Conditional algebras

TL;DR

This paper introduces a new algebraic framework for modeling the logical 'if... then...' conditional, linking it to modal necessity, and develops duality and canonical extension theories for these algebras.

Contribution

It proposes a general algebraic structure for conditionals, extending Chellas's work, and establishes duality and canonical extension theories for these algebras.

Findings

Developed a variety of conditional algebras.

Established duality theory for the algebraic structures.

Created canonical extension theory for the proposed algebras.

Abstract

Drawing on the classic paper by Chellas "Basic conditional logic" (1975), we propose a general algebraic framework for studying a binary operation of conditional that models universal features of the "if..., then..." connective as strictly related to the unary modal necessity operator. To this end, we introduce a variety of conditional algebras, and we develop its duality and canonical extensions theory.