1 Citation (Scopus)


Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5 formulas commonly rely on Skolemisation to convert them into propositional logic formulas, essentially by introducing copies of propositional atoms for each set of interpretations (possible worlds). This approach is simple, but often results into large formulas that are too difficult to process, and therefore more parsimonious constructions are required. In this work, we propose to use Answer Set Programming for implementing such constructions, and in particular for identifying the propositional atoms that are relevant in every world by means of a reachability relation. The proposed encodings are designed to take advantage of other properties such as entailment relations of subformulas rooted by modal operators. An empirical assessment of the proposed encodings shows that the reachability relation is very effective and leads to comparable performance to a state-of-the-art S5 solver based on SAT, while entailment relations are possibly too expensive to reason about and may result in overhead.

Original languageEnglish
Pages (from-to)527-542
Number of pages16
JournalTheory and Practice of Logic Programming
Issue number5
Publication statusPublished - 1 Sep 2021
Event37th International Conference on Logic Programming - Virtual event due to COVID-19, Virtual
Duration: 20 Sep 202127 Sep 2021
Conference number: 37


Dive into the research topics of 'Modal Logic S5 Satisfiability in Answer Set Programming'. Together they form a unique fingerprint.
  • Modal Logic S5 in Answer Set Programming with Lazy Creation of Worlds

    Alviano, M., Batsakis, S. & Baryannis, G., 29 Aug 2022, Logic Programming and Nonmonotonic Reasoning: 16th International Conference, LPNMR 2022, Genoa, Italy, September 5–8, 2022, Proceedings. Gottlob, G., Inclezan, D. & Maratea, M. (eds.). Cham: Springer, Cham, Vol. 13416. p. 16-28 13 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 13416 LNAI).

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Open Access

Cite this