arithmetic, but based on computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html) instead of the more traditional classical or intuitionistic logics.…
G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…
Reproducibility is a key requirement for scientific progress. It allows the reproduction of the works of others, and, as a consequence, to fully trust the reported claims and results. In this work, we argue that, by facilitating…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…
We argue that progress toward AGI is theory limited rather than data or scale limited. Building on the critical rationalism of Popper and Deutsch, we challenge the Platonic Representation Hypothesis. Observationally equivalent worlds can…
We exhibit a sound and complete implicit-complexity formalism for functions feasibly computable by structural recursions over inductively defined data structures. Feasibly computable here means that the structural-recursive definition runs…
We show that it is possible to define a realizability interpretation for the $\Sigma_2$-fragment of classical Analysis using G\"odel's System T only. This supplements a previous result of Schwichtenberg regarding bar recursion at types 0…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
Self-play, where the algorithm learns by playing against itself without requiring any direct supervision, has become the new weapon in modern Reinforcement Learning (RL) for achieving superhuman performance in practice. However, the…
We introduce a notion of realizability with ordinal Turing machines based on recognizability rather than computability, i.e., the ability to uniquely identify an object. We show that the arising concept of $r$-realizabilty has the property…
A significant challenge for the practical application of reinforcement learning in the real world is the need to specify an oracle reward function that correctly defines a task. Inverse reinforcement learning (IRL) seeks to avoid this…
Agentic theorem provers combine a reasoning model, retrieval, search, and a proof assistant verifier, yet it remains unclear which components actually improve finite-budget proof success and why they help on real mathematical workloads. We…