Related papers: Comparing Non-minimal Semantics for Disjunction in…

Nested logic programs have recently been introduced in order to allow for arbitrarily nested formulas in the heads and the bodies of logic program rules under the answer sets semantics. Nested expressions can be formed using conjunction,…

Answer-set programming (ASP) has emerged recently as a viable programming paradigm well attuned to search problems in AI, constraint satisfaction and combinatorics. Propositional logic is, arguably, the simplest ASP system with an intuitive…

In two earlier papers we derived congruence formats with regard to transition system specifications for weak semantics on the basis of a decomposition method for modal formulas. The idea is that a congruence format for a semantics must…

We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of…

Distributed system theory literature often argues for correctness using an informal, Hoare-like style of reasoning. While these arguments are intuitive, they have not all been foolproof, and whether they directly correspond to formal proofs…

Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint…

Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the forall-quantifier or lambda-binder are just…

This note presents a historical survey of informal semantics that are associated with logic programming under answer set semantics. We review these in uniform terms and align them with two paradigms: Answer Set Programming and ASP-Prolog --…

Disjunctive Logic Programming (\DLP) is an advanced formalism for Knowledge Representation and Reasoning (KRR). \DLP is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is…

In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…

Modern shared memory multiprocessors permit reordering of memory operations for performance reasons. These reorderings are often a source of subtle bugs in programs written for such architectures. Traditional approaches to verify weak…

In traditional semantics for classical logic and its extensions, such as modal logic, propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a Stone space, as in topological duality. A point in such a…

This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to…

Generalized topological spaces are not necessarily closed under finite intersections. Moreover, the whole universe does not need to be open. We use modified version of this framework to establish certain models for non-normal modal logics.…

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the…

We present alternative definitions of the first-order stable model semantics and its extension to incorporate generalized quantifiers by referring to the familiar notion of a reduct instead of referring to the SM operator in the original…

We introduce the notion of coherent graphs, and show how those can be used to define dynamic semantics for Multiplicative Linear Logic (MLL) extended with non-determinism. Thanks to the use of a coherence relation rather than mere formal…

Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary first-order sentences. We show its relation to the idea of loop formulas with…

We develop a compositional approach for automatic and symbolic differentiation based on categorical constructions in functional analysis where derivatives are linear functions on abstract vectors rather than being limited to scalars,…

Do norms of rationality apply to machine learning models, in particular language models? In this paper we investigate this question by focusing on a special subset of rational norms: coherence norms. We consider both logical coherence norms…