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Answer set programming (ASP) is an efficient problem-solving approach, which has been strongly supported both scientifically and technologically by several solvers, ongoing active research, and implementations in many different fields.…

In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms). These approaches generalize the fixpoint-based and the level mapping based answer…

We propose a new paradigm for Belief Change in which the new information is represented as sets of models, while the agent's body of knowledge is represented as a finite set of formulae, that is, a finite base. The focus on finiteness is…

We present evidence that language models (LMs) of code can learn to represent the formal semantics of programs, despite being trained only to perform next-token prediction. Specifically, we train a Transformer model on a synthetic corpus of…

AGM's belief revision is one of the main paradigms in the study of belief change operations. Recently, several logics for belief and information change have been proposed in the literature and used to encode belief change operations in rich…

It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…

Answer Set Programming (ASP) is a popular declarative reasoning and problem solving approach in symbolic AI. Its rule-based formalism makes it inherently attractive for explainable and interpretive reasoning, which is gaining importance…

Abductive logic programs offer a formalism to declaratively represent and reason about problems in a variety of areas: diagnosis, decision making, hypothetical reasoning, etc. On the other hand, logic program updates allow us to express…

For each axiom of KM belief update we provide a corresponding axiom in a modal logic containing three modal operators: a unimodal belief operator $B$, a bimodal conditional operator $>$ and the unimodal necessity operator $\square$. We then…

Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…

The last decade witnessed an ever-increasing stream of successes in Machine Learning (ML). These successes offer clear evidence that ML is bound to become pervasive in a wide range of practical uses, including many that directly affect…

Subset models provide a new semantics for justifcation logic. The main idea of subset models is that evidence terms are interpreted as sets of possible worlds. A term then justifies a formula if that formula is true in each world of the…

In (Bezem 1999; Bezem 2001), M. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated in (Rondogiannis and Symeonidou 2016) that Bezem's technique can be extended to higher-order…

Advances in NLP have yielded impressive results for the task of machine reading comprehension (MRC), with approaches having been reported to achieve performance comparable to that of humans. In this paper, we investigate whether…

We examine the practicality for a user of using Answer Set Programming (ASP) for representing logical formalisms. Our example is a formalism aiming at capturing causal explanations from causal information. We show the naturalness and…

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…

Logical reasoning with large language models (LLMs) has received growing attention. One mainstream approach translates natural language into formal logic and then applies symbolic solvers for deduction. While effective in many tasks, these…

Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we…

Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…

We develop an extensional semantics for higher-order logic programs with negation, generalizing the technique that was introduced in [Bezem99,Bezem01] for positive higher-order programs. In this way we provide an alternative extensional…