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2 results on '"octant tiling problem"'

1. Undecidability of the Logic of Overlap Relation over Discrete Linear Orderings.

Author

Bresolin, Davide, Della Monica, Dario, Goranko, Valentin, Montanari, Angelo, and Sciavicco, Guido

Subjects
LOGIC programming, LINEAR orderings, COMBINATORICS, MATHEMATICAL logic, NP-complete problems, TILING (Mathematics)
Abstract

Abstract: The validity/satisfiability problem for most propositional interval temporal logics is (highly) undecidable, under very weak assumptions on the class of interval structures in which they are interpreted. That, in particular, holds for most fragments of Halpern and Shoham''s interval modal logic HS. Still, decidability is the rule for the fragments of HS with only one modal operator, based on an Allen''s relation. In this paper, we show that the logic O of the Overlap relation, when interpreted over discrete linear orderings, is an exception. The proof is based on a reduction from the undecidable octant tiling problem. This is one of the sharpest undecidability result for fragments of HS. [Copyright &y& Elsevier]

Published
2010
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2. Undecidability of the Logic of Overlap Relation over Discrete Linear Orderings

Author

Davide Bresolin, Angelo Montanari, Guido Sciavicco, Valentin Goranko, Dario Della Monica, Bresolin D., Della Monica D., Goranko V., Montanari A., and Sciavicco G.

Subjects
General Computer Science, Normal modal logic, Interval temporal logic, Modal Logic, interval temporal logics, Modal operator, Interval Logic, Theoretical Computer Science, Combinatorics, Interval Temporal Logic, Undecidability, Linear temporal logic, Computer Science::Logic in Computer Science, Accessibility relation, Mathematics, Discrete mathematics, interval temporal logic, Allen's relations, undecidability, overlap relation, Modal logic, Modal μ-calculus, octant tiling problem, Decidability, TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES, Computer Science(all)
Abstract

The validity/satisfiability problem for most propositional interval temporal logics is (highly) undecidable, under very weak assumptions on the class of interval structures in which they are interpreted. That, in particular, holds for most fragments of Halpern and Shoham's interval modal logic HS. Still, decidability is the rule for the fragments of HS with only one modal operator, based on an Allen's relation. In this paper, we show that the logic O of the Overlap relation, when interpreted over discrete linear orderings, is an exception. The proof is based on a reduction from the undecidable octant tiling problem. This is one of the sharpest undecidability result for fragments of HS.

Published
2010

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