Consequence as preservation: Some refinements

Abstract

Preservationism generalises the idea of consequence beyond the standard focus on ‘preservation of truth’ or, syntactically, preservation of consistency. Instead, we preservationists suggest that other properties of premise sets can also worthy of preservation by a consequence relation. This paper presents a broader view of the properties that consequence relations can preserve, focusing on symmetrical treatments of consequence relations in multiple-conclusion logics that preserve variations on proof-theoretic consistent deniability from right to left as well as consistent assertability from left to right. The paper closes with remarks on another approach to producing preservationist logics, viz. the preservation of a ‘base’ consequence relation across a range of images of premise and conclusion sets, rather than preservation of properties of premise and conclusion sets. Further formal definitions and results appear in two appendices.