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Answer Set Programming (ASP) is a prominent rule-based language for knowledge representation and reasoning with roots in logic programming and non-monotonic reasoning. The aim to capture the essence of removing (ir)relevant details in ASP…
Answer Set Programming (ASP) is a generic problem modeling and solving framework with a strong focus on knowledge representation and a rapid growth of industrial applications. So far, the study of complexity resulted in characterizing…
Logic programs with aggregates (LPA) are one of the major linguistic extensions to Logic Programming (LP). In this work, we propose a generalization of the notions of unfounded set and well-founded semantics for programs with monotone and…
State-of-the-art answer set programming (ASP) solvers rely on a program called a grounder to convert non-ground programs containing variables into variable-free, propositional programs. The size of this grounding depends heavily on the size…
Answer Set Programming (ASP) emerged in the late 1990ies as a paradigm for Knowledge Representation and Reasoning. The attractiveness of ASP builds on an expressive high-level modeling language along with the availability of powerful…
In this paper, we propose a variant of Answer Set Programming (ASP) with evaluable functions that extends their application to sets of objects, something that allows a fully logical treatment of aggregates. Formally, we start from the…
The paper introduces the notion of off-line justification for Answer Set Programming (ASP). Justifications provide a graph-based explanation of the truth value of an atom w.r.t. a given answer set. The paper extends also this notion to…
In this paper, we propose a comprehensive benchmark to investigate models' logical reasoning capabilities in complex real-life scenarios. Current explanation datasets often employ synthetic data with simple reasoning structures. Therefore,…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
Answer Set Programming (ASP) is a well-established formalism for logic programming. Problem solving in ASP requires to write an ASP program whose answers sets correspond to solutions. Albeit the non-existence of answer sets for some ASP…
Answer set programming (ASP) is a logic programming paradigm that can be used to solve complex combinatorial search problems. Aggregates are an ASP construct that plays an important role in many applications. Defining a satisfactory…
This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented…
Answer Set Programming (ASP) is a logic-based knowledge representation framework, supporting---among other reasoning modes---the central task of query answering. In the propositional case, query answering amounts to computing cautious…
Answer set programming (ASP) is a popular nonmonotonic-logic based paradigm for knowledge representation and solving combinatorial problems. Computing the answer set of an ASP program is NP-hard in general, and researchers have been…
Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, i.e., syntactically, sets of sets of atoms.…
Answer Set Programming (ASP) is a well-known declarative formalism in logic programming. Efficient implementations made it possible to apply ASP in many scenarios, ranging from deductive databases applications to the solution of hard…
Stable model semantics has become a very popular approach for the management of negation in logic programming. This approach relies mainly on the closed world assumption to complete the available knowledge and its formulation has its basis…
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.…
Answer Set Programming (ASP) with stable model semantics has proven highly effective for knowledge representation and reasoning. However, the minimality requirement of stable models can be restrictive for applications requiring exploration…
Ethical and legal concerns make it necessary for programs that may directly influence the life of people (via, e.g., legal or health counseling) to justify in human-understandable terms the advice given. Answer Set Programming has a rich…