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Answer Set Programming (ASP) is logic programming under the stable model or answer set semantics. During the last decade, this paradigm has seen several extensions by generalizing the notion of atom used in these programs. Among these,…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
Deductive formalisms have been strongly developed in recent years; among them, Answer Set Programming (ASP) gained some momentum, and has been lately fruitfully employed in many real-world scenarios. Nonetheless, in spite of a large number…
Autoformalization is the task of automatically translating mathematical content written in natural language to a formal language expression. The growing language interpretation capabilities of Large Language Models (LLMs), including in…
In this contribution we present arbitrary arrow update model logic (AAUML). This is a dynamic epistemic logic or update logic. In update logics, static/basic modalities are interpreted on a given relational model whereas dynamic/update…
Probabilistic epistemic argumentation allows for reasoning about argumentation problems in a way that is well founded by probability theory. Epistemic states are represented by probability functions over possible worlds and can be adjusted…
Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that…
In database theory, the term $\textit{database transformation}$ was used to refer to a unifying treatment for computable queries and updates. Recently, it was shown that non-deterministic database transformations can be captured exactly by…
Sentence Embedding stands as a fundamental task within the realm of Natural Language Processing, finding extensive application in search engines, expert systems, and question-and-answer platforms. With the continuous evolution of large…
This paper contributes to the mathematical foundations of logic programming by introducing and studying the sequential composition of answer set programs. On the semantic side, we show that the immediate consequence operator of a program…
The design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor.…
This paper presents a method of computing a revision of a function-free normal logic program. If an added rule is inconsistent with a program, that is, if it leads to a situation such that no stable model exists for a new program, then…
In real-world applications, knowledge bases consisting of all the information at hand for a specific domain, along with the current state of affairs, are bound to contain contradictory data coming from different sources, as well as data…
Autoformalization aims to produce formal statements that compile and faithfully preserve the intended meaning of informal mathematics. Yet standard single-output evaluation protocols collapse a many-to-many problem into a single-output…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…
The stability rule for belief, advocated by Leitgeb [Annals of Pure and Applied Logic 164, 2013], is a rule for rational acceptance that captures categorical belief in terms of $\textit{probabilistically stable propositions}$: propositions…
The decoupling between the representation of a certain problem, i.e., its knowledge model, and the reasoning side is one of main strong points of model-based Artificial Intelligence (AI). This allows, e.g. to focus on improving the…
In the Declarative Networking paradigm, Datalog-like languages are used to express distributed computations. Whereas recently formal operational semantics for these languages have been developed, a corresponding declarative semantics has…
The (extended) AGM postulates for belief revision seem to deal with the revision of a given theory K by an arbitrary formula, but not to constrain the revisions of two different theories by the same formula. A new postulate is proposed and…