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A Proof Search Specification of the πCalculus
 IN 3RD WORKSHOP ON THE FOUNDATIONS OF GLOBAL UBIQUITOUS COMPUTING
, 2004
"... We present a metalogic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite πcalculus within this metalogic ..."
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We present a metalogic that contains a new quantifier (for encoding "generic judgment") and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite πcalculus within this metalogic. Since we
Proof search specifications of bisimulation and modal logics for the πcalculus
 ACM Trans. on Computational Logic
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
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Cited by 15 (9 self)
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We shall illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode the πcalculus with replications, in an extended logic with induction and coinduction.
Mixing finite success and finite failure in an automated prover
 In Proceedings of ESHOL’05: Empirically Successful Automated Reasoning in HigherOrder Logics, pages 79 – 98
, 2005
"... Abstract. The operational semantics and typing judgements of modern programming and specification languages are often defined using relations and proof systems. In simple settings, logic programming languages can be used to provide rather direct and natural interpreters for such operational semantic ..."
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Cited by 15 (8 self)
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Abstract. The operational semantics and typing judgements of modern programming and specification languages are often defined using relations and proof systems. In simple settings, logic programming languages can be used to provide rather direct and natural interpreters for such operational semantics. More complex features of specifications such as names and their bindings, proof rules with negative premises, and the exhaustive enumeration of state spaces, all pose significant challenges to conventional logic programming systems. In this paper, we describe a simple architecture for the implementation of deduction systems that allows a specification to interleave between finite success and finite failure. The implementation techniques for this prover are largely common ones from higherorder logic programming, i.e., logic variables, (higherorder pattern) unification, backtracking (using streambased computation), and abstract syntax based on simply typed λterms. We present a particular instance of this prover’s architecture and its prototype implementation, Level 0/1, based on the dual interpretation of (finite) success and finite failure in proof search. We show how Level 0/1 provides a highlevel and declarative implementation of model checking and bisimulation checking for the (finite) πcalculus. 1
Model checking for πcalculus using proof search
 CONCUR, volume 3653 of LNCS
, 2005
"... Abstract. Model checking for transition systems specified in πcalculus has been a difficult problem due to the infinitebranching nature of input prefix, namerestriction and scope extrusion. We propose here an approach to model checking for πcalculus by encoding it into a logic which supports rea ..."
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Abstract. Model checking for transition systems specified in πcalculus has been a difficult problem due to the infinitebranching nature of input prefix, namerestriction and scope extrusion. We propose here an approach to model checking for πcalculus by encoding it into a logic which supports reasoning about bindings and fixed points. This logic, called F Oλ ∆ ∇ , is a conservative extension of Church’s Simple Theory of Types with a “generic ” quantifier. By encoding judgments about transitions in picalculus into this logic, various conditions on the scoping of names and restrictions on name instantiations are captured naturally by the quantification theory of the logic. Moreover, standard implementation techniques for (higherorder) logic programming are applicable for implementing proof search for this logic, as illustrated in a prototype implementation discussed in this paper. The use of logic variables and eigenvariables in the implementation allows for exploring the state space of processes in a symbolic way. Compositionality of properties of the transitions is a simple consequence of the meta theory of the logic (i.e., cut elimination). We illustrate the benefits of specifying systems in this logic by studying several specifications of modal logics for picalculus. These specifications are also executable directly in the prototype implementation of F Oλ ∆ ∇. 1
Model checking for picalculus using proof search
 In CONCUR, volume 3653 of LNCS
, 2005
"... Abstract. Model checking for transition systems specified in picalculus has been a difficult problem due to the infinitebranching nature of input prefix, namerestriction and scope extrusion. We propose here an approach to model checking for picalculus by encoding it into a logic which supports ..."
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Abstract. Model checking for transition systems specified in picalculus has been a difficult problem due to the infinitebranching nature of input prefix, namerestriction and scope extrusion. We propose here an approach to model checking for picalculus by encoding it into a logic which supports reasoning about bindings and fixed points. This logic, called FOλ∆∇, is a conservative extension of Church’s Simple Theory of Types with a “generic ” quantifier. By encoding judgments about transitions in picalculus into this logic, various conditions on the scoping of names and restrictions on name instantiations are captured naturally by the quantification theory of the logic. Moreover, standard implementation techniques for (higherorder) logic programming are applicable for implementing proof search for this logic, as illustrated in a prototype implementation discussed in this paper. The use of logic variables and eigenvariables in the implementation allows for exploring the state space of processes in a symbolic way. Compositionality of properties of the transitions is a simple consequence of the meta theory of the logic (i.e., cut elimination). We illustrate the benefits of specifying systems in this logic by studying several specifications of modal logics for picalculus. These specifications are also executable directly in the prototype implementation of FOλ∆∇. 1
How to Incorporate Negation in a Prolog Compiler
"... . Knowledge representation based applications require a more complete set of capabilities than those offered by conventional Prolog compilers. Negation is, probably, the most important one. The inclusion of negation among the logical facilities of LP has been a very active area of research, and ..."
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Cited by 2 (0 self)
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. Knowledge representation based applications require a more complete set of capabilities than those offered by conventional Prolog compilers. Negation is, probably, the most important one. The inclusion of negation among the logical facilities of LP has been a very active area of research, and several techniques have been proposed. However, the negation capabilities accepted by current Prolog compilers are very limited. In this paper, we discuss the possibility to incorporate some of these techniques in a Prolog compiler in an efficient way. Our idea is to mix some of the existing proposals guided by the information provided by a global analysis of the source code. Keywords: Semantics of Negation, Global Analysis, Implementation of Negation. 1 Introduction Knowledge representation based applications are a natural area for logic programming. However, this kind of applications requires a more complete set of capabilities than those offered by conventional Prolog compilers. ...
Negationcomplete logic programs
 Computer Science Logic, selected papers from CSL ’92
, 1993
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Regular Search Spaces (I): Horn and Nor
, 1993
"... The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or other reproductions of copyrighted material. Any copying of this document without permission of its author may be prohibited by law. ..."
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The copyright law of the United States (title 17, U.S. Code) governs the making of photocopies or other reproductions of copyrighted material. Any copying of this document without permission of its author may be prohibited by law.
The Australian National University
"... We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allo ..."
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We specify the operational semantics and bisimulation relations for the finite πcalculus within a logic that contains the ∇ quantifier for encoding generic judgments and definitions for encoding fixed points. Since we restrict to the finite case, the ability of the logic to unfold fixed points allows this logic to be complete for both the inductive nature of operational semantics and the coinductive nature of bisimulation. The ∇ quantifier helps with the delicate issues surrounding the scope of variables within πcalculus expressions and their executions (proofs). We illustrate several merits of the logical specifications permitted by this logic: they are natural and declarative; they contain no sideconditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations arise from familar logic distinctions; the interplay between the three quantifiers (∀, ∃, and ∇) and their scopes can explain the differences between early and late bisimulation and between various modal operators based on bound input and output actions; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for onestep transitions, bisimulation, and satisfaction in modal logic. We also illustrate how one can encode
ProofTheoretic Notions for Software Maintenance
, 2000
"... In this report we give an outline how prooftheoretic notions can be useful for questions related to software maintenance. ..."
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In this report we give an outline how prooftheoretic notions can be useful for questions related to software maintenance.