Temporal Modalities in Answer Set Programming (Invited Talk)

Author Pedro Cabalar

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Pedro Cabalar
  • University of Corunna, Spain


This document is a summary of a long term project jointly developed by the Knowledge Representation group (inside IRLab) at the University of Corunna, Spain, led by Pedro Cabalar and the Potassco group at the University of Potsdam, Germany, directed by Torsten Schaub. This includes joint work with, among others, Felicidad Aguado, Martín Diéguez, Roland Kaminski, Fançois Laferriere, Philip Morkisch, Gilberto Pérez, Anna Schuhmann and Concepción Vidal. Authors from other universities that have undoubtely contributed to the project are David Pearce, Philip Balbiani, Luis Fariñas and Jorge Fandinno.

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Pedro Cabalar. Temporal Modalities in Answer Set Programming (Invited Talk). In 27th International Symposium on Temporal Representation and Reasoning (TIME 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 178, pp. 2:1-2:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Based on the answer set (or stable model) semantics for logic programs, Answer Set Programming (ASP) has become one of the most successful paradigms for practical Knowledge Representation and problem solving. Although ASP is naturally equipped for solving static combinatorial problems up to NP complexity (or ΣP2 in the disjunctive case) its application to temporal scenarios has been frequent since its very beginning, partly due to its early use for reasoning about actions and change. Temporal problems normally suppose an extra challenge for ASP for several reasons. On the one hand, they normally raise the complexity (in the case of classical planning, for instance, it becomes PSPACE-complete), although this is usually accounted for by making repeated calls to an ASP solver. On the other hand, temporal scenarios also pose a representational challenge, since the basic ASP language does not support temporal expressions. To fill this representational gap, a temporal extension of ASP called Temporal Equilibrium Logic (TEL) was proposed in and extensively studied later. This formalism constitutes a modal, linear-time extension of Equilibrium Logic which, in its turn, is a complete logical characterisation of (standard) ASP based on the intermediate logic of Here-and-There (HT). As a result, TEL is an expressive non-monotonic modal logic that shares the syntax of Linear-Time Temporal Logic (LTL) but interprets temporal formulas under a non-monotonic semantics that properly extends stable models.

Subject Classification

ACM Subject Classification
  • Theory of computation → Modal and temporal logics
  • Theory of computation → Constraint and logic programming
  • Computing methodologies → Nonmonotonic, default reasoning and belief revision
  • Computing methodologies → Logic programming and answer set programming
  • Computing methodologies → Temporal reasoning
  • Logic Programming
  • Temporal Logic
  • Answer Set Programming
  • Modal Logic


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