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SOLOVAY-TYPE THEOREMS FOR CIRCULAR DEFINITIONS

Published online by Cambridge University Press:  03 February 2015

SHAWN STANDEFER*
Affiliation:
Department of Philosophy, University of Pittsburgh
*
*DEPARTMENT OF PHILOSOPHY 1001 CATHEDRAL OF LEARNING UNIVERSITY OF PITTSBURGH PITTSBURGH, PA 15260 USA E-mail: standefer@gmail.com

Abstract

We present an extension of the basic revision theory of circular definitions with a unary operator, □. We present a Fitch-style proof system that is sound and complete with respect to the extended semantics. The logic of the box gives rise to a simple modal logic, and we relate provability in the extended proof system to this modal logic via a completeness theorem, using interpretations over circular definitions, analogous to Solovay’s completeness theorem for GL using arithmetical interpretations. We adapt our proof to a special class of circular definitions as well as to the first-order case.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2014 

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