Completing the Picture: Complexity of Graded Modal Logics with Converse. Issue 4 (27th July 2021)

• Record Type: Journal Article
• Authors: BEDNARCZYK, BARTOSZ; KIEROŃSKI, EMANUEL; WITKOWSKI, PIOTR
• Is Part Of: Theory and practice of logic programming. Volume 21:Issue 4(2021)
• Page Start: 493
• Page End: 520
• Publication Date: 2021-07-27
• Subjects: modal logic -- complexity -- graded modalities -- satisfiability; Logic programming -- Periodicals; Artificial intelligence -- Computer programs -- Periodicals; Constraint programming (Computer science) -- Periodicals; 005.115
• DOI: 10.1017/S1471068421000065
• Languages: English
• ISSNs: 1471-0684

Abstract

Abstract: A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames has already been established. By "traditional" classes of frames, we mean those characterized by any positive combination of reflexivity, seriality, symmetry, transitivity, and the Euclidean property. In this paper, we fill the gaps remaining in an analogous classification of the graded modal language with graded converse modalities. In particular, we show its NExp Time -completeness over the class of Euclidean frames, demonstrating this way that over this class the considered language is harder than the language without graded modalities or without converse modalities. We also consider its variation disallowing graded converse modalities, but still admitting basic converse modalities. Our most important result for this variation is confirming an earlier conjecture that it is decidable over transitive frames. This contrasts with the undecidability of the language with graded converse modalities.