Property-Dependent Reductions for the Modal Mu-Calculus

Electronic Notes in Theoretical Computer Science, 2000

EPiC series in computing, 2018

RAIRO - Theoretical Informatics and Applications, 2003

Electronic Notes in Theoretical Computer Science, 1998

Demonstratio Mathematica, 1987

Citeseer

Modal µ-calculus is a modal logic with fixed-point operators and well-known in mathematics and computer scince. For example, many verification properties of a system are expressed by formulas of modal µcalculus in computer science. However some verification properties of a system can not be expressed by a formula of modal µ-calculus as we will show later, and quantifiers of first-order logic are essentially required for expressing the verification properties. Therefore a first-order extension of modal µ-calculus is needed for expressing such verification properties. In this paper we introduce a first-order extension of modal µ-calculus and show that it is Σ 1 1 -complete. Moreover we express some verification properties of a system by its formulas for showing its usefulness.

imm.dtu.dk

We study the general problem of axiomatizing s tructures in the framework of modal logic and present a u niform method for complete axiomatization of the modal l ogics determined by a large family of classes o f s tructures of any signature.

2003