Kozen and Tiuryn have introduced the substructural logic S for reasoning about correctness of while programs (ACM TOCL, 2003). The logic S distinguishes between tests and partial correctness assertions, representing the latter by special implicational formulas. Kozen and Tiuryn’s logic extends Kleene altebra with tests, where partial correctness assertions are represented by equations, not terms. Kleene algebra with codomain, KAC, is a one-sorted alternative to Kleene algebra with tests that expands Kleene algebra with an operator that allows to construct a Boolean subalgebra of tests. In this paper we show that Kozen and Tiuryn’s logic embeds into the equational theory of the expansion of KAC with residuals of Kleene algebra multiplication and the upper adjoint of the codomain operator.
CITATION STYLE
Sedlár, I., & Wannenburg, J. J. (2022). Embedding Kozen-Tiuryn Logic into Residuated One-Sorted Kleene Algebra with Tests. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 13468 LNCS, pp. 221–236). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-15298-6_14
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