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Fall 1998 Uncompactness of Stit Logics Containing Generalized Refref Conditionals
Ming Xu
Notre Dame J. Formal Logic 39(4): 485-506 (Fall 1998). DOI: 10.1305/ndjfl/1039118864

Abstract

In this paper we prove the uncompactness of every stit logic that contains a generalized refref conditional and is a sublogic of the stit logic with refref equivalence, a syntactical condition of uncompactness that covers infinitely many stit logics. This result is established through the uncompactness of every stit logic whose semantic structures contain no chain of busy choice sequences with cardinality $n$, where $n$ is any natural number $ > 0$. The basic idea in the proof is to apply the notion of companions to stit sentences in finding busy choice sequences in structures, and to make use of a relation between chains of busy choice sequences and generalized refref conditionals in connecting the two conditions of uncompactness mentioned above.

Citation

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Ming Xu. "Uncompactness of Stit Logics Containing Generalized Refref Conditionals." Notre Dame J. Formal Logic 39 (4) 485 - 506, Fall 1998. https://doi.org/10.1305/ndjfl/1039118864

Information

Published: Fall 1998
First available in Project Euclid: 5 December 2002

zbMATH: 0966.03021
MathSciNet: MR1776221
Digital Object Identifier: 10.1305/ndjfl/1039118864

Subjects:
Primary: 03B45

Rights: Copyright © 1998 University of Notre Dame

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Vol.39 • No. 4 • Fall 1998
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