A Complete Axiomatisation for the Logic of Lattice Effect Algebras

TL;DR

This paper provides a complete axiomatisation of the logic associated with lattice effect algebras, extending previous work on their logical connectives and semantic models.

Contribution

It introduces a comprehensive set of axioms for the logic of lattice effect algebras, advancing the theoretical understanding of their logical structure.

Findings

Established a complete axiomatisation for the logic of lattice effect algebras

Analyzed properties of lattice effect algebras relevant to logical calculus

Extended previous studies on logical connectives in effect algebras

Abstract

In a recent work Foulis and Pulmannov\' a \cite{Foulis2012} studied the logical connectives in lattice effect algebras. In this paper we extend their study and investigate further the logical calculus for which the lattice effect algebras can serve as semantic models. We shall first focus on some properties of lattice effect algebras and will then give a complete axiomatisation of this logic.