Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E
Bulletin of the Section of Logic (2019)
- Volume: 48, Issue: 1
- ISSN: 0138-0680
Access Full Article
top
Abstract
topHow to cite
topLidia Typańska-Czajka. "Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E." Bulletin of the Section of Logic 48.1 (2019): null. <http://eudml.org/doc/295540>.
@article{LidiaTypańska2019,
abstract = {The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].},
author = {Lidia Typańska-Czajka},
journal = {Bulletin of the Section of Logic},
keywords = {relevant logic; non-classical logics; lattice; universal algebra},
language = {eng},
number = {1},
pages = {null},
title = {Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E},
url = {http://eudml.org/doc/295540},
volume = {48},
year = {2019},
}
TY - JOUR
AU - Lidia Typańska-Czajka
TI - Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E
JO - Bulletin of the Section of Logic
PY - 2019
VL - 48
IS - 1
SP - null
AB - The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite sequences of premaximal extensions of the logic E. Note that for the relevant logic R there exist exactly three pre-maximal logics, i.e. coatoms in the interval [R,CL].
LA - eng
KW - relevant logic; non-classical logics; lattice; universal algebra
UR - http://eudml.org/doc/295540
ER -
References
top- W. Ackermann, Begründung Einer Strengen Implikation, The Journal of Symbolic Logic, Vol. 21, 2 (1956), pp. 113–128.
- A. R. Anderson, N. D. Belnap, Jr., Entailment. The Logic of relevance and necessity, Princeton University Press, Vol. I (1975).
- N. D. Belnap, Jr., Intesional Models for First Degree Formula, The Journal of Symbolic Logic, Vol. 32, 1 (1967), pp. 1–22.
- W. J. Blok, D. Pigozzi, Algbebraizable logics, Memoirs of the American Mathematical Society, 1989.
- J. M. Font, G. B. Rodriguez, Note on algebraic models for relevance logic, Zeitschrift für Matematische Logik und Grundlagen der Mathematik, Vol. 36, 6 (1990), pp. 535–540.
- W. Dziobiak, There are 2ℵ0 Logics with the Relevance Principle Between R and RM, Studia Logica, Vol. XLII (1983), pp. 49–61.
- L. Maksimowa, Implication lattices, Algebra and Logic, Vol. 12, 4 (1973), pp. 445–467.
- L. Maksimowa, O Modeljach iscislenija E, Algebra and Logic, Vol. 6, 6 (1967), pp. 5–20.
- R. M. Martin, Twenty-Third Annual Meeting of the Association for Symbolic Logic, The Journal of Symbolic Logic, Vol. 23, 4 (1958), pp. 456–461.
- R. K. Meyer, E and S4, Notre Dame Journal of Formal Logic, Vol. XI, 2 (1970), pp. 181–199.
- K. Świrydowicz, There exists exactly two maximal strictly relevant extensions of the relevant logic R, The Journal of Symbolic Logic, Vol. 64, 3 (1999), pp. 1125–1154.
- K. Świrydowicz, A Remark on the Maximal Extensions of the Relevant Logic R, Reports on Mathematical Logic, 29 (1995), pp. 19–33.
- M. Tokarz, Essays in matrix semantics of relevant logics, The Institute of Philosophy and Sociology of the Polish Academy of Sciences, Warsaw 1980.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.