On Hoare-McCarthy algebras

TL;DR

This paper explores an algebraic framework for propositional logic with side effects, utilizing Hoare's conditional and McCarthy's sequential evaluation to characterize valuation congruences.

Contribution

It introduces Hoare-McCarthy algebras as structures that characterize various valuation congruences in propositional logic with side effects.

Findings

Defines valuation congruences based on sequential evaluation

Introduces Hoare-McCarthy algebras as algebraic models

Characterizes logical structures with side effects

Abstract

We discuss an algebraic approach to propositional logic with side effects. To this end, we use Hoare's conditional [1985], which is a ternary connective comparable to if-then-else. Starting from McCarthy's notion of sequential evaluation [1963] we discuss a number of valuation congruences and we introduce Hoare-McCarthy algebras as the structures that characterize these congruences.