Modal-type orthomodular logic

TL;DR

This paper introduces a modal extension to orthomodular logic motivated by physics, developing a logical system with algebraic and Kripke-style semantics based on Baer *-semigroups.

Contribution

It presents a novel modal orthomodular logic with algebraic completeness and a new Kripke-style semantics grounded in Baer *-semigroups.

Findings

Algebraic completeness of the modal orthomodular logic

Development of a Kripke-style semantics based on Baer *-semigroups

Extension of orthomodular logic with a physically motivated modal operator

Abstract

In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripke-style semantic founded on Baer *-semigroups as in [20].