Mu-calculus(a.k.a.μTL)is built up from modal/dynamic logic via adding the least fixpoint operatorμ.This type of logic has attracted increasing attention since Kozen’s seminal work.PμTL is a succinct probabilistic ...Mu-calculus(a.k.a.μTL)is built up from modal/dynamic logic via adding the least fixpoint operatorμ.This type of logic has attracted increasing attention since Kozen’s seminal work.PμTL is a succinct probabilistic extension of the standardμTL obtained by making the modal operators probabilistic.Properties of this logic,such as expressiveness and satisfiability decision,have been studied elsewhere.We consider another important problem:the axiomatization of that logic.By extending the approaches of Kozen and Walukiewicz,we present an axiom system for PμTL.In addition,we show that the axiom system is complete for aconjunctive formulas.展开更多
基金supported by the National Science Foundation of China(No.61872371)the National Science Foundation of China(Nos.61761136011 and 61836005)+2 种基金the Open Fund from the State Key Laboratory of High Performance Computing of China(HPCL)(No.2020001-07)the National Key Research and Development Program of China(No.2018YFB0204301)supported by the Guangdong Science and Technology(No.2018B010107004)。
文摘Mu-calculus(a.k.a.μTL)is built up from modal/dynamic logic via adding the least fixpoint operatorμ.This type of logic has attracted increasing attention since Kozen’s seminal work.PμTL is a succinct probabilistic extension of the standardμTL obtained by making the modal operators probabilistic.Properties of this logic,such as expressiveness and satisfiability decision,have been studied elsewhere.We consider another important problem:the axiomatization of that logic.By extending the approaches of Kozen and Walukiewicz,we present an axiom system for PμTL.In addition,we show that the axiom system is complete for aconjunctive formulas.
