Axiomatization of non-associative generalisations of Hájek's BL and psBL

Journal of Applied Non-Classical Logics 30 (1):1-15 (2020)
  Copy   BIBTEX

Abstract

ABSTRACTIn this paper, we consider non-associative generalisations of Hájek's logics BL and psBL. As it was shown by Cignoli, Esteva, Godo, and Torrens, the former is the logic of continuous t-norms and their residua. Botur introduced logic naBL which is the logic of non-associative continuous t-norms and their residua. Thus, naBL can be viewed as a non-associative generalisation of BL. However, Botur has not presented axiomatization of naBL. We fill this gap by constructing an adequate Hilbert-style calculus for naBL. Although, as was shown by Flondor, Georgescu, and Iorgulescu, there are no non-commutative continuous t-norms, Hájek's psBL can be viewed as BL's non-commutative generalisation. We present the logic psnaBL of psnaBL-algebras which can be viewed as naBL's non-commutative generalisation as well as psBL's non-associative generalisation and BL's both non-commutative and non-associative generalisation.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

An equational axiomatization of associative Newman algebras.Bolesław Sobociński - 1972 - Notre Dame Journal of Formal Logic 13 (2):265-269.
A new axiomatization of the mixed associative Newman algebras.Bolesław Sobociński - 1978 - Notre Dame Journal of Formal Logic 19 (3):467-474.
Unavailability and associative loss in in RI and PI.John Ceraso & Ann Henderson - 1965 - Journal of Experimental Psychology 70 (3):300.
Hájek’s Faulty Discussion of Philosophical Heuristics.Danny Frederick - 2020 - In Against thec Philosophical Tide. Yeovil: Critias Publishing. pp. 191-193.
What conditional probability could not be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
Schemata and associative processes in pragmatics.Marco Mazzone - 2011 - Journal of Pragmatics 43 (8):2148-2159.
Particles Do Not Conspire.Arianne Shahvisi - 2019 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 50 (4):521-543.
Popper on Laws and Counterfactuals.Danilo Šuster - 2005 - Croatian Journal of Philosophy 5 (1):109-119.

Analytics

Added to PP
2019-12-19

Downloads
7 (#1,356,784)

6 months
5 (#629,136)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Yaroslav Petrukhin
Moscow State University

Citations of this work

No citations found.

Add more citations

References found in this work

Introduction to Logical Theory.Peter Frederick Strawson - 1952 - London, England: Routledge.
Introduction to Logical Theory.P. F. Strawson - 1954 - Philosophy 29 (108):78-80.
Mathematical logic.Stephen Cole Kleene - 1967 - Mineola, N.Y.: Dover Publications.
Introduction to Logical Theory.Arthur Smullyan - 1954 - Philosophical Review 63 (1):117.
Metamathematics of Fuzzy Logic.Petr Hájek - 1998 - Dordrecht, Boston and London: Kluwer Academic Publishers.

View all 9 references / Add more references