https://scholars.lib.ntu.edu.tw/handle/123456789/587929
Title: | SOLOVAY-TYPE THEOREMS FOR CIRCULAR DEFINITIONS | Authors: | SHAWN MICHAEL STANDEFER | Issue Date: | 2015 | Journal Volume: | 8 | Journal Issue: | 3 | Source: | Review of Symbolic Logic | 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. |
URI: | https://scholars.lib.ntu.edu.tw/handle/123456789/587929 | ISSN: | 1755-0203 1755-0211 |
DOI: | 10.1017/S1755020314000458 |
Appears in Collections: | 哲學系 |
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