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PRIORITY MERGE AND INTERSECTION MODALITIES

Part of: Mathematical economics Philosophical aspects of logic and foundations General logic

Published online by Cambridge University Press:  22 February 2021

ZOÉ CHRISTOFF ,
NORBERT GRATZL  and
OLIVIER ROY
ZOÉ CHRISTOFF
Affiliation:
DEPARTMENT OF ARTIFICIAL INTELLIGENCE UNIVERSITY OF GRONINGEN GRONINGEN, NETHERLANDSE-mail: z.l.christoff@rug.nl
NORBERT GRATZL
Affiliation:
MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHENMÜNCHEN, GERMANYE-mail: norbert.gratzl@lrz.uni-muenchen.de
OLIVIER ROY
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BAYREUTH BAYREUTH, GERMANYE-mail: olivier.roy@uni-bayreuth.de
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Abstract

We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for priority merge for which we also provide a complete set of reduction axioms.

Keywords

epistemic logicgroup knowledgepriority mergelogic of beliefsdynamic epistemic logic

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03B42: Logics of knowledge and belief (including belief change) 03B45: Modal logic (including the logic of norms) 03B70: Logic in computer science 91B14: Social choice
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 1 , March 2022 , pp. 165 - 196
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Copyright
© Association for Symbolic Logic, 2021

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