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Complexity of First Order ID-Logic

John Stewart Schlipf, Marc Denecker

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Abstract

First Order ID-Logic interprets general first order, nonmonotone, inductive definability by generalizing the wellfounded semantics for logic programs. We show that, for general (thus perhaps infinite) structures, inference in First Order ID-Logic is complete Π 1 2 over the natural numbers. We also prove a Skolem Theorem for the logic: every consistent formula of First Order ID-Logic has a countable model.

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What this paper is about

First Order ID-Logic interprets general first order, nonmonotone, inductive definability by generalizing the wellfounded semantics for logic programs. We show that, for general (thus perhaps infinite) structures, inference in First Order ID-Logic is complete Π 1 2 over the natural numbers. We also prove a Skolem Theorem for the logic: every consistent formula of First Order ID-Logic has a countable model.

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Available abstract

First Order ID-Logic interprets general first order, nonmonotone, inductive definability by generalizing the wellfounded semantics for logic programs. We show that, for general (thus perhaps infinite) structures, inference in First Order ID-Logic is complete Π 1 2 over the natural numbers. We also prove a Skolem Theorem for the logic: every consistent formula of First Order ID-Logic has a countable model.

Key concepts: Higher-order logic, Second-order logic, First-order logic, Countable set, Predicate logic, Many-valued logic, Dynamic logic (digital electronics), Multimodal logic

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