2020/07/26 by Ivan Chajda, Chajda, Ivan, Helmut Länger +1
Computer Science · #06A11 #06D15 #06D20 #08A30 #08B05 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2007.13198
openalex publication_date 2020/07/26 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
In our previous papers, together with J. Paseka we introduced so-called\nsectionally pseudocomplemented lattices and posets and illuminated their role\nin algebraic constructions. We believe that - similar to relatively\npseudocomplemented lattices - these structures can serve as an algebraic\nsemantics of certain intuitionistic logics. The aim of the present paper is to\ndefine congruences and filters in these structures, derive mutual relationships\nbetween them and describe basic properties of congruences in strongly\nsectionally pseudocomplemented posets. For the description of filters both in\nsectionally pseudocomplemented lattices and posets, we use the tools introduced\nby A. Ursini, i.e. ideal terms and the closedness with respect to them. It\nseems to be of some interest that a similar machinery can be applied also for\nstrongly sectionally pseudocomplemented posets in spite of the fact that the\ncorresponding ideal terms are not everywhere defined.\n