## Journal of Symbolic Logic

- J. Symbolic Logic
- Volume 70, Issue 1 (2005), 282-318.

### On an algebra of lattice-valued logic

#### 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.

#### Article information

**Source**

J. Symbolic Logic Volume 70, Issue 1 (2005), 282-318.

**Dates**

First available in Project Euclid: 1 February 2005

**Permanent link to this document**

http://projecteuclid.org/euclid.jsl/1107298521

**Digital Object Identifier**

doi:10.2178/jsl/1107298521

**Mathematical Reviews number (MathSciNet)**

MR2119134

**Zentralblatt MATH identifier**

05004799

#### Citation

Hansen, Lars. On an algebra of lattice-valued logic. J. Symbolic Logic 70 (2005), no. 1, 282--318. doi:10.2178/jsl/1107298521. http://projecteuclid.org/euclid.jsl/1107298521.