Filters and congruences in sectionally pseudocomplemented lattices and posets
| Autor: | Chajda, Ivan, Länger, Helmut |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Deductive system
0209 industrial biotechnology Pure mathematics Partial term Sectionally pseudocomplemented lattice 02 engineering and technology Theoretical Computer Science 020901 industrial engineering & automation Congruence permutability Congruence (geometry) Maltsev term FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Ideal (order theory) Filter (mathematics) Algebraic number Mathematics Congruence class Filter Weak regularity Closedness of a subset Mathematics - Logic Congruence relation Congruence Sectionally pseudocomplemented poset Algebraic semantics 06A11 06D15 06D20 08B05 08A30 020201 artificial intelligence & image processing Geometry and Topology Logic (math.LO) Software Foundations Ideal term |
| Zdroj: | Soft Computing |
| Popis: | Together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that—similar to relatively pseudocomplemented lattices—these structures can serve as an algebraic semantics of certain intuitionistic logics. The aim of the present paper is to define congruences and filters in these structures, derive mutual relationships between them and describe basic properties of congruences in strongly sectionally pseudocomplemented posets. For the description of filters in both sectionally pseudocomplemented lattices and posets, we use the tools introduced by A. Ursini, i.e., ideal terms and the closedness with respect to them. It seems to be of some interest that a similar machinery can be applied also for strongly sectionally pseudocomplemented posets in spite of the fact that the corresponding ideal terms are not everywhere defined. |
| Databáze: | OpenAIRE |
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