Related papers: PSPACE Reasoning for Graded Modal Logics

We consider the satisfiability problem for the two-variable fragment of the first-order logic extended with modulo counting quantifiers and interpreted over finite words or trees. We prove a small-model property of this logic, which gives a…

We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…

Graded path modalities count the number of paths satisfying a property, and generalize the existential (E) and universal (A) path modalities of CTL*. The resulting logic is called GCTL*. We settle the complexity of satisfiability of GCTL*,…

It is shown that the decision problem for the temporal logic with until and since connectives over real-numbers time is PSPACE-complete.

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.…

We present a type system for an extension of lambda calculus with a conditional construction, named STAB, that characterizes the PSPACE class. This system is obtained by extending STA, a type assignment for lambda-calculus inspired by…

It was shown in Alur et al. [1] that the problem of verifying finite concurrent systems through Linearizability is in EXPSPACE. However, there was still a complexity gap between the easy to obtain PSPACE lower bound and the EXPSPACE upper…

In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…

It is known that the existential theory of equations in free groups is decidable. This is a famous result of Makanin. On the other hand it has been shown that the scheme of his algorithm is not primitive recursive. In this paper we present…

We introduce a new logic of graded distributed belief that allows us to express the fact that a group of agents distributively believe that a certain fact holds with at least strength k. We interpret our logic by means of computationally…

Prime implicates and prime implicants have proven relevant to a number of areas of artificial intelligence, most notably abductive reasoning and knowledge compilation. The purpose of this paper is to examine how these notions might be…

This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…

The characterization of PSPACE-queries over ordered structures as exactly those expressible in first-order logic with partial fixpoints (Vardi'82) is one of the classical results in the field of descriptive complexity. In this paper, we…

We present a simple theory explaining the construction and the correctness of an incremental and worst-case optimal decision procedure for modal logic with eventualities. The procedure gives an abstract account of important aspects of…

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a positive cost function c: V-> Z^{+}, a partition $P_1,..., P_r$ of the edge set $E$, and a parameter $k_i$ for each…

Standard epistemic logic studies propositional knowledge, yet many other types of knowledge such as "knowing whether", "knowing what", "knowing how" are frequently and widely used in everyday life as well as academic fields. In…

We investigate the computational complexity of admissibility of inference rules in infinite-valued {\L}ukasiewicz propositional logic (\L). It was shown in [13] that admissibility in {\L} is checkable in PSPACE. We establish that this…

This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…

This article shows that PSPACE not equal EXP. A simple but novel proof technique has been used to separate these two classes. Whether an arbitrary Turing machine accepts an input when the running time is limited has been computed in this…

We investigate the complexity of the satisfiability problem for a modal logic expressing `knowing how' assertions, related to an agent's abilities to achieve a certain goal. We take one of the most standard semantics for this kind of logics…