Abstract
An extension of Hennessy-Milner Logic with recursion is presented. A recursively specified formula will have two standard interpretations: a minimal one and a maximal one. Minimal interpretations of formulas are useful for expressing liveness properties of processes, whereas maximal interpretations are useful for expressing safety properties. We present sound and complete proof systems for both interpretations for when a process satisfies a (possibly recursive) formula. The rules of the proof systems consist of an introduction rule for each possible structure of a formula and are intended to extend the work of Stirling and Winskel. Moreover the proof systems may be presented directly in PROLOG to yield a decision procedure for verifying when a finite-state process satisfies a specification given as a (possibly recursive) formula.
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Aczel, P.: An Introduction to Inductive Definitions, North-Holland, in the Handbook of Mathematical Logic, 1983.
Ben-Ari, M., Pnueli, A. and Manna, Z.: The Temporal Logic of Branching Time, Acta Informatica, 20, pp 207–226, 1983.
Bloom and Troeger: A Logical Characterization of Observation Equivalence, TCS, vol 35, no 1, 1985
Brookes, S. and Rounds, R.: Behavioural Equivalence Relations Induced by Programming Logics, LNCS 154, 1983.
Clarke, E.M. and Emerson, E.A.: Design and Synthesis of Synchronization Skeletons using Branching Time Temporal Logic, in: Logics of Programs, LNCS 131, 52–71, 1981.
Clarke, E.M., Emerson, E.A, Sistla, A.P.: Automatic Verification of Finite State Concurrent Systems Using Temporal Logic Specifications: A Practical Approach, Proc 10th ACM POPL, 117–126, 1983.
Graf, S. and Sifakis, J.: A modal Characterization of observational congruence on finite terms of CCS, LNCS 172, 1984.
Graf, S. and Sifakis, J.: A Logic for the Specification and Proof of Regular Controllable Processes of CCS, Acta Informatica, 23, pp 507–527, 1986.
Graf, S. Sifakis, J.: A Logic for the Description of Non-deterministic Programs and Their Properties, Information and Control, vol. 68, nos 1–3, 1986.
Hennessy, M. and Milner, R.: Algebraic Laws for Nondeterminism and Concurrency, Journal of the Association for Computing Machinery, 1985.
Kozen, D.: Results on the Propositional Mu-Calculus, 9th ICALP, LNCS 140, 1982.
Larsen, K.G.: Proof Systems for Hennessy-Milner Logic with Recursion, Aalborg University, Department of Mathematics and Computer Science, R 87-20, 1987.
Manna, Z. and Wolper, P. Synthesis of Communicating Processes from Temporal Logic Specifications, LNCS 131, 1981.
Milner, R.: A Calculus of Communicating Systems, LNCS 92, 1980.
Milner, R.: A Modal Characterization of Observable Machine-behaviour, LNCS 112, 1981.
Milner, R.: Calculi for Synchrony and Asynchrony, TCS 25, pp 267–310, 1983.
Park, D.: Concurrency and automata on infinite sequences, LNCS 84, 1980.
Plotkin, G.: A Structural Approach to Operational Semantics, DAIMI-FN-19, Aarhus University, Computer Science Department, Denmark, 1981.
Pnueli, A.: Linear and Branching Structures in the Semantics and Logics of Reactive Systems, 12th ICALP, LNCS 194, 1985.
Stirling, C.: A Proof Theoretic Characterization of Observationl Equivalence, FCT-TCS Bangalore, To appear in TCS, 1983.
Stirling, C.: A Complete Proof System for a Subset of SCCS, LNCS 185, to appear in CAAP'85, 1985.
Stirling, C.: A Compositional Modal Proof System for a Subset of CCS, 12th ICALP, LNCS 194, full version to appear in TCS., 1985.
Stirling, C.: Modal Logics for Communicating Systems, to appear in TCS., 1986.
Tarski, A.: A Lattice-Theoretical Fixpoint Theorem and its Applications, Pacific Journal of Math. 5, 1955.
Winskel, G.: On the Composition and Decomposition of Assertions, LNCS 197, 1984.
Winskel, G.: A Complete Proof System for SCCS with Modal Assertions, Technical Report, Computer Laboratory, University of Cambridge, 1985.
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© 1988 Springer-Verlag Berlin Heidelberg
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Larsen, K.G. (1988). Proof systems for Hennessy-Milner Logic with recursion. In: Dauchet, M., Nivat, M. (eds) CAAP '88. CAAP 1988. Lecture Notes in Computer Science, vol 299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0026106
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DOI: https://doi.org/10.1007/BFb0026106
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