Diamond formulas: a fragment of dynamic logic with recursively enumerable validity problem
Information and Control
Theoretical Computer Science
Total correctness in nonstandard logics of programs
Theoretical Computer Science
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 Science of Programming
First-Order Dynamic Logic
Dynamic Logic
Proving Termination Assertions in Dynamic Logics
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Inductive Completeness of Logics of Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
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Total correctness assertions (TCAs) have long been considered a natural formalization of successful program termination. However, research dating back to the 1980s suggests that validity of TCAs is a notion of limited interest; we corroborate this by proving compactness and Herbrand properties for the valid TCAs, defining in passing a new sound, complete, and syntax-directed deductive system for TCAs. It follows that proving TCAs whose truth depends on underlying inductive data-types is impossible in logics of programs that are sound for all structures, such as Dynamic Logic (DL) based on Segerberg-Pratt's PDL, even when augmented with powerful first-order theories like Peano Arithmetic. The Convergence Rule of [6] bypasses this difficulty, but is methodologically and conceptually problematic, in addition to being unsound for general validity. We propose instead to bind variables to inductive data via DL's box operator, leading to an alternative formalization of termination assertions, which we dub Inductive TCA (ITCA). We show that validity of ITCAs is directly reducible to validity of partial correctness assertions, confirming the foundational importance of the latter.