Acceptance, inference, and the multiple-conclusion sequent

Tor Sandqvist

pp. 913-924

in: Sten Lindström, Erik Palmgren, Dag Westerståhl (eds), The philosophy of logical consequence and inference, Synthese 187 (3), 2012.

Abstract

This paper offers an interpretation of multiple-conclusion sequents as a kind of meta-inference rule: just as single-conclusion sequents represent inferences from sentences to sentences, so multiple-conclusion sequents represent a certain kind of inference from single-conclusion sequents to single-conclusion sequents. The semantics renders sound and complete the standard structural rules of reflexivity, monotonicity (or thinning), and transitivity (or cut). The paper is not the first one to attempt to account for multiple-conclusion sequents without invoking notions of truth or falsity—but unlike earlier such efforts, which have typically helped themselves to primitive notions of both acceptance and rejection, the present one makes do with the former alone. For technical reasons, the treatment is limited to sequents with non-empty succedents.