Undecidability of Multi-modal Hybrid Logics | Zendy

Martin Mundhenk | Zendy; Thomas Schneider | Zendy

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Undecidability of Multi-modal Hybrid Logics

Author(s) -

Martin Mundhenk,

Thomas Schneider

Publication year - 2007

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2006.11.024

Subject(s) - decidability , normal modal logic , modal , accessibility relation , modal logic , satisfiability , frame (networking) , modal operator , computer science , modality (human–computer interaction) , range (aeronautics) , contrast (vision) , algorithm , mathematics , algebra over a field , theoretical computer science , discrete mathematics , pure mathematics , artificial intelligence , telecommunications , chemistry , materials science , polymer chemistry , composite material

This paper establishes undecidability of satisfiability for multi-modal logic equipped with the hybrid binder @7, with respect to frame classes over which the same language with only one modality is decidable. This is in contrast to the usual behaviour of many modal and hybrid logics, whose uni-modal and multi-modal versions do not differ in terms of decidability and, quite often, complexity. The results from this paper apply to a wide range of frame classes including temporally and epistemically relevant ones.

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