Related papers: The Complexity of Temporal Logic over the Reals
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 present the proof that the temporal logic of two-dimensional Minkowski spacetime is decidable, PSPACE-complete. The proof is based on a type of two-dimensional mosaic. Then we present the modification of the proof so as to work for…
We show that the decision problem for the basic system of interpretability logic IL is PSPACE-complete. For this purpose we present an algorithm which uses polynomial space with respect to the complexity of a given formula. The existence of…
In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional…
We work primarily with the Kripke frame consisting of two-dimensional Minkowski spacetime with the irreflexive accessibility relation 'can reach with a slower-than-light signal'. We show that in the basic temporal language, the set of…
We consider Minkowski spacetime, the set of all point-events of spacetime under the relation of causal accessibility. That is, ${\sf x}$ can access ${\sf y}$ if an electromagnetic or (slower than light) mechanical signal could be sent from…
We introduce the completeness problem for Modal Logic and examine its complexity. For a definition of completeness for formulas, given a formula of a modal logic, the completeness problem asks whether the formula is complete for that logic.…
In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PTL, the spatial logics RCC-8,…
We investigate a non-classical version of linear temporal logic whose propositional fragment is G\"odel--Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural…
Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…
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…
We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property…
We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for…
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…
We investigate the decidability of the ${0,\infty}$ fragment of Timed Propositional Temporal Logic (TPTL). We show that the satisfiability checking of TPTL$^{0,\infty}$ is PSPACE-complete. Moreover, even its 1-variable fragment…
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.…
Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have…
Although Dynamic Epistemic Logic (DEL) is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
Even after the proposal of various solution algorithms, the precise computational complexity of checking whether a Conditional Temporal Network is Dynamically Controllable had still remained widely open. This issue gets settled in this…