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Answer Set Programming Modulo Theories (ASPMT) is an approach to combining answer set programming and satisfiability modulo theories based on the functional stable model semantics. It is shown that the tight fragment of ASPMT programs can…

Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…

Despite significant progress in natural language understanding, Large Language Models (LLMs) remain error-prone when performing logical reasoning, often lacking the robust mental representations that enable human-like comprehension. We…

Input languages of answer set solvers are based on the mathematically simple concept of a stable model. But many useful constructs available in these languages, including local variables, conditional literals, and aggregates, cannot be…

Rule-based systems remain central in safety-critical domains but often struggle with scalability, brittleness, and goal misspecification. These limitations can lead to reward hacking and failures in formal verification, as AI systems tend…

We describe a variant of resolution rule of proof and show that it is complete for stable semantics of logic programs. We show applications of this result.

We present a general, consistency-based framework for belief change. Informally, in revising K by A, we begin with A and incorporate as much of K as consistently possible. Formally, a knowledge base K and sentence A are expressed, via…

An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…

Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…

Neural-symbolic methods have demonstrated efficiency in enhancing the reasoning abilities of large language models (LLMs). However, existing methods mainly rely on syntactically mapping natural languages to complete formal languages like…

We present a method for computing stable models of normal logic programs, i.e., logic programs extended with negation, in the presence of predicates with arbitrary terms. Such programs need not have a finite grounding, so traditional…

The AGM model is the most remarkable framework for modeling belief revision. However, it is not perfect in all aspects. Paraconsistent belief revision, multi-agent belief revision and non-prioritized belief revision are three different…

Recent advancements in large language models have led to significant improvements across various tasks, including mathematical reasoning, which is used to assess models' intelligence in logical reasoning and problem-solving. Models are…

Answer set programming (ASP) is a well-established knowledge representation formalism. Most ASP solvers are based on (extensions of) technology from Boolean satisfiability solving. While these solvers have shown to be very successful in…

In this paper, we examine the concept of modularity, an often cited advantage of the ruled-based representation methodology. We argue that the notion of modularity consists of two distinct concepts which we call syntactic modularity and…

In this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define…

Game semantics is a powerful method of semantic analysis for programming languages. It gives mathematically accurate models ("fully abstract") for a wide variety of programming languages. Game semantic models are combinatorial…

A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…

Large Language Models (LLMs) have driven substantial progress in artificial intelligence in recent years, exhibiting impressive capabilities across a wide range of tasks, including mathematical problem-solving. Inspired by the success of…

In this paper we introduce a Conditional Answer Set Programming framework (Conditional ASP) for the definition of conditional extensions of Answer Set Programming (ASP). The approach builds on a conditional logic with typicality, and on the…