Related papers: FO(C) and Related Modelling Paradigms
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
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…
In this paper, we study whether transformer-based language models can extract predicate argument structure from simple sentences. We firstly show that language models sometimes confuse which predicates apply to which objects. To mitigate…
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic.…
Lin and Zhaos theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the…
In this paper we present the core of LoCo, a logic-based high-level representation language for expressing configuration problems. LoCo shall allow to model these problems in an intuitive and declarative way, the dynamic aspects of…
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
We investigate an operator on classes of languages. For each class $C$, it outputs a new class $FO^2(I_C)$ associated with a variant of two-variable first-order logic equipped with a signature$I_C$ built from $C$. For $C = \{\emptyset,…
Sequential programming and work-flow programming are two useful, but radically different, ways of describing computational processing. Of the two, it is sequential programming that we teach all programmers and support by programming…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…
The importance of taking individual, potentially conflicting perspectives into account when dealing with knowledge has been widely recognised. Many existing ontology management approaches fully merge knowledge perspectives, which may…
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…
Reasoning in language models is difficult to evaluate: natural-language traces are unverifiable, symbolic datasets are too small, and most benchmarks conflate heuristics with inference. We present FOL-Traces, the first large-scale dataset…
We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This…
We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…