Abstract
Using algebras over some signature to model the notion of state is quite common in specification languages. Some specification formalisms, e.g. COLD and Evolving Algebras, also allow for the dynamic change of states. Two kinds of elementary procedures are used: creation (of a new object) and modification (of a function or predicate at some point).
In this paper we present and investigate MLCM (Modal Logic of Creation and Modification), a multimodal predicate logic for reasoning over programs built up from such procedures. MLCM deviates from traditional dynamic predicate logic in two respects: creation is added as a primitive program construct and assignment (to variables) is replaced by assignment to constants and parametrized assignment to function and predicate symbols.
We present a definition of syntax, semantics and axiomatisation of MLCM and establish completeness for the repetition-free fragment via a traditional Henkin construction.
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References
E. Börger, A logical operational semantics for full prolog, In: Proceedings CSL ‘89, E. Börger, H. Kleine Büning and M.M. Richter (Eds.), LNCS 440, Springer Verlag, 1990, pp. 36–64.
E. Börger and D. Rosenzweig, The WAM — definition and Compiler Correctness, Technical Report TR - 14/92, Department of Computer Science, University of Pisa, 1992.
C.C. Chang and H.J. Keisler, Model Theory, North Holland, Second revised editon, 1990.
E.W. Dijkstra and C.S. Scholten, Predicate Calculus and Program Semantics, Springer Verlag, 1990.
L.M.G. Feijs and H.B.M. Jonkers, Formal Specification and Design, Cambridge Tracts in Theoretical Computer Science 35, 1992.
L.M.G. Feijs, H.B.M. Jonkers, C.P.J. Koymansar G.h. Renardel de Lavalette, Formal definition of the design language COLD-K (Preliminary version), ESPRIT document METEOR/t7/PRLE/7, April 1987 ( Final version: August 1989 ).
R. Goldblatt, Axiomatising the logic of computer science, LNCS 130, Springer Verlag, 1982.
Y. Gurevich, Logic and the challenge of computer science, In: Trends in Theoretical computer science, E. Börger (ed.), Computer Science Press, 1988, pp. 1–57.
Y. Gurevich, Evolving algebras; a tutorial introduction, Bulletin of the EATCS 43, Febr. 1991, pp. 264–284
Y. Gurevich and L. Moss, Algebraic operational semantics and Occam, In: Peoceedings CSL ‘89, E. Börger, H. Kleine Büning and M.M. Richter (Eds.), LNCS 440, Springer Verlag, 1990, pp. 176–192.
J.V. Guttag and J.J. Horning, The algebraic specification of abstract data types, Acta Informatica 10, 1978, pp. 27–52.
D. Harel, Dynamic Logic, In: Handbook of Philosophical Logic, Vol. II, D. Gabbay and F. Guenthner (eds.), D. Reidel Publishing Company, 1984, pp. 497–604.
M. Heisel, W. Reif and W. Stephan, A dynamic logic for program verfication, In: Logic at Botik 89,A. Meyer, M. Taitslin (eds), LNCS 363, Springer Verlag, pp. 134–145.
M. Heisel, W. Reif and W. Stephan, Tactical Theorem Proving in Program Verification, In: Conference on Automated Deduction, Siekmann (ed), LNAI, Spinger Verlag, 1990.
L. Henkin, The completeness of the first order functional calculus, The Journal of Symbolic Logic 14, 1949, pp. 159–166.
C.P.J. Koymans and G.R. Renardel de Lavalette, The logic MPLW, In: Algebraic Methods: Theory, tools and applications, M. Wirsing and J.A. Bergstra (eds.), LNCS 394, Springer Verlag, 1989, pp. 247–282.
V.R. Pratt, Semantical considerations on Floyd-Hoare logic, Proc. 17th annual IEEE symp. on foundations of computer science, 1976, pp. 109–121.
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© 1994 British Computer Society
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Groenboom, R., Renardel de Lavalette, G.R. (1994). Reasoning about Dynamic Features in Specification Languages. In: Andrews, D.J., Groote, J.F., Middelburg, C.A. (eds) Semantics of Specification Languages (SoSL). Workshops in Computing. Springer, London. https://doi.org/10.1007/978-1-4471-3229-5_19
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DOI: https://doi.org/10.1007/978-1-4471-3229-5_19
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