Related papers: Resolution in Linguistic First Order Logic based o…
In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
We study the problem of deciding satisfiability of first order logic queries over views, our aim being to delimit the boundary between the decidable and the undecidable fragments of this language. Views currently occupy a central place in…
The bivariate difference field provides an algebraic framework for a sequence satisfying a recurrence of order two. Based on this, we focus on sequences satisfying a recurrence of higher order, and consider the multivariate difference…
Semiring semantics evaluates logical statements by values in some commutative semiring K. Random semiring interpretations, induced by a probability distribution on K, generalise random structures, and we investigate here the question of how…
We present a sequent calculus for first-order logic with lambda terms and definite descriptions. The theory formalised by this calculus is essentially Russellian, but avoids some of its well known drawbacks and treats definite description…
The Univalent Foundations requires a logic that allows us to define structures on homotopy types, similar to how first-order logic with equality ($\text{FOL}_=$) allows us to define structures on sets. We develop the syntax, semantics and…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Classical logic has a serious limitation in that it cannot cope with the issues of vagueness and uncertainty into which fall most modes of human reasoning. In order to provide a foundation for human knowledge representation and reasoning in…
We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called…
Large language models (LLMs) have generated significant attention since their inception, finding applications across various academic and industrial domains. However, these models often suffer from the "hallucination problem", where…
This paper provides two extensions of first order logic by `$\omega$-rules'. In each case we characterize the countable structures whose theory in the logic is categorical (has a unique model). In the one-sorted inferential $\omega$-logic,…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
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…
First-Order Logic (FOL), also called first-order predicate calculus, is a formal language that provides a framework to comprehensively represent a world and its present state, including all of its entities, attributes, and complex…
The volume and diversity of digital information have led to a growing reliance on Machine Learning techniques, such as Natural Language Processing, for interpreting and accessing appropriate data. While vector and graph embeddings represent…
Program logics for bug-finding (such as the recently introduced Incorrectness Logic) have framed correctness and incorrectness as dual concepts requiring different logical foundations. In this paper, we argue that a single unified theory…
A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…