Algebraically closed theories
The present work takes place in the study of infinitary behaviours for CCS-like communicating processes. A problem in that area arises from the fact that most of the abstraction morphisms we are interested in don't commute with least fixed points. In order to offer an alternative to least fixed point semantics we present an axiomatization of the notion of fixed point calculus within the formalism of algebraic theories. Such a calculus fixes one solution for each equation resulting from the interpretation of a set of recursive definitions in a way consistent with the free interpretation of the equations. This leads us to the notion of algebraically closed theory which stands for an algebraic theory equipped with a fixed point calculus. The rational theories by ADJ appear to be a special case of algebraically closed theories when least solutions are always chosen.
KeywordsOperator Symbol Rational Expression Rational Theory Algebraic Theory Recursive Definition
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