Proof Systems and Models for the First-Order Primal Logic

TL;DR

This paper explores the first-order primal infon logic, providing Gentzen-style calculi, semantics, and completeness proofs for two non-equivalent versions, advancing understanding of its foundational properties.

Contribution

It introduces two Gentzen-style calculi for the first-order primal infon logic and establishes their semantics, completeness, and disjunction property, which were previously unstudied.

Findings

Two non-equivalent Gentzen-style calculi are developed.

Completeness results are proven for both semantics.

Disjunction property is established for both logics.

Abstract

We study the first-order primal infon logic. It is the core of the policy language DKAL. We provide Gentzen-style calculi for two versions of this logic that are not equivalent. For both versions we investigate the semantics: one of them is a generalization of the so-called quasi-boolean semantics, the other one is a Krypke-style semantics. We prove the completeness results and the disjunction property for both logics.