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CLASSICALLY ARCHETYPAL RULES

Published online by Cambridge University Press:  15 May 2018

TOMASZ POŁACIK  and
LLOYD HUMBERSTONE
TOMASZ POŁACIK*
Affiliation:
Institute of Mathematics, University of Silesia
LLOYD HUMBERSTONE*
Affiliation:
Department of Philosophy, Monash University
*
*INSTITUTE OF MATHEMATICS UNIVERSITY OF SILESIA BANKOWA 14, 40-007 KATOWICE, POLAND E-mail: tomasz.polacik@us.edu.pl
†DEPARTMENT OF PHILOSOPHY MONASH UNIVERSITY MELBOURNE VICTORIA 3800, AUSTRALIA E-mail: lloyd.humberstone@monash.edu
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Abstract

A one-premiss rule is said to be archetypal for a consequence relation when not only is the conclusion of any application of the rule a consequence (according to that relation) of the premiss, but whenever one formula has another as a consequence, these formulas are respectively equivalent to a premiss and a conclusion of some application of the rule. We are concerned here with the consequence relation of classical propositional logic and with the task of extending the above notion of archetypality to rules with more than one premiss, and providing an informative characterization of the set of rules falling under the more general notion.

Keywords

03B2203B05inference rulesconsequence relationsarchetypal rules
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 2 , June 2018 , pp. 279 - 294
Copyright
Copyright © Association for Symbolic Logic 2018 

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