Additive G\"{o}del Logic

TL;DR

This paper explores an extension of G"{o}del logic where the algebraic structure is an ordered Abelian group, and extends these ideas from propositional to first-order logic.

Contribution

It introduces a novel extension of G"{o}del logic based on ordered Abelian groups and generalizes the framework to first-order logic.

Findings

Defined the algebraic semantics using ordered Abelian groups

Extended propositional G"{o}del logic to first-order case

Provided foundational properties of the extended logic

Abstract

We study an extension of \g propositional logic whose corresponding algebra is an ordered Abelian group. Then we expand the ideas to first-order case of this logic.