{\L}ukasiewicz {\mu}-calculus
نویسندگان
چکیده
The paper explores properties of the Lukasiewicz μ-calculus, or Lμ for short, an extension of Lukasiewicz logic with scalar multiplication and least and greatest fixed-point operators (for monotone formulas). We observe that Lμ terms, with n variables, define monotone piecewise linear functions from [0, 1]n to [0, 1]. Two effective procedures for calculating the output of Lμ terms on rational inputs are presented. We then consider the Lukasiewicz modal μ-calculus, which is obtained by adding box and diamond modalities to Lμ. Alternatively, it can be viewed as a generalization of Kozen’s modal μ-calculus adapted to probabilistic nondeterministic transition systems (PNTS’s). We show how properties expressible in the well-known logic PCTL can be encoded as Lukasiewicz modal μ-calculus formulas. We also show that the algorithms for computing values of Lukasiewicz μ-calculus terms provide automatic (albeit impractical) methods for verifying Lukasiewicz modal μ-calculus properties of finite rational PNTS’s.
منابع مشابه
Similarity DH-Algebras
In cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...
متن کاملPreservation theorems in {L}ukasiewicz \model theory
We present some model theoretic results for {L}ukasiewiczpredicate logic by using the methods of continuous model theorydeveloped by Chang and Keisler.We prove compactness theorem with respect to the class of allstructures taking values in the {L}ukasiewicz $texttt{BL}$-algebra.We also prove some appropriate preservation theorems concerning universal and inductive theories.Finally, Skolemizatio...
متن کاملSymbolic Model Checking: 10^20 States and Beyond
Many diierent methods have been devised for automatically verifying nite state systems by examining state-graph models of system behavior. These methods all depend on decision procedures that explicitly represent the state space using a list or a table that grows in proportion to the number of states. We describe a general method that represents the state space symbolically instead of explicitl...
متن کامل