In Katalin Bimbó (ed.), Relevance Logics and other Tools for Reasoning. Essays in Honor of J. Michael Dunn. London: College Publications. pp. 261-265 (2022)

Saul Kripke
CUNY Graduate Center
This paper is dedicated to the memory of Mike Dunn. His untimely death is a loss not only to logic, computer science, and philosophy, but to all of us who knew and loved him. The paper gives an argument for closure under γ in standard systems of relevance logic (first proved by Meyer and Dunn 1969). For definiteness, I chose the example of R. The proof also applies to E and to the quantified systems RQ and EQ. The argument uses semantic tableaux (with one exceptional rule not satisfying the subformula property). It avoids the previous arguments’ use of cutting down inconsistent sets of formulas to consistent sets. Like all tableau arguments, it extends partial valuations to total valuations.
Keywords Completeness  Partial valuation  Relevance logic  Rule γ  Semantic tableau
Categories (categorize this paper)
Buy the book Find it on
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 70,163
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Cut and Gamma I: Propositional and Constant Domain R.Yale Weiss - 2020 - Review of Symbolic Logic 13 (4):887-909.

Add more citations

Similar books and articles

Counterfactuals and Semantic Tableaux.Daniel Rönnedal - 2009 - Logic and Logical Philosophy 18 (1):71-91.
Partial Logic as a Logic of Extensional Alethic Modality.Daisuke Kachi - 2007 - Journal of the Japan Association for Philosophy of Science 34 (2):61-70.
Dyadic Deontic Logic and Semantic Tableaux.Daniel Rönnedal - 2009 - Logic and Logical Philosophy 18 (3-4):221-252.
Dynamic Tableaux for Dynamic Modal Logics.Jonas De Vuyst - 2013 - Dissertation, Vrije Universiteit Brussel
Partial and Paraconsistent Three-Valued Logics.Vincent Degauquier - 2016 - Logic and Logical Philosophy 25 (2):143-171.
Probabilistic Canonical Models for Partial Logics.François Lepage & Charles Morgan - 2003 - Notre Dame Journal of Formal Logic 44 (3):125-138.


Added to PP index

Total views
121 ( #96,648 of 2,506,844 )

Recent downloads (6 months)
121 ( #5,727 of 2,506,844 )

How can I increase my downloads?


My notes