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Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
This paper presents a distributed agent-based automated theorem proving framework based on order-sorted first-order logic. Each agent in our framework has its own knowledge base, communicating to its neighboring agent(s) using…
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…
Flow networks have attracted a lot of research in computer science. Indeed, many questions in numerous application areas can be reduced to questions about flow networks. Many of these applications would benefit from a framework in which one…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…
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 problem of model checking procedural programs has fostered much research towards the definition of temporal logics for reasoning on context-free structures. The most notable of such results are temporal logics on Nested Words, such as…
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…
First-order logic (FOL) can represent the logical entailment semantics of natural language (NL) sentences, but determining natural language entailment using FOL remains a challenge. To address this, we propose the Entailment-Preserving FOL…
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…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
This paper presents a method for inducing logic programs from examples that learns a new class of concepts called first-order decision lists, defined as ordered lists of clauses each ending in a cut. The method, called FOIDL, is based on…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its…
We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
This paper describes an algorithm for the computation of FIRST and FOLLOW sets for use with feature-theoretic grammars in which the value of the sets consists of pairs of feature-theoretic categories. The algorithm preserves as much…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…