On an Algebra of Lattice-Valued Logic

Journal of Symbolic Logic 70 (1):282 - 318 (2005)
  Copy   BIBTEX

Abstract

The purpose of this paper is to present an algebraic generalization of the traditional two-valued logic. This involves introducing a theory of automorphism algebras, which is an algebraic theory of many-valued logic having a complete lattice as the set of truth values. Two generalizations of the two-valued case will be considered, viz., the finite chain and the Boolean lattice. In the case of the Boolean lattice, on choosing a designated lattice value, this algebra has binary retracts that have the usual axiomatic theory of the propositional calculus as suitable theory. This suitability applies to the Boolean algebra of formalized token models [2] where the truth values are, for example, vocabularies. Finally, as the actual motivation for this paper, we indicate how the theory of formalized token models [2] is an example of a many-valued predicate calculus

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,466

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

Analytics

Added to PP
2010-08-24

Downloads
25 (#459,695)

6 months
1 (#417,143)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

Introduction to Mathematical Logic.John Corcoran - 1964 - Journal of Symbolic Logic 54 (2):618-619.
Many-Valued Logics.J. B. Rosser & A. R. Turquette - 1954 - British Journal for the Philosophy of Science 5 (17):80-83.
Lattice Theory.Garrett Birkhoff - 1940 - Journal of Symbolic Logic 5 (4):155-157.

Add more references