Related papers: Generating proof systems for three-valued proposit…
We explore the use of small language models (SLMs) for automatic question generation as a complement to the prevalent use of their large counterparts in learning analytics research. We present a novel question generation pipeline that…
We show how to generate and validate logical proofs of unsatisfiability from delta-complete decision procedures that rely on error-prone numerical algorithms. Solving this problem is important for ensuring correctness of the decision…
Fact verification on tabular evidence incentivises the use of symbolic reasoning models where a logical form is constructed (e.g. a LISP-style program), providing greater verifiability than fully neural approaches. However, these systems…
Teaching logic effectively requires an understanding of the factors which cause logic students to struggle. Formalization exercises, which require the student to produce a formula corresponding to the natural language sentence, are a good…
Applying automated reasoning tools for decision support and analysis in law has the potential to make court decisions more transparent and objective. Since there is often uncertainty about the accuracy and relevance of evidence,…
Autoformalisation, the task of expressing informal mathematical statements in formal language, is often viewed as a direct translation process. This, however, disregards a critical preceding step: conjecturing. Many mathematical problems…
Skolemization, with Herbrand's theorem, underpins automated theorem proving and various transformations in computer science and mathematics. Skolemization removes strong quantifiers by introducing new function symbols, enabling efficient…
In these notes we propose a new, simpler proof system for first-order matching logic with application and definedness. The new proof system is inspired by Tarski's axiomatization for first order-logic with equality (simplified by Kalish and…
This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…
Large language models (LLMs) have recently attracted considerable interest for their ability to perform complex reasoning tasks, such as chain-of-thought (CoT) reasoning. However, most of the existing approaches to enhance this ability rely…
A common technique to verify complex logic specifications for dynamical systems is the construction of symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. Typically, abstractions…
Constructing artificial lexicons that are pronounceable, typologically plausible, and semantically structured remains an open challenge in computational linguistics. Existing conlang generators either lack formal phonotactic guarantees or…
We provide a complete axiomatization of modal inclusion logic - team-based modal logic extended with inclusion atoms. We review and refine an expressive completeness and normal form theorem for the logic, define a natural deduction proof…
The clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…
The idea of representing symbolic knowledge in connectionist systems has been a long-standing endeavour which has attracted much attention recently with the objective of combining machine learning and scalable sound reasoning. Early work…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…