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PROOF ANALYSIS FOR LEWIS COUNTERFACTUALS

Published online by Cambridge University Press:  01 December 2015

SARA NEGRI  and
GIORGIO SBARDOLINI
SARA NEGRI*
Affiliation:
Department of Philosophy University of Helsinki
GIORGIO SBARDOLINI*
Affiliation:
Department of Philosophy The Ohio State University
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF HELSINKI E-mail: [email protected]
†DEPARTMENT OF PHILOSOPHY THE OHIO STATE UNIVERSITY E-mail: [email protected]
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Abstract

A deductive system for Lewis counterfactuals is presented, based directly on the influential generalisation of relational semantics through ternary similarity relations introduced by Lewis. This deductive system builds on a method of enriching the syntax of sequent calculus by labels for possible worlds. The resulting labelled sequent calculus is shown to be equivalent to the axiomatic system VC of Lewis. It is further shown to have the structural properties that are needed for an analytic proof system that supports root-first proof search. Completeness of the calculus is proved in a direct way, such that for any given sequent either a formal derivation or a countermodel is provided; it is also shown how finite countermodels for unprovable sequents can be extracted from failed proof search, by which the completeness proof turns into a proof of decidability.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 9 , Issue 1 , March 2016 , pp. 44 - 75
Copyright
Copyright © Association for Symbolic Logic 2015 

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