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The Complexity of One-Agent Refinement Modal Logic

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNAI,volume 7519)

Abstract

We investigate the complexity of satisfiability for one-agent Refinement Modal Logic (\(\text{\sffamily RML}\)), a known extension of basic modal logic (\(\text{\sffamily ML}\)) obtained by adding refinement quantifiers on structures. It is known that \(\text{\sffamily RML}\) has the same expressiveness as \(\text{\sffamily ML}\), but the translation of \(\text{\sffamily RML}\) into \(\text{\sffamily ML}\) is of non-elementary complexity, and \(\text{\sffamily RML}\) is at least doubly exponentially more succinct than \(\text{\sffamily ML}\). In this paper, we show that \(\text{\sffamily RML}\)-satisfiability is ‘only’ singly exponentially harder than \(\text{\sffamily ML}\)-satisfiability, the latter being a well-known PSPACE-complete problem. More precisely, we establish that \(\text{\sffamily RML}\)-satisfiability is complete for the complexity class AEXP\(_{\text{\sffamily pol}}\), i.e., the class of problems solvable by alternating Turing machines running in single exponential time but only with a polynomial number of alternations (note that NEXPTIMEAEXP\(_{\text{\sffamily pol}}\)EXPSPACE).

Keywords

  • Tree Structure
  • Modal Logic
  • Turing Machine
  • Constraint System
  • Atomic Proposition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bozzelli, L., van Ditmarsch, H., Pinchinat, S. (2012). The Complexity of One-Agent Refinement Modal Logic. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds) Logics in Artificial Intelligence. JELIA 2012. Lecture Notes in Computer Science(), vol 7519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33353-8_10

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  • DOI: https://doi.org/10.1007/978-3-642-33353-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33352-1

  • Online ISBN: 978-3-642-33353-8

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