Bulletin of the Section of Logic 47/2 (2018)http://hdl.handle.net/11089/263472020-08-06T07:50:47Z2020-08-06T07:50:47ZGrzegorczyk Algebras RevisitedStronkowski, Michał M.http://hdl.handle.net/11089/264172019-03-21T02:17:48Z2018-01-01T00:00:00ZGrzegorczyk Algebras Revisited
Stronkowski, Michał M.
We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.
2018-01-01T00:00:00ZPseudo-BCH SemilatticesWalendziak, Andrzejhttp://hdl.handle.net/11089/264162019-03-21T02:17:46Z2018-01-01T00:00:00ZPseudo-BCH Semilattices
Walendziak, Andrzej
In this paper we study pseudo-BCH algebras which are semilattices or lattices with respect to the natural relations ≤; we call them pseudo-BCH join-semilattices, pseudo-BCH meet-semilattices and pseudo-BCH lattices, respectively. We prove that the class of all pseudo-BCH join-semilattices is a variety and show that it is weakly regular, arithmetical at 1, and congruence distributive. In addition, we obtain the systems of identities defininig pseudo-BCH meet-semilattices and pseudo-BCH lattices.
2018-01-01T00:00:00ZVariable Sharing in Substructural Logics: an Algebraic CharacterizationBadia, Guillermohttp://hdl.handle.net/11089/264152019-03-21T02:17:47Z2018-01-01T00:00:00ZVariable Sharing in Substructural Logics: an Algebraic Characterization
Badia, Guillermo
We characterize the non-trivial substructural logics having the variable sharing property as well as its strong version. To this end, we find the algebraic counterparts over varieties of these logical properties.
2018-01-01T00:00:00ZFree Modal Pseudocomplemented De Morgan AlgebrasFigallo, Aldo V.Oliva, NoraZiliani, Aliciahttp://hdl.handle.net/11089/264142019-03-21T02:17:45Z2018-01-01T00:00:00ZFree Modal Pseudocomplemented De Morgan Algebras
Figallo, Aldo V.; Oliva, Nora; Ziliani, Alicia
Modal pseudocomplemented De Morgan algebras (or mpM-algebras) were investigated in A. V. Figallo, N. Oliva, A. Ziliani, Modal pseudocomplemented De Morgan algebras, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 53, 1 (2014), pp. 65–79, and they constitute a proper subvariety of the variety of pseudocomplemented De Morgan algebras satisfying xΛ(∼x)* = (∼(xΛ(∼x)*))* studied by H. Sankappanavar in 1987. In this paper the study of these algebras is continued. More precisely, new characterizations of mpM-congruences are shown. In particular, one of them is determined by taking into account an implication operation which is defined on these algebras as weak implication. In addition, the finite mpM-algebras were considered and a factorization theorem of them is given. Finally, the structure of the free finitely generated mpM-algebras is obtained and a formula to compute its cardinal number in terms of the number of the free generators is established. For characterization of the finitely-generated free De Morgan algebras, free Boole-De Morgan algebras and free De Morgan quasilattices see: [16, 17, 18].
2018-01-01T00:00:00Z