Related papers: Stratified Negation in Limit Datalog Programs
Answer set programming - the most popular problem solving paradigm based on logic programs - has been recently extended to support uninterpreted function symbols. All of these approaches have some limitation. In this paper we propose a…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Constraint Programming (CP) is a powerful declarative programming paradigm where inference and search are interleaved to find feasible and optimal solutions to various type of constraint systems. However, handling logical connectors with…
Prolog is a well known declarative programming language based on propositional Horn formulas. It is useful in various areas, including artificial intelligence, automated theorem proving, mathematical logic and so on. An active research area…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
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…
We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property…
This article describes a very high-level language for clear description of distributed algorithms and optimizations necessary for generating efficient implementations. The language supports high-level control flows where complex…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
Although large language models (LLMs) have apparently acquired a certain level of grammatical knowledge and the ability to make generalizations, they fail to interpret negation, a crucial step in Natural Language Processing. We try to…
Despite great performance on many tasks, language models (LMs) still struggle with reasoning, sometimes providing responses that cannot possibly be true because they stem from logical incoherence. We call such responses \textit{strong…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…
Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive…
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several…
Negation is both an operation in formal logic and in natural language by which a proposition is replaced by one stating the opposite, as by the addition of "not" or another negation cue. Treating negation in an adequate way is required for…
We consider an extension of linear-time temporal logic (LTL) with both local and remote data constraints interpreted over a concrete domain. This extension is a natural extension of constraint LTL and the Temporal Logic of Repeating Values,…
We look at characterizing which formulas are expressible in rich decidable logics such as guarded fixpoint logic, unary negation fixpoint logic, and guarded negation fixpoint logic. We consider semantic characterizations of definability, as…
Several queries and scores have recently been proposed to explain individual predictions over ML models. Given the need for flexible, reliable, and easy-to-apply interpretability methods for ML models, we foresee the need for developing…