scholarly journals Interval temporal logics over strongly discrete linear orders: Expressiveness and complexity

2014 ◽  
Vol 560 ◽  
pp. 269-291 ◽  
Author(s):  
Davide Bresolin ◽  
Dario Della Monica ◽  
Angelo Montanari ◽  
Pietro Sala ◽  
Guido Sciavicco
Keyword(s):  
Linear Orders ◽  
Temporal Logics ◽  
Interval Temporal Logics

scholarly journals Interval Temporal Logics over Strongly Discrete Linear Orders: the Complete Picture

2012 ◽  
Vol 96 ◽  
pp. 155-168 ◽  
Author(s):  
Davide Bresolin ◽  
Dario Della Monica ◽  
Angelo Montanari ◽  
Pietro Sala ◽  
Guido Sciavicco
Keyword(s):  
Complete Picture ◽  
Linear Orders ◽  
Temporal Logics ◽  
Interval Temporal Logics

Relational dual tableaux for interval temporal logics ★

2006 ◽  
Vol 16 (3-4) ◽  
pp. 251-277 ◽  
Author(s):  
Davide Bresolin ◽  
Joanna Golińska-Pilarek ◽  
Ewa Orlowska
Keyword(s):  
Temporal Logics ◽  
Interval Temporal Logics

scholarly journals Guest editors’ preface to special issue on interval temporal logics

2014 ◽  
Vol 71 (1-3) ◽  
pp. 1-9 ◽  
Author(s):  
Ben Moszkowski ◽  
Dimitar Guelev ◽  
Martin Leucker
Keyword(s):  
Special Issue ◽  
Temporal Logics ◽  
Interval Temporal Logics

scholarly journals Two-sorted Point-Interval Temporal Logics

2011 ◽  
Vol 278 ◽  
pp. 31-45 ◽  
Author(s):  
Philippe Balbiani ◽  
Valentin Goranko ◽  
Guido Sciavicco
Keyword(s):  
Temporal Logics ◽  
Interval Temporal Logics

scholarly journals A Road Map of Interval Temporal Logics and Duration Calculi

2004 ◽  
Vol 14 (1-2) ◽  
pp. 9-54 ◽  
Author(s):  
Valentin Goranko ◽  
Angelo Montanari ◽  
Guido Sciavicco
Keyword(s):  
Temporal Logics ◽  
Road Map ◽  
Interval Temporal Logics

ON BEGINS, MEETS AND BEFORE

2012 ◽  
Vol 23 (03) ◽  
pp. 559-583 ◽  
Author(s):  
DAVIDE BRESOLIN ◽  
PIETRO SALA ◽  
GUIDO SCIAVICCO
Keyword(s):  
Temporal Logic ◽  
Decision Procedure ◽  
Linear Models ◽  
Complete Classification ◽  
Temporal Logics ◽  
Logic Formula ◽  
Current Interval ◽  
Finite Domains ◽  
Interval Temporal Logics

Interval temporal logics (ITLs) are logics for reasoning about temporal statements expressed over intervals, i.e., periods of time. The most famous temporal logic for intervals studied so far is probably Halpern and Shoham's HS, which is the logic of the thirteen Allen's interval relations. Unfortunately, HS and most of its fragments are undecidable. This discouraged the research in this area until recently, when a number non-trivial decidable ITLs have been discovered. This paper is a contribution towards the complete classification of all different fragments of HS. We consider here different combinations of the interval relations begins (B), meets (A), later (L) and their inverses [Formula: see text], [Formula: see text] and [Formula: see text]. We know from previous work that the combination [Formula: see text] is decidable only when finite domains are considered (and undecidable elsewhere), and that [Formula: see text] is decidable over the natural numbers. In the present paper we show that, over strongly discrete linear models (e.g. finite orders, the naturals, the integers), decidability of [Formula: see text] can be further extended to capture the language [Formula: see text], which lies strictly in between [Formula: see text] and [Formula: see text]. The logic [Formula: see text] turns out to be maximal w.r.t decidability over the considered classes, and its satisfiability problem is EXPSPACE-complete. In this paper we also provide an optimal non-deterministic decision procedure, and we show that the language is powerful enough to polynomially encode metric constraints on the length of the current interval.

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