Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-25T03:46:21.414Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

de Jongh, D., & Chagrova, L. A. (1995). The decidability of dependency in intuitionistic propositional logic. Journal of Symbolic Logic, 60, 498–504.CrossRefGoogle Scholar
Humberstone, L. (1997). Two types of circularity. Philosophy and Phenomenological Research, 57, 249–280.CrossRefGoogle Scholar
Humberstone, L. (2004). Archetypal forms of inference. Synthese, 141, 45–76.CrossRefGoogle Scholar
Humberstone, L. (2010). Smiley’s distinction between rules of inference and rules of proof. In Lear, J. and Oliver, A., editors. The Force of Argument: Essays in Honor of Timothy Smiley. New York: Routledge, pp. 107–126.Google Scholar
Humberstone, L. (2011). The Connectives. Cambridge, MA: MIT Press.Google Scholar
Humberstone, L. (2013). Logical relations. Philosophical Perspectives, 27, 176–230.CrossRefGoogle Scholar
Humberstone, L. (2016). Philosophical Applications of Modal Logic. London: College Publications.Google Scholar
Łoś, J. & Suszko, R. (1958). Remarks on sentential logics. Indagationes Mathematicae, 20, 177–183.CrossRefGoogle Scholar
Mendelson, E. (2015). Introduction to Mathematical Logic (sixth edition). Boca Raton, FL: CRC Press (Taylor and Francis). (First edition, Van Nostrand, NY, 1964.)Google Scholar
Połacik, T. (2005). The unique intermediate logic whose every rule is archetypal. Logic Journal of the IGPL, 13, 269–275.CrossRefGoogle Scholar
Połacik, T. (2012). Archetypal rules and intermediate logics. In Peliš, M. and Punčochář, V., editors. The Logica Yearbook 2011. London: College Publications, pp. 227–237.Google Scholar
Rautenberg, W. (1985). Consequence relations of 2-element algebras. In Dorn, G. and Weingartner, P., editors. Foundations of Logic and Linguistics: Problems and their Solutions. New York: Plenum Press, pp. 3–23.CrossRefGoogle Scholar
Segerberg, K. (1982). Classical Propositional Operators. Oxford: Oxford University Press.Google Scholar