Mathematical logic and computational complexity have close connections that can be traced to the roots of computability theory and the classical decision problem. In the context of complexity, some well-known fundamental problems are: satisfiability testing of formulas (in some logic), proof complexity, and the complexity of checking if a given model satisfies a given formula. The Model Checkin...

This paper continues the investigation of rudimentary Kripke models, i.e. non-quasiordered Kripke-style models for the Heyting propositional calculus H. Three topics, which make three companion pieces of [3], are pursued. The first topic is Beth-style models for H called rudimentary Beth models. Rudimentary Kripke models may be conceived as a particular type of these models, which are analogous...

This paper considers QLtl, a quantitative analagon of Ltl and presents algorithms for model checking QLtl over quantitative versions of Kripke structures and Markov chains.

I characterize the first-order definable, bi-orthogonally closed subsets of a quasiquantum Kripke frame satisfying a reasonable assumption. The techniques are generalization of those in Goldblatt’s paper published in 1984. Combining these techniques with Goldblatt’s idea, I prove that quantum Kripke frames are not firstorder definable in the class of quasi-quantum Kripke frames.

In this paper, we investigate the finite satisfiability and model checking problems for the logic D of the sub-interval relation under the homogeneity assumption, that constrains a proposition letter to hold over an interval if and only if it holds over all its points. First, we prove that the satisfiability problem for D, over finite linear orders, is PSPACE-complete; then, we show that its mo...

We use Kripke structures of autoepistemic logic to classify various semantics for disjunctive logic programs with default negation. We have observed that nonmonotonic reasoning can be characterized by Kripke structures whose beliefs are justiied. We also observed that two diierent types of negative introspection in autoepistemic reasoning present two diierent interpretations of default negation...

This paper studies abstraction and refinement techniques in the setting of multi-valued model checking for the μ-calculus. Two dimensions of abstractions are identified and studied: Abstraction by joining states of the underlying multi-valued Kripke structure as well as abstraction of truth values, for each following both an optimistic and pessimistic account. It is shown that our notion of abs...

Let Gm be the m-valued Gödel-Dummett fuzzy logic. If m ≥ 3 then neither conjunction nor implication is in Gm expressible in terms of the remaining connectives. This fact remains true even if the propositional language is enriched by propositional constants for all truth values. Gödel-Dummett fuzzy propositional logic can be defined as an extension of the intuitionistic propositional logic by th...

In the paper a novel methodology, TS-U, is proposed based on existing model checking techniques that were extended to successfully model the systems in a ubiquitous environment by introducing time and space constraints relevant in modeling of some ubiquitous system for its validation. Method proposed requires only slight modification of the existing model checking tools by introducing the notio...