HSP Type Theorems in the Category of Posets
نویسنده
چکیده
As a computer science application of our techniques we may take the action logic of [Pratt, 1990]. Action logic is a finitely based equational theory conservatively extending the equational theory of regular expressions. An action algebra (model of action logic) is implicitly partially ordered via a ≤ b just when a + b = b . However a + b plays no other essential role in action logic, and may be dropped provided we introduce the relation ≤ explicitly into the language. The equations defining the residuals a −→ b and a← b and for star a∗ may then be rephrased as inequalities. This then raises the sorts of foundational questions addressed in [the present] paper; indeed [the present] paper was in direct response to my having raised them myself.
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