Abstract
A model-intersection problem (MI problem) is a pair of a set of clauses and an exit mapping. We define MI problems on specialization systems, which include many useful classes of logical problems, such as proof problems on first-order logic and query-answering (QA) problems in pure Prolog and deductive databases. The theory presented in this paper makes clear the central and fundamental structure of representation and computation for many classes of logical problems by (i) axiomatization and (ii) equivalent transformation. Clauses in this theory are constructed based on abstract atoms and abstract operation on them, which can be used for representation of many specific subclasses of problems with concrete syntax. Various computation can be realized by repeated application of many equivalent transformation rules, allowing many possible computation procedures, for instance, computation procedures based on resolution and unfolding. This theory can also be useful for inventing solutions for new classes of logical problems.
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