Related papers: Revisiting Explicit Negation in Answer Set Program…
Several methodologies have recently been proposed to evaluate the ability of Pretrained Language Models (PLMs) to interpret negation. In this article, we build on Gubelmann and Handschuh (2022), which studies the modification of PLMs'…
Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been…
In this paper we investigate forgetting in disjunctive logic programs, where forgetting an atom from a program amounts to a reduction in the signature of that program. The goal is to provide an approach that is syntax-independent, in that…
This paper is an extended version of our work in \cite{Ca2025}. We extend the concept of effective reducibility between statements of set theory with ordinal Turing machines (OTMs) explored in \cite{Ca2018} for $\Pi_{2}$-statements to…
In [Hitzler and Wendt 2002, 2005], a new methodology has been proposed which allows to derive uniform characterizations of different declarative semantics for logic programs with negation. One result from this work is that the well-founded…
This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the form n(n(t))…
The surge of state-of-the-art Transformer-based models has undoubtedly pushed the limits of NLP model performance, excelling in a variety of tasks. We cast the spotlight on the underexplored task of Natural Language Inference (NLI), since…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
There are various interesting semantics' (extensions) designed for argumentation frameworks. They enable to assign a meaning, e.g., to odd-length cycles. Our main motivation is to transfer semantics' proposed by Baroni, Giacomin and Guida…
Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that…
We study how Large Language Models (LLMs) process negation mechanistically. First, we establish that even though open-weight models often provide wrong answers to questions involving negation, they do possess internal components that…
Prompt-based methods have gained increasing attention on NLP and shown validity on many downstream tasks. Many works have focused on mining these methods' potential for knowledge extraction, but few explore their ability to make logical…
In contrast to the prevailing view in the literature, it is shown that even extremely stiff sets of ordinary differential equations may be solved efficiently by explicit methods if limiting algebraic solutions are used to stabilize the…
A sequential pattern with negation, or negative sequential pattern, takes the form of a sequential pattern for which the negation symbol may be used in front of some of the pattern's itemsets. Intuitively, such a pattern occurs in a…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
In this work, we measure the impact of affixal negation on modern English large language models (LLMs). In affixal negation, the negated meaning is expressed through a negative morpheme, which is potentially challenging for LLMs as their…
A well-established and fundamental insight in database theory is that negation (also known as complementation) tends to make queries difficult to process and difficult to reason about. Many basic problems are decidable and admit practical…
We introduce negation under the stable model semantics in DatalogMTL - a temporal extension of Datalog with metric temporal operators. As a result, we obtain a rule language which combines the power of answer set programming with the…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
We present an overview on Temporal Logic Programming under the perspective of its application for Knowledge Representation and declarative problem solving. Such programs are the result of combining usual rules with temporal modal operators,…