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An Epistemic Halpern–Shoham Logic
, 2013
"... We define a family of epistemic extensions of Halpern–Shoham logic for reasoning about temporalepistemic properties of multiagent systems. We exemplify their use and study the complexity of their model checking problem. We show a range of results ranging from PTIME to PSPACE– hard depending on the ..."
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We define a family of epistemic extensions of Halpern–Shoham logic for reasoning about temporalepistemic properties of multiagent systems. We exemplify their use and study the complexity of their model checking problem. We show a range of results ranging from PTIME to PSPACE– hard depending on the logic considered.
Decidability of the interval temporal logic AĀBB̄ over the rationals
, 2014
"... Abstract. The classification of the fragments of Halpern and Shoham’s logic with respect to decidability/undecidability of the satisfiability problem is now very close to the end. We settle one of the few remaining questions concerning the fragment AĀBB̄, which comprises Allen’s interval relation ..."
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Abstract. The classification of the fragments of Halpern and Shoham’s logic with respect to decidability/undecidability of the satisfiability problem is now very close to the end. We settle one of the few remaining questions concerning the fragment AĀBB̄, which comprises Allen’s interval relations “meets ” and “begins ” and their symmetric versions. We already proved that AĀBB ̄ is decidable over the class of all finite linear orders and undecidable over ordered domains isomorphic to N. In this paper, we first show that AĀBB ̄ is undecidable over R and over the class of all Dedekindcomplete linear orders. We then prove that the logic is decidable over Q and over the class of all linear orders. 1
Crossing the undecidability border with extensions of propositional neighborhood logic over natural numbers
 Journal of Universal Computer Science
"... Abstract: Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen’s relations, meets and met by). Recently, it has been shown that PNL interp ..."
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Abstract: Propositional Neighborhood Logic (PNL) is an interval temporal logic featuring two modalities corresponding to the relations of right and left neighborhood between two intervals on a linear order (in terms of Allen’s relations, meets and met by). Recently, it has been shown that PNL interpreted over several classes of linear orders, including natural numbers, is decidable (NEXPTIMEcomplete) and that some of its natural extensions preserve decidability. Most notably, this is the case with PNL over natural numbers extended with a limited form of metric constraints and with the future fragment of PNL extended with modal operators corresponding to Allen’s relations begins, begun by, and before. This paper aims at demonstrating that PNL and its metric version MPNL, interpreted over natural numbers, are indeed very close to the border with undecidability, and even relatively weak extensions of them become undecidable. In particular, we show that (i) the addition of binders on integer variables ranging over interval lengths makes the resulting hybrid extension of MPNL undecidable, and (ii) a very weak firstorder extension of the future fragment of PNL, obtained by replacing proposition letters by a restricted subclass of firstorder formulae where only one variable is allowed, is undecidable (in contrast with the decidability of similar firstorder extensions of pointbased temporal logics).
Bounded Variability of Metric Temporal Logic
, 2013
"... Previous work has shown that reasoning with realtime temporal logics is often simpler when restricted to models with bounded variability—where no more than v events may occur every V time units, for given v, V. When reasoning about formulas with intrinsic bounded variability, one can employ the sim ..."
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Previous work has shown that reasoning with realtime temporal logics is often simpler when restricted to models with bounded variability—where no more than v events may occur every V time units, for given v, V. When reasoning about formulas with intrinsic bounded variability, one can employ the simpler techniques that rely on bounded variability, without any loss of generality. What is then the complexity of algorithmically deciding which formulas have intrinsic bounded variability? In this paper, we study the problem with reference to Metric Temporal Logic (MTL). We prove that deciding bounded variability of MTL formulas is undecidable over densetime models, but with a undecidability degree lower than generic densetime MTL satisfiability. Over discretetime models, instead, deciding MTL bounded variability has the same exponentialspace complexity as satisfiability. To complement these negative results, we also discuss fragments of MTL that are more amenable to reasoning about bounded variability, again both for discrete and for densetime models. 1 The Benefits of Bounding Variability In yet another instance of the principle that “there ain’t no such thing as a free lunch”, expressiveness of formal languages comes with a significant cost to pay in terms of complexity—and possibly undecidability—of algorithmic analysis. The tradeoff between expressiveness and complexity is particularly critical for the realtime temporal logics, which dwell on the border of intractability. A chief research challenge is, therefore, identifying expressive temporal logic fragments without letting the “dark side ” of undecidability [6] prevail and abate practical usability.
DLLite and Interval Temporal Logics: a Marriage Proposal (extended version)
, 2014
"... Description logics [10] (DLs) are widelyused logical formalisms for knowledge representation, where the domain of interest is structured in concepts whose properties are specified by roles. Complex concepts and role expressions are constructed, starting from atomic ones, by applying suitable (log ..."
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Description logics [10] (DLs) are widelyused logical formalisms for knowledge representation, where the domain of interest is structured in concepts whose properties are specified by roles. Complex concepts and role expressions are constructed, starting from atomic ones, by applying suitable (log