ISSN:
1573-0670
Keywords:
hyperidentity
;
hyperbase
;
lattice
;
quasilattice
;
Otter
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract We define an identity ε to be hypersatisfied by a variety V if, whenever the operation symbols of V, are replaced by arbitrary terms (of appropriate arity) in the operations of V, the resulting identity is satisfied by V in the usual sense. Whenever the identity ε is hypersatisfied by a variety V, we shall say that ε is a V hyperidentity. For example, the identity x + x ⋅ y = x ⋅(x + y) is hypersatisfied by the variety L of all lattices. A proof of this consists of a case-by-case examination of { + , ⋅} {x, y, x ∨ y, x ∧ y}, the set of all binary lattice terms. In an earlier work, we exhibited a hyperbase Σ L for the set of all binary lattice (or, equivalently, quasilattice) hyperidentities of type 2, 2. In this paper we provide a greatly refined hyperbase Σ L . The proof that Σ L is a hyperbase was obtained by using the automated reasoning program Otter 3.0.4.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1006279127474
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