<abstract xmlns="http://www.w3.org/1999/xhtml">
<p><bold>Summary</bold>. The main aim of this article is to introduce formally two generalizations of lattices, namely weakly associative lattices and near lattices, which can be obtained from the former by certain weakening of the usual well-known axioms. We show selected propositions devoted to weakly associative lattices and near lattices from Chapter 6 of [15], dealing also with alternative versions of classical axiomatizations. Some of the results were proven in the Mizar [1], [2] system with the help of Prover9 [14] proof assistant.</p>
</abstract>

Summary. The main aim of this article is to introduce formally two generalizations of lattices, namely weakly associative lattices and near lattices, which can be obtained from the former by certain weakening of the usual well-known axioms. We show selected propositions devoted to weakly associative lattices and near lattices from Chapter 6 of [15], dealing also with alternative versions of classical axiomatizations. Some of the results were proven in the Mizar [1], [2] system with the help of Prover9 [14] proof assistant.

On Weakly Associative Lattices and Near Lattices

Formalized Mathematics

{"article-title":"On Weakly Associative Lattices and Near Lattices"}

Summary. The main aim of this article is to introduce formally two generalizations of lattices, namely weakly associative lattices and near lattices, which can...

On Weakly Associative Lattices and Near Lattices

Article Category: Artikel

Published Online: Dec 30, 2021

Page range: 77 - 85

Accepted: Jun 30, 2021

DOI: https://doi.org/10.2478/forma-2021-0008

Keywords
weakly associative lattice, near lattice

© 2021 University of Białystok, published by Sciendo

CC-BY-SA License ver. 3.0 or later

On Weakly Associative Lattices and Near Lattices

Article Category: Artikel

Published Online: Dec 30, 2021

Page range: 77 - 85

Accepted: Jun 30, 2021

DOI: https://doi.org/10.2478/forma-2021-0008

Keywordsweakly associative lattice, near lattice

© 2021 University of Białystok, published by Sciendo

CC-BY-SA License ver. 3.0 or later

Keywords
weakly associative lattice, near lattice