Propositional modal logic of programs
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Non-standard algorithmic and dynamic logic
Journal of Symbolic Computation
Propositional logics of programs: systems, models, and complexity
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Dynamic algebras and the nature of induction
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
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In this paper, we show that by dropping the restrictions on interpretations of arbitrary programs and requiring only that very natural deductive systems are sound, we get classes of semantics which give good representations of program behavior and are more well-suited for applications involving an axiomatic approach (for example program verification). In addition, by tying the restrictions on the behavior of arbitrary programs or specified axiom schema, we get both a powerful formal tool and properties more widely used specifications lack such as compactness and completeness. Completeness is a very desirable property. It is fairly straightforward to show given any reasonable deductive system D for a class of models A that Pr(D) @@@@ Th(A) . But given an application such as program verification, if it is not true that Th(A) @@@@ Pr(D) , we may be able to find correct programs which we cannot verify. In this paper we show that by using the “axiomatizability” of programming constructs, we can obtain a technique for showing completeness results for some of the more widely used variations of PDL. We begin with some definitions.