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Kripke Semantics for Intersection Formulas

Kripke Semantics for Intersection Formulas We propose a notion of the Kripke-style model for intersection logic. Using a game interpretation, we prove soundness and completeness of the proposed semantics. In other words, a formula is provable (a type is inhabited) if and only if it is forced in every model. As a by-product, we obtain another proof of normalization for the Barendregt–Coppo–Dezani intersection type assignment system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Kripke Semantics for Intersection Formulas

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2021 Copyright held by the owner/author(s).
ISSN
1529-3785
eISSN
1557-945X
DOI
10.1145/3453481
Publisher site
See Article on Publisher Site

Abstract

We propose a notion of the Kripke-style model for intersection logic. Using a game interpretation, we prove soundness and completeness of the proposed semantics. In other words, a formula is provable (a type is inhabited) if and only if it is forced in every model. As a by-product, we obtain another proof of normalization for the Barendregt–Coppo–Dezani intersection type assignment system.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Jun 28, 2021

Keywords: Intersection types

References