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On Disallowing Punctual Intervals in Reflexive Semantics of Halpern-Shoham Logic

16 pagesPublished: November 18, 2018


Halpern-Shoham logic (HS) is a very expressive and elegant formalism for interval temporal reasoning in which the satisfiability problem is undecidable. One of the methods to obtain HS-fragments of lower computational complexity is to adopt the softened (reflexive) seman- tics of the accessibility relations. In the paper we consider disallowing punctual intervals in reflexive semantics. We show that in this case we gain additional expressive power, which over discrete orders of time points results in PSpace-hardness of the Horn fragment of HS without diamond modal operators is and in undecidability of the core fragment of HS.

Keyphrases: computational complexity, Halpern-Shoham logic, interval logic, Sub-propositional Fragments

In: Gilles Barthe, Konstantin Korovin, Stephan Schulz, Martin Suda, Geoff Sutcliffe and Margus Veanes (editors). LPAR-22 Workshop and Short Paper Proceedings, vol 9, pages 91--106

BibTeX entry
  author    = {Przemys\{\textbackslash{}l\}aw Andrzej Wa\{\textbackslash{}l\}\textbackslash{}k\{e\}ga},
  title     = {On Disallowing Punctual Intervals in Reflexive Semantics of Halpern-Shoham Logic},
  booktitle = {LPAR-22 Workshop and Short Paper Proceedings},
  editor    = {Gilles Barthe and Konstantin Korovin and Stephan Schulz and Martin Suda and Geoff Sutcliffe and Margus Veanes},
  series    = {Kalpa Publications in Computing},
  volume    = {9},
  pages     = {91--106},
  year      = {2018},
  publisher = {EasyChair},
  bibsource = {EasyChair,},
  issn      = {2515-1762},
  url       = {},
  doi       = {10.29007/fl6v}}
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