Wo propose a new framework for the .syntax and semantics of logic programming, based on programming over finite, product cate-gories which incorporate constraint information directly into the notion of signature. In this framework, we generalize the Kowalski-van Emden fixed point interpretation, a cornerstone of the declarative paradigm, to an opera-tional, non-ground, categorical semantics for generalized languages baaed on uniform proof systems. Our treatment forniH the basis of a semantics-based definition of declar-ative programming.
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