2016/09/13 by Davide Bresolin, Emilio Muñoz-Velasco, Emilio Muñoz‐Velasco +1
Computer Science · Mathematics · #Accessibility relation #Algorithm #Autoepistemic logic #Computer science #Decidability #Description logic #Dynamic logic (digital electronics) #Expressive power #Fragment (logic) #Intermediate logic #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematics #Modal #Modal logic #Modal μ-calculus #Multimodal logic #Normal modal logic #Programming language #Propositional calculus #Propositional variable #Rotation formalisms in three dimensions #Semantic Web and Ontologies #Theoretical computer science #Undecidable problem #cs.LO
paper · pdf · doi:10.4204/eptcs.226.7
published as EPTCS 226, 2016, pp. 91-104 · In Proceedings GandALF 2016, arXiv:1609.03648
openalex publication_date 2016/09/13 · arxiv created 2016/09/14 · arxiv updated 2016/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal, and spatial logic, where the most expressive formalisms have a very high complexity or are even undecidable. In search of computationally well-behaved fragments, clausal forms and other sub-propositional restrictions of temporal and description logics have been recently studied. This renewed interest on sub-propositional logics, which mainly focus on the complexity of the various fragments, raise natural questions on their the relative expressive power, which we try to answer here for the basic multi-modal logic Kn. We consider the Horn and the Krom restrictions, as well as the combined restriction (known as the core fragment) of modal logic, and, orthogonally, the fragments that emerge by disallowing boxes or diamonds from positive literals. We study the problem in a very general setting, to ease transferring our results to other meaningful cases.