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arXiv · 1502.05632

Capturing k-ary Existential Second Order Logic with k-ary Inclusion-Exclusion Logic

Raine Rönnholm
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Abstract

In this paper we analyze k-ary inclusion-exclusion logic, INEX[k], which is obtained by extending first order logic with k-ary inclusion and exclusion atoms. We show that every formula of INEX[k] can be expressed with a formula of k-ary existential second order logic, ESO[k]. Conversely, every formula of ESO[k] with at most k-ary free relation variables can be expressed with a formula of INEX[k]. From this it follows that, on the level of sentences, INEX[k] captures the expressive power of ESO[k]. We also introduce several useful operators that can be expressed in INEX[k]. In particular, we define inclusion and exclusion quantifiers and so-called term value preserving disjunction which is essential for the proofs of the main results in this paper. Furthermore, we present a novel method of relativization for team semantics and analyze the duality of inclusion and exclusion atoms.

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Raine Rönnholm. 2015-02-19. Capturing k-ary Existential Second Order Logic with k-ary Inclusion-Exclusion Logic. https://arxiv.org/abs/1502.05632

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