Diamond formulas: a fragment of dynamic logic with recursively enumerable validity problem
Information and Control
Logical and mathematical reasoning about imperative programs: preliminary report
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Axiomatic Definitions of Programming Languages: A Theoretical Assessment
Journal of the ACM (JACM)
The underlying logic of hoare logic
Current trends in theoretical computer science
Dynamic Logic
Matching Explicit and Modal Reasoning about Programs: A Proof Theoretic Delineation of Dynamic Logic
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
Reasoning in dynamic logic about program termination
Pillars of computer science
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We propose a new approach to delineating logics of programs, based directly on inductive definition of program semantics. The ingredients are elementary and well-known, but their fusion yields a simple yet powerful approach, surprisingly overlooked for decades. The denotational semantics of a regular program can be construed as a relation, easily definable by structural induction on programs. Invoking the framework of canonical theories for (iterated) inductive definitions, we consider the first-order theory for program semantic, i.e. with the generative clauses as construction (introduction) rules, and their dual templates as deconstruction (elimination) rules. We prove that Hoare's logic is inductively complete, in the sense that a partial-correctness assertion is Hoare provable iff it is provable in the inductive theory (with deconstruction for formulas in the base vocabulary). Thus first-order automated theorem-proving can be applied directly to program verification. Proceeding to program termination, we show that a total correctness assertion is valid iff it is provable in the inductive theory without any use of deconstruction. This is yet another take on the first-order nature of total correctness.