Abstract

This dissertation examines the semantics of a new paradigm of logic programming called subset-logic programming. The most novel construct of a subset-logic program is the subset assertion, which in conjuction with the more conventional relational and equational assertions provide a declarative alternative to many common uses of Prolog's extra-logical features: cut, assert, retract, setof, and mode declarations. These three forms effectively allow to specify function and relation definitions involving (finite) sets as first-class data objects. Our study of the semantics of subset-logic languages begins by laying the logical foundations for these languages. Because of the need for new set constructors in representating finite sets, we first axiomatize their meaning through suitable axioms, and then use these axioms in a variety of ways: (i) to show that the set constructors indeed behave like finite sets; (ii) to provide a framework for establishing the correctness of set-unification; (...

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