Nontrivial definability by flow-chart programs
Information and Control
On relative completeness of Hoare logics
Information and Control - The MIT Press scientific computation series
The foundations of program verification (2nd ed.)
The foundations of program verification (2nd ed.)
Some relationships between logics of programs and complexity theory
Theoretical Computer Science
Reasoning about procedures as parameters in the language L4
Information and Computation
A New Incompleteness Result for Hoare's System
Journal of the ACM (JACM)
Effective Axiomatizations of Hoare Logics
Journal of the ACM (JACM)
Ten Years of Hoare's Logic: A Survey—Part I
ACM Transactions on Programming Languages and Systems (TOPLAS)
First-Order Dynamic Logic
Hoare Calculi for Higher-Type Control Structures and Their Completeness in the Sense of Cook
MFCS '88 Proceedings of the Mathematical Foundations of Computer Science 1988
Correstness of Programs over Poor Signatures
Proceedings of the 11th Conference on Foundations of Software Technology and Theoretical Computer Science
A necessary and sufficient condition for the existence of hoare logics
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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The notion of an expressive interpretation was originally introduced by Cook in order to formulate completeness results for Hoare-style proof systems. An interpretation is called expressive for a programming language if the input/output relation of every program can be expressed by a first-order formula. Various necessary or sufficient conditions for an interpretation to be expressive are known. In this paper a characterization is given which improves on these results. It holds for a wide spectrum of programming languages. An interpretation is expressive iff it is either 1. uniformly locally finite or 2. weakly arithmetic and it has evaluation predicates (which return the truth value of a boolean expression, given its gödel number and the values of its free variables). Besides this characterization, it is investigated which first-order signatures allow nontrivial (i.e. non uniformly locally finite) expressive interpretations. Signatures which have (besides constants) only one unary function symbol and only unary relation symbols, have only trivial expressive interpretations. All other signatures allow nontrivial expressive interpretations as well.