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We define a family of epistemic extensions of Halpern–Shoham logic for reasoning about temporal-epistemic properties of multi-agent 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.

We define and illustrate the expressiveness of the A ¯ BL fragment of the Epistemic Halpern–Shoham Logic as a specification language for multi-agent systems. We consider the model checking problem for systems against specifications given in the logic. We show its decidability by means of a novel technique that may be reused in other contexts for showing… (More)

—The Halpern–Shoham logic is a modal logic of time intervals. Some effort has been put in last ten years to classify fragments of this beautiful logic with respect to decidability of its satisfiability problem. We complete this classification by showing — what we believe is quite an unexpected result — that the logic of subintervals, the fragment of the… (More)

We consider the satisfiability and finite satisfiability problems for extensions of the two-variable fragment of first-order logic in which an equivalence closure operator can be applied to a fixed number of binary predicates. We show that the satisfiability problem for two-variable, first-order logic with equivalence closure applied to two binary… (More)

The HalpernShoham logic is a modal logic of time intervals. Some eort has been put in last ten years to classify fragments of this beautiful logic with respect to decidability of its satisability problem. We contribute to this eort by showing (among other results), that the fragment (where only the operators begins and during are allowed) is undecidable… (More)

The Halpern–Shoham logic is a modal logic of time intervals. Some effort has been put in last ten years to classify fragments of this beautiful logic with respect to decidability of its satisfiability problem. We complete this classification by showing — what we believe is quite an unexpected result — that the logic of subintervals, the fragment of the… (More)

We prove that the satisfiability problem for the two-variable, universal fragment of first-order logic with constants (or, alternatively phrased, for the Bernays-Schönfinkel class with two universally quantified variables) remains decidable after augmenting the fragment by the transitive closure of a single binary relation. We give a 2-NExpTime-upper bound… (More)

In this paper, the modal logic over classes of structures definable by universal first-order Horn formulas is studied. We show that the satisfiability problems for that logics are decidable, confirming the conjecture from [E. Hemaspaandra and H. Schnoor, On the Complexity of Elementary Modal Logics, STACS 08]. We provide a full classification of logics… (More)

We consider an extension of the guarded fragment in which one can guard quantiers using the transitive closure of some binary relations. The obtained logic captures the guarded fragment with transitive guards, and in fact extends its expressive power non-trivially, preserving the complexity: we prove that its satisability problem is 2Exptime-complete.

We consider the satisfiability problem for modal logic over classes of structures definable by universal first-order formulas with three variables. We exhibit a simple formula for which the problem is undecidable. This improves an earlier result in which nine variables were used. We also show that for classes defined by three-variable, universal Horn… (More)