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2000•ACM Transactions on Computational LogicRequires access

On Hoare logic and Kleene algebra with tests

Dexter Kozen

Open publisher page 151 citations

Abstract

We show that Kleene algebra with tests (KAT) subsumes propositional Hoare logic (PHL). Thus the specialized syntax and deductive apparatus of Hoare logic are inessential and can be replaced by simple equational reasoning. In addition, we show that all relationally valid inference rules are derivable in KAT and that deciding the relational validity of such rules is PSPACE -complete.

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What this paper is about

We show that Kleene algebra with tests (KAT) subsumes propositional Hoare logic (PHL). Thus the specialized syntax and deductive apparatus of Hoare logic are inessential and can be replaced by simple equational reasoning. In addition, we show that all relationally valid inference rules are derivable in KAT and that deciding the relational validity of such rules is PSPACE -complete.

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OpenAlex reports 151 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We show that Kleene algebra with tests (KAT) subsumes propositional Hoare logic (PHL). Thus the specialized syntax and deductive apparatus of Hoare logic are inessential and can be replaced by simple equational reasoning. In addition, we show that all relationally valid inference rules are derivable in KAT and that deciding the relational validity of such rules is PSPACE -complete.

Key concepts: Kleene algebra, Hoare logic, Kleene's recursion theorem, Axiomatic semantics, Programming language, Algebra over a field, Mathematics, Equational logic

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