The Modal Μ-calculus: a Survey
نویسندگان
چکیده
The modal μ-calculus is an extension of modal logic with two operators μ and ν, which give the least and greatest fixpoints of monotone operators on powersets. This powerful logic is widely used in computer science, in the area of verification of correctness of concurrent systems. In this survey we review both the theoretical aspects of the modal μ-calculus and its applications to computer science.
منابع مشابه
Deductive Systems for the Modal mu-Calculus
We survey deductive systems for the modal μ-calculus. The distinguishing feature between different such systems is how minimality of least fixed points is guaranteed. There are basically three ways to achieve this: (i) by induction rules, (ii) by semi-formal rules with infinitely many premises, or (iii) by a global condition on infinitely long proof branches.
متن کاملA First-Order Extension of Modal μ- calculus
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 ar...
متن کاملExpressiveness of the modal mu-calculus on monotone neighborhood structures
We characterize the expressive power of the modal μ-calculus on monotone neighborhood structures, in the style of the Janin-Walukiewicz theorem for the standard modal μ-calculus. For this purpose we consider a monadic second-order logic for monotone neighborhood structures. Our main result shows that the monotone modal μ-calculus corresponds exactly to the fragment of this second-order language...
متن کاملComplexity of Monadic inf-datalog. Application to temporal logic
In [] we defined Inf-Datalog and characterized the fragments of Monadic inf-Datalog that have the same expressive power as Modal Logic (resp. CTL, alternation-free Modal μ-calculus and Modal μ-calculus). We study here the time and space complexity of evaluation of Monadic inf-Datalog programs on finite models. We deduce a new unified proof that model checking has 1. linear data and program comp...
متن کاملCompleteness Theorem of First - Order Modal μ - calculus
We prove that a natural axiom system of first-order modal μ-calculus is complete with respect to “general” models.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005