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Maximal decidable fragments of Halpern and Shoham’s modal logic of intervals (2010)
| Citations: | 14 - 10 self |
BibTeX
@TECHREPORT{Montanari10maximaldecidable,
author = {Angelo Montanari and Pietro Sala},
title = {Maximal decidable fragments of Halpern and Shoham’s modal logic of intervals},
institution = {},
year = {2010}
}
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Abstract
Abstract. In this paper, we focus our attention on the fragment of Halpern and Shoham’s modal logic of intervals (HS) that features four modal operators corresponding to the relations “meets”, “met by”, “be-gun by”, and “begins ” of Allen’s interval algebra (AĀBB ̄ logic). AĀBB̄ properly extends interesting interval temporal logics recently investigated in the literature, such as the logic BB ̄ of Allen’s “begun by/begins ” rela-tions and propositional neighborhood logic AĀ, in its many variants (in-cluding metric ones). We prove that the satisfiability problem for AĀBB̄, interpreted over finite linear orders, is decidable, but not primitive recur-sive (as a matter of fact, AĀBB ̄ turns out to be maximal with respect to decidability). Then, we show that it becomes undecidable when AĀBB ̄ is interpreted over classes of linear orders that contains at least one linear order with an infinitely ascending sequence, thus including the natural time flows N, Z, and R. 1
Keyphrases
modal logic aa bb maximal decidable fragment linear order many variant relation meet interesting interval temporal logic logic bb begin rela-tions natural time finite linear order propositional neighborhood logic aa in-cluding metric one satisfiability problem modal operator interval algebra aa bb logic
