Journal ArticleDOI
Computer Solutions of Problems in Inverse Semigroups
João Araújo,William McCune +1 more
TLDR
In this paper, the authors used automated reasoning to solve a number of problems regarding the axiomatic definition of inverse semigroups and provided a single identity for groups in terms of two binary operations.Abstract:
In 1981, Tamura posed a number of problems regarding the axiomatic definition of inverse semigroups. The main goal of this article is to use automated reasoning to solve these problems. In the process, we find some new defining sets of identities for the class of inverse semigroups and provide a single identity for groups in terms of two binary operations.read more
Citations
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Journal ArticleDOI
A method for finding new sets of axioms for classes of semigroups
João Araújo,Janusz Konieczny +1 more
TL;DR: A general technique for finding sets of axioms for a given class of semigroups for groups of exponent n, bands, and semilattices is introduced.
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An elegant 3-basis for inverse semigroups
TL;DR: In this paper, it was shown that the binary operation and the unary operation coincide with the usual inversion on inverse semigroups, and that an algebra of type $ $ satisfying these three identities is an inverse semigroup.
Journal ArticleDOI
An elegant 3-basis for inverse semigroups
TL;DR: In this paper, it was shown that the binary operation and the unary operation of inversion coincide with the usual inversion on inverse semigroups, and that an algebra of type 〈2,1〉 satisfying these three identities is an inverse semigroup.
Journal ArticleDOI
Axioms for Unary Semigroups via Division Operations
João Araújo,Michael Kinyon +1 more
TL;DR: In this article, the authors provide characterizations for several classes of unary semigroups, including E-inversive, regular, completely regular, inverse, Clifford, etc., in terms of left and right division.
Journal ArticleDOI
Basis reduction for cryptogroups and orthogroups
Ana Casimiro,Eduardo Skapinakis +1 more
TL;DR: In this paper, the authors provide equivalent bases of identities for subvarieties of completely regular semigroups for the purpose of providing equivalent identities for classes of semigroup subgroups.
References
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Book
Fundamentals of semigroup theory
TL;DR: Inverse semigroups as discussed by the authors are a subclass of regular semigroup classes and can be seen as semigroup amalgamations of semigroup groups, which is a special case of regular semiigroups.
Journal ArticleDOI
Cylindric Algebras. Part II
Journal ArticleDOI
Solution of the Robbins Problem
TL;DR: This article shows that the three equations known as commutativity, association, and the Robbins equation are a basis for the variety oflean algebras and presents the proof and the search strategies that enabled the program EQP to find the proof.
Journal ArticleDOI
A set of five independent postulates for Boolean algebras, with application to logical constants
TL;DR: In this article, the class of Boolean algebrasf has been given by Schröder, Whttehead, § and Huntington, and a set of ten postulate sets for determining Boolean algebraic classes have been given.
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OTTER 3.3 Reference Manual
TL;DR: OTTER as mentioned in this paper is a theorem prover for first-order logic with equality that includes the inference rules binary resolution, hyperresolution, UR-resolution, and binary paramodulation.