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The choice of the right trade-off between expressiveness and complexity is the main issue in interval temporal logic. In their seminal paper, Halpern and Shoham showed that the satisfiability problem for HS (the temporal logic of Allen's…

A classic result by Stockmeyer gives a non-elementary lower bound to the emptiness problem for star-free generalized regular expressions. This result is intimately connected to the satisfiability problem for interval temporal logic, notably…

We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…

The expressive power of interval temporal logics (ITLs) makes them one of the most natural choices in a number of application domains, ranging from the specification and verification of complex reactive systems to automated planning.…

In the plethora of fragments of Halpern and Shoham's modal logic of time intervals (HS), the logic AB of Allen's relations Meets and Started-by is at a central position. Statements that may be true at certain intervals, but at no…

We introduce the synthesis problem for Halpern and Shoham's modal logic of intervals extended with an equivalence relation over time points, abbreviated HSeq. In analogy to the case of monadic second-order logic of one successor, the…

In this paper, we investigate the model checking (MC) problem for Halpern and Shoham's interval temporal logic HS. In the last years, interval temporal logic MC has received an increasing attention as a viable alternative to the traditional…

The Epistemic Halpern-Shoham logic (EHS) is a temporal-epistemic logic that combines the interval operators of the Halpern-Shoham logic with epistemic modalities. The semantics of EHS is based on interpreted systems whose labelling function…

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 contribute to this effort…

Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…

Modal logics are widely used in computer science. The complexity of modal satisfiability problems has been investigated since the 1970s, usually proving results on a case-by-case basis. We prove a very general classification for a wide…

Interval temporal logics provide a general framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. In this paper, we identify all fragments…

The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…

We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…

The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…

We consider the temporal logic with since and until modalities. This temporal logic is expressively equivalent over the class of ordinals to first-order logic by Kamp's theorem. We show that it has a PSPACE-complete satisfiability problem…

We first show that infinite satisfiability can be reduced to finite satisfiability for all prenex formulas of Separation Logic with $k\geq1$ selector fields ($\seplogk{k}$). Second, we show that this entails the decidability of the finite…

Modal dependence logic was introduced recently by V\"a\"an\"anen. It enhances the basic modal language by an operator =(). For propositional variables p_1,...,p_n, =(p_1,...,p_(n-1);p_n) intuitively states that the value of p_n is…

We consider the satisfiability problem for the two-variable fragment of first-order logic over finite unranked trees. We work with signatures consisting of some unary predicates and the binary navigational predicates child, right sibling,…

We study the complexity of problems related to subgame-perfect equilibria (SPEs) in infinite duration non zero-sum multiplayer games played on finite graphs with parity objectives. We present new complexity results that close gaps in the…