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The p-semisimple property for some generalizations of BCI algebras and its applications

100%

Obojska L., Walendziak A.

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

2020

tom 19

79-94

This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra.

A comparison of two systems of point-free topology

63%

Gruszczyński R., Pietruszczak A.

Bulletin of the Section of Logic

2018

tom 47

nr 3

This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide (in the sense that their axioms are satisfied in the same class of structures) in presence of axiom stipulating non-existence of atoms.

Ograniczanie wyników

1 Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

1 Bulletin of the Section of Logic

1 Gruszczyński R.

1 Obojska L.

1 Pietruszczak A.

1 Walendziak A.

1 2020

1 2018

Wyniki wyszukiwania

The p-semisimple property for some generalizations of BCI algebras and its applications

A comparison of two systems of point-free topology