Related papers: Revisiting Explicit Negation in Answer Set Program…
Numerical reasoning over natural language has been a long-standing goal for the research community. However, cutting-edge language models have proven difficult to reliably generalize to a broad range of numbers, although they have shown…
We generalize a theorem by Francois Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negation as failure. The study of this relationship is important in connection…
We provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the…
We propose a set of transformation rules for constraint logic programs with negation. We assume that every program is locally stratified and, thus, it has a unique perfect model. We give sufficient conditions which ensure that the proposed…
The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O(|At(P)|size(P))…
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. These justifications are expressed in terms of causal graphs…
We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with the Kleene property (called the `Kleene negation') always…
In recent work we defined resource-based answer set semantics, which is an extension to answer set semantics stemming from the study of its relationship with linear logic. In fact, the name of the new semantics comes from the fact that in…
We develop an inductive proof-technique to generate imperative programs for pointer data structures from behavioural specifications expressed in the Answer Set Programming (ASP) formalism. ASP is a non-monotonic logic based formalism that…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
This paper explores the contributions of Answer Set Programming (ASP) to the study of an established theory from the field of Second Language Acquisition: Input Processing. The theory describes default strategies that learners of a second…
Logic-based abduction finds important applications in artificial intelligence and related areas. One application example is in finding explanations for observed phenomena. Propositional abduction is a restriction of abduction to the…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
The introduction of explicit notions of rejection, or disbelief, into logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the…
Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…
This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada,…
Current vision-language detection and grounding models predominantly focus on prompts with positive semantics and often struggle to accurately interpret and ground complex expressions containing negative semantics. A key reason for this…
The connections among natural language processing and argumentation theory are becoming stronger in the latest years, with a growing amount of works going in this direction, in different scenarios and applying heterogeneous techniques. In…