The dark side of interval temporal logic: marking the undecidability border

  • Davide Bresolin
  • Dario Della Monica
  • Valentin Goranko
  • Angelo Montanari
  • Guido Sciavicco
Article

Abstract

Unlike the Moon, the dark side of interval temporal logics is the one we usually see: their ubiquitous undecidability. Identifying minimal undecidable interval logics is thus a natural and important issue in that research area. In this paper, we identify several new minimal undecidable logics amongst the fragments of Halpern and Shoham’s logic HS, including the logic of the overlaps relation, over the classes of all finite linear orders and all linear orders, as well as the logic of the meets and subinterval relations, over the classes of all and dense linear orders. Together with previous undecidability results, this work contributes to bringing the identification of the dark side of interval temporal logics very close to the definitive picture.

Keywords

Interval temporal logic Undecidability Tiling problems 

Mathematics Subject Classifications (2010)

03B44 03D35 68T27 05B45 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Davide Bresolin
    • 1
  • Dario Della Monica
    • 2
  • Valentin Goranko
    • 3
    • 4
  • Angelo Montanari
    • 5
  • Guido Sciavicco
    • 6
  1. 1.Department of Computer ScienceUniversity of VeronaVeronaItaly
  2. 2.ICE-TCS, School of Computer ScienceReykjavik UniversityReykjavikIceland
  3. 3.Department of Informatics and Mathematical ModellingTechnical University of DenmarkLynbgyDenmark
  4. 4.(visiting professor), Department of MathematicsUniversity of JohannesburgJohannesburgSouth Africa
  5. 5.Department of Mathematics and Computer ScienceUniversity of UdineUdineItaly
  6. 6.Department of Information and Communication EngineeringUniversity of MurciaMurciaSpain

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