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Pushdown Processes: Games and Model Checking
, 1996
"... Games given by transition graphs of pushdown processes are considered. It is shown that ..."
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Cited by 136 (4 self)
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Games given by transition graphs of pushdown processes are considered. It is shown that
Games for the µCalculus
"... Given a formula of the propositional µcalculus, we construct a tableau of the formula and define an infinite game of two players of which one wants to show that the formula is satisfiable, and the other seeks the opposite. The strategy for the first player can be further transformed into a model of ..."
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Cited by 52 (5 self)
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Given a formula of the propositional µcalculus, we construct a tableau of the formula and define an infinite game of two players of which one wants to show that the formula is satisfiable, and the other seeks the opposite. The strategy for the first player can be further transformed into a model of the formula while the strategy for the second forms what we call a refutation of the formula. Using Martin's Determinacy Theorem, we prove that any formula has either a model or a refutation. This completeness result is a starting point for the completeness theorem for the µcalculus to be presented elsewhere. However, we argue that refutations have some advantages of their own. They are generated by a natural system of sound logical rules and can be presented as regular trees of the size exponential in the size of a refuted formula. This last aspect completes the small model theorem for the µcalculus established by Emerson and Jutla [3]. Thus, on a more practical side, refutations can be...
Completeness of Kozen's Axiomatisation of the Propositional µCalculus
 Inform. and Comput
, 1995
"... Propositional calculus is an extension of the propositional modal logic with the least fixpoint operator. In the paper introducing the logic Kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the modal system K. It is shown that this ..."
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Cited by 23 (0 self)
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Propositional calculus is an extension of the propositional modal logic with the least fixpoint operator. In the paper introducing the logic Kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the modal system K. It is shown that this axiomatisation is complete.
Monadic Second Order Logic on TreeLike Structures
, 1996
"... An operation M* which constructs from a given structure M a treelike structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such treelike structures is defined. It is shown that automata of this kind characterise expressive power of ..."
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Cited by 19 (6 self)
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An operation M* which constructs from a given structure M a treelike structure whose domain consists of the finite sequences of elements of M is considered. A notion of automata running on such treelike structures is defined. It is shown that automata of this kind characterise expressive power of monadic second order logic (MSOL) over treelike structures. Using this characterisation it is proved that MSOL theory of treelike structures is effectively reducible to that of the original structures. As another application of the characterisation it is shown that MSOL on trees of arbitrary degree is equivalent to first order logic extended with unary least fixpoint operator.
A Complete Deductive System for the µCalculus
, 1995
"... The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper ..."
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Cited by 13 (0 self)
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The propositional µcalculus as introduced by Kozen in [12] is considered. In that paper
Automata for the µcalculus and Related Results
, 1995
"... The propositional µcalculus as introduced by Kozen in [4] is considered. The notion of disjunctive formula is defined and it is shown that every formula is semantically equivalent to a disjunctive formula. For these ..."
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Cited by 11 (2 self)
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The propositional µcalculus as introduced by Kozen in [4] is considered. The notion of disjunctive formula is defined and it is shown that every formula is semantically equivalent to a disjunctive formula. For these
Modal Logic and nonwellfounded Set Theory: translation, bisimulation, interpolation.
, 1998
"... Contents Acknowledgments vii 1 Introduction. 1 2 General preliminaries. 7 2.1 Logics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Languages and structures. . . . . . . . . . . . . . . . . . . 7 2.1.2 Syntax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1 ..."
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Cited by 6 (1 self)
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Contents Acknowledgments vii 1 Introduction. 1 2 General preliminaries. 7 2.1 Logics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Languages and structures. . . . . . . . . . . . . . . . . . . 7 2.1.2 Syntax. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.3 Semantics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.4 Translations. . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.1.5 Derivability in Basic Modal Logic. . . . . . . . . . . . . . . 10 2.2 Bisimulation and the like. . . . . . . . . . . . . . . . . . . . . . . 12 2.3 A brief introduction to the Calculus. . . . . . . . . . . . . . . . 17 2.4 The family of graded modal logics and their semantics. . . . . . . 22 2.5 Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5.1 Uniform interpolation. . . . . . . . . . . . . . . . . . . . . 29 2.5.2 Elementary interpolation. . . . . . . . . . . . . . . . . . . 30 2.6 N
Notes on the Propositional µcalculus: Completeness and Related Results
, 1995
"... Contents 1 Introduction 1 1.1 Synopsis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 Preliminaries 3 2.1 Syntax and semantics of the calculus : : : : : : : : : : : : : : : 3 2.2 Restrictions and extensions of the syntax : : : : : : : : : : : : : 4 2.3 Binding definitions : : ..."
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Cited by 5 (0 self)
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Contents 1 Introduction 1 1.1 Synopsis : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 2 Preliminaries 3 2.1 Syntax and semantics of the calculus : : : : : : : : : : : : : : : 3 2.2 Restrictions and extensions of the syntax : : : : : : : : : : : : : 4 2.3 Binding definitions : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.4 Automata on infinite objects : : : : : : : : : : : : : : : : : : : : 7 3 Tableaux, markings and "operational semantics" 10 3.1 Formulas as automata : : : : : : : : : : : : : : : : : : : : : : : : 10 3.2 Formalisation : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14 4 Applications of operational semantics 21 4.1 Small model theorem, decidability, syntactic characterisations : : 21 4.2 Tableau equivalence : : : : : : : :
Equational axioms of test algebra
 Computer Science Logic, 11th International Workshop, CSL ’97, volume 1414 of LNCS
, 1997
"... We presentacomplete axiomatization of test algebra ([24, 18, 29]), the twosorted algebraic variant of Propositional Dynamic Logic (PDL, [21, 7]). The axiomatization consists of adding a nite number of equations to any axiomatization of Kleene algebra ([15, 26, 17, 4]) and algebraic translations of ..."
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Cited by 4 (0 self)
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We presentacomplete axiomatization of test algebra ([24, 18, 29]), the twosorted algebraic variant of Propositional Dynamic Logic (PDL, [21, 7]). The axiomatization consists of adding a nite number of equations to any axiomatization of Kleene algebra ([15, 26, 17, 4]) and algebraic translations of the Segerberg ([27]) axioms for PDL. Kleene algebras are not nitely axiomatizable ([25, 6]), so our result does not give us a nite axiomatization of test algebra: in fact, no nite equational axiomatization exists. We alsopresent a singlesorted version of test algebra, using the notion of dynamic negation ([9, 2, 11]), to which the previous results carry over. 1
Logical specification and analysis of fault tolerant systems through partial model checking
 In: Proceedings of the International Workshop on Software Verification and Validation (SVV 2003
, 2003
"... This paper presents a framework for a logical characterization of fault tolerance and its formal analysis based on partial model checking techniques. The framework requires a fault tolerant system to be modeled using a formal calculus, here the CCS process algebra. To this aim we propose a uniform m ..."
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This paper presents a framework for a logical characterization of fault tolerance and its formal analysis based on partial model checking techniques. The framework requires a fault tolerant system to be modeled using a formal calculus, here the CCS process algebra. To this aim we propose a uniform modeling scheme in which to specify a formal model of the system, its failing behaviour and possibly its faultrecovering procedures. Once a formal model is provided into our scheme, fault tolerance with respect to a given property can be formalized as an equational µcalculus formula. This formula expresses, in a logic formalism, all the fault scenarios satisfying that fault tolerance property. Such a characterization understands the analysis of fault tolerance as a form of analysis of open systems and, thank to partial model checking strategies, it can be made independent from any particular fault assumption. Moreover this logical characterization makes possible the faulttolerance verification problem be expressed as a general µcalculus validation problem, for solving which many theorem proof techniques and tools are available. We present several analysis methods showing the flexibility of our approach.