Related papers: A Logical Framework with Higher-Order Rational (Ci…

Large language models (LLMs) are often constrained by rigid reasoning processes, limiting their ability to generate creative and diverse responses. To address this, a novel framework called LADDER is proposed, combining Chain-of-Thought…

We contribute to the refined understanding of the language-logic-algebra interplay in the context of first-order properties of countable words. We establish decidable algebraic characterizations of one variable fragment of FO as well as…

Logics for knowledge representation suffer from over-specialization: while each logic may provide an ideal representation formalism for some problems, it is less than optimal for others. A solution to this problem is to choose from several…

LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…

While Chain-of-Thought (CoT) prompting boosts Language Models' (LM) performance on a gamut of complex reasoning tasks, the generated reasoning chain does not necessarily reflect how the model arrives at the answer (aka. faithfulness). We…

Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible…

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer…

Dependently typed lambda calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic…

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing…

The unique capabilities of Large Language Models (LLMs), such as the natural language text generation ability, position them as strong candidates for providing explanation for recommendations. However, despite the size of the LLM, most…

We advocates here the use of (mathematical) logic for systems biology, as a unified framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these properties. The…

Optical systems are becoming increasingly important by resolving many bottlenecks in today's communication, electronics, and biomedical systems. However, given the continuous nature of optics, the inability to efficiently analyze optical…

Non-wellfounded proof theory results from allowing proofs of infinite height in proof theory. To guarantee that there is no vicious infinite reasoning, it is usual to add a constraint to the possible infinite paths appearing in a proof.…

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…

After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…

Constrained decoding approaches aim to control the meaning or style of text generated by the pre-trained large language models (LLMs or also PLMs) for various tasks at inference time. However, these methods often guide plausible…

An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

While large language models (LLMs) are proficient at question-answering (QA), it is not always clear how (or even if) an answer follows from their latent "beliefs". This lack of interpretability is a growing impediment to widespread use of…

This position statement looks back on two decades of work on shallow embeddings of non-classical logics in classical higher-order logic (HOL), a line of research that expanded into a range of logic embeddings in HOL and inspired the LogiKEy…