FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 2, PAGES 627-632
M. R. Pentus
Abstract
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A residuated semigroup is a partially ordered semigroup
together with two binary operations
$ \backslash $ and $ / $ ,
such that
the assertions
$ a \leq c / b $ ,
$ a \cdot b \leq c $ ,
and
$ b \leq a \backslash c $
are equivalent.
We formulate a necessary and sufficient condition
for an arbitrary set of atomic formulas of the signature
$ \{ \leq , \cdot , \backslash , / \} $
to be the atomic theory of some residuated semigroup family.
We also consider some specific residuated semigroups and
residuated semigroup families.
All articles are published in Russian.
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Last modified: September 1, 2000