A Complete Deductive System for the mu-Calculus
نویسندگان
چکیده
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.
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The propositional μ-calculus as introduced by Kozen in [12] is considered. In that paper a finitary axiomatisation of the logic was presented but its completeness remained an open question. Here a different finitary axiomatisation of the logic is proposed and proved to be complete. The two axiomatisations are compared.
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We introduce a version of the probabilistic μ-calculus (PMC) built on top of a probabilistic modal logic that allows encoding n-ary inequational conditions on transition probabilities. PMC extends previously studied calculi and we prove that, despite its expressiveness, it enjoys a series of good metaproperties. Firstly, we prove the decidability of satisfiability checking by establishing the s...
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We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal μ-calculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal μ-calculus and combines it with techniques from work on local model checking. The proof system is sound for all pro...
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This article presents an outline of a system of equational deductions in the calculus that can be the basis of a computer program. We intend that our system be as faithful as possible to the usual (Leibniz) calculus notation and inferences. The language, however, is restricted mainly to equations, so the system is not sufficient to provide a basis for proving theorems, but we think it is suffic...
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ژورنال
عنوان ژورنال: BRICS Report Series
سال: 1995
ISSN: 1601-5355,0909-0878
DOI: 10.7146/brics.v2i6.19508