Abstract
A unified single proof is given which implies theorems in such diverse fields as continuous algebras of algebraic semantics, dynamic algebras of logics of programs and program verification methods for total correctness. The proof concerns ultraproducts and diagonalization.
Research partially supported by ADI contrat No. 83/695.
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References
ADJ. Initial algebra semantics and continuous algebras. J. ACM 24 (1977), 68–95.
H. Andréka, I. Németi, I. Sain, A complete logic for reasoning about programs via nonstandard model theory. Theoretical Computer Science 17 (1982) 193–212, 259–278.
B. Courcelle, I. Guessarian, On some classes of interpretations, JCSS 17 (1978), 388–413.
I. Guessarian, Algebraic semantics, LNCS 99 Springer Verlag, Berlin (1981).
L. Henkin, D. Monk, A. Tarski, H. Andréka, I. Néméti, Cylindric set algebras, LN Maths 883, Springer Verlag, Berlin (1981).
B. Jonsson, The theory of binary relations, Proc. Séminaire de Mathématiques supérieures de l'Université de Montréal (1984).
D.J. Kfoury, D.M. Park, On the termination of program schemas. Information and Control 29 (1975), 243–251.
D. Kozen, On induction vs. *-continuity. In: Logics of Programs (Proc. New York 1981) Lecture Notes in Computer Science 131, Springer Verlag 1982, 167–176.
I. Németi, Dynamic algebras of programs FCT 81, LNCS 117 Springer Verlag, Berlin (1981), 281–290.
I. Németi. Every free algebra in the variety generated by separable dynamic algebras is separable and representable, TCS 17 (1982), 343–347.
I. Németi, Nonstandard dynamic logic. In: Logics of Programs (Proc. New York 1981) Lecture Notes in Computer Science 131, Springer-Verlag 1982, 311–348.
M. Nivat, On the interpretation of recursive polyadic program schemes Symp. Mathematica 15, Rome (1975), 255–281.
G. Plotkin, A power domain construction. SIAM J. Comp. 5 (1976), 452–487.
V. R. Pratt, Dynamic Logic. In: Logic, Methodology and Philosophy of Science VI. (Proc. Hannover 1979) Studies in Logic and the foundations of math. Vol. 104, North Holland (1982), 251–261.
J. Relterman, V. Trnkova, From dynamic algebras to test algebras. Preprint, Charles University Prague, (1984).
I. Sain, On the applicability of a category-theoretic notion of ultraproducts (in Hungarian). Matematikai lapok 31, No 1, 3 (1983).
I. Sain, Bui Huy Hien, Category theoretic notions of ultraproducts, Studia Math. Sci. Hungar., to appear.
D. Scott, Data types as lattices, SIAM J. Comput. 5 (1976), 522–587.
M. Smyth, Powerdomains, J. CCS 15 (1978), 23–36.
K.C. Ng, A. Tarski, Relation algebras with transitive closure. Notices Amer. Math. Soc., vol. 24 (1977), p. A-29.
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Andreka, H., Guessarian, I., Németi, I. (1985). A unifying theorem for algebraic semantics and dynamic logics. In: Budach, L. (eds) Fundamentals of Computation Theory. FCT 1985. Lecture Notes in Computer Science, vol 199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028786
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DOI: https://doi.org/10.1007/BFb0028786
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