Logic, Computational Complexity and Rule Based Systems

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This project concerns three areas of research that deal with particular kinds of rule based systems: (1) logic programming, (2) stratification and knowledge base management, and (3) Petri nets and vector addition systems. In area (1) several problems are being investigated that deal with the analysis of fundamental algorithms of unification & generalization and semantic & recursion theoretic issues for Prolog and extensions such as Constraint Logic Programming. In area (2), the PI is seeking applications of the notion of stratification to rule based systems whose semantics are those of propositional logic. Intended Model Semantics, querying and related issues are also under study. In area (3), the PI is making proof-theoretic analyses of algorithms for Petri nets and possible extensions. The problems proposed are important ones for which solutions are needed to make logic programming sound and more generally applicable. Results that will have practical impact are anticipated.