Abstract
Proposition algebra is based on Hoareās conditional connective, which is a ternary connective comparable to if-then-else and used in the setting of propositional logic. Conditional statements are provided with a simple semantics that is based on evaluation trees and that characterizes so-called free valuation congruence: two conditional statements are free valuation congruent if, and only if, they have equal evaluation trees. Free valuation congruence is axiomatized by the four basic equational axioms of proposition algebra that define the conditional connective. A valuation congruence that is axiomatized in proposition algebra and that identifies more conditional statements than free valuation congruence is repetition-proof valuation congruence, which we characterize by a simple transformation on evaluation trees.
Dedicated to Ernst-RĆ¼diger Olderog on the occasion of his sixtieth birthday. Jan Bergstra recalls many discussions during various meetings as well as joint work with Ernst-RĆ¼diger and Jan Willem Klop on readies, failures, and chaos back in 1987. Alban Ponse has pleasant memories of the process of publishingĀ [8], the Selected Papers from the Workshop on Assertional Methods, of which Ernst-RĆ¼diger, who was one of the invited speakers at this workshop (held at CWI in NovemberĀ 1992), is one of the guest editors. An extended version of this paper appeared as reportĀ [6].
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Bergstra, J.A., Ponse, A. (2015). Evaluation Trees for Proposition Algebra. In: Meyer, R., Platzer, A., Wehrheim, H. (eds) Correct System Design. Lecture Notes in Computer Science(), vol 9360. Springer, Cham. https://doi.org/10.1007/978-3-319-23506-6_6
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DOI: https://doi.org/10.1007/978-3-319-23506-6_6
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