A propositional modal logic of time intervals
Journal of the ACM (JACM)
An Adequate First Order Interval Logic
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
An Optimal Decision Procedure for Right Propositional Neighborhood Logic
Journal of Automated Reasoning
Optimal Tableaux for Right Propositional Neighborhood Logic over Linear Orders
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
Back to Interval Temporal Logics
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Temporal prepositions and their logic
Artificial Intelligence
An optimal Tableau-based decision algorithm for propositional neighborhood logic
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Maximal decidable fragments of Halpern and Shoham's modal logic of intervals
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
The importance of the past in interval temporal logics: the case of propositional neighborhood logic
Logic Programs, Norms and Action
Optimal decision procedures for MPNL over finite structures, the natural numbers, and the integers
Theoretical Computer Science
Adding an Equivalence Relation to the Interval Logic ABB: Complexity and Expressiveness
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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In this paper, we focus our attention on tableau systems for the propositional interval logic of temporal neighborhood (Propositional Neighborhood Logic, PNL for short). PNL is the proper subset of Halpern and Shoham's modal logic of intervals whose modalities correspond to Allen's relations meets and met by. We first prove by a model-theoretic argument that the satisfiability problem for PNL over the class of all (resp., dense, discrete) linear orders is decidable (and NEXPTIME-complete). Then, we develop sound and complete tableau-based decision procedures for all the considered classes of orders, and we prove their optimality. (As a matter of fact, decidability with respect to the class of all linear orders had been already proved via a reduction to the decidable satisfiability problem for the two-variable fragment of first-order logic of binary relational structures over ordered domains).