http://hdl.handle.net/11089/35157 2026-04-06T17:53:18Z 2026-04-06T17:53:18Z Borzooei, Rajab Ali Rezaei, Gholam Reza Kologhani, Mona Aaly Jun, Young Bae http://hdl.handle.net/11089/35354 2021-05-06T01:12:57Z 2020-12-30T00:00:00Z

Soju Filters in Hoop Algebras Borzooei, Rajab Ali; Rezaei, Gholam Reza; Kologhani, Mona Aaly; Jun, Young Bae The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The extension property of an implicative soju filter is established.

2020-12-30T00:00:00Z Bandaru, Ravikumar Saeid, Arsham Borumand Jun, Young Bae http://hdl.handle.net/11089/35353 2021-05-06T01:12:55Z 2020-08-30T00:00:00Z

On GE-algebras Bandaru, Ravikumar; Saeid, Arsham Borumand; Jun, Young Bae Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.

2020-08-30T00:00:00Z Płaczek, Paweł http://hdl.handle.net/11089/35352 2021-05-06T01:12:57Z 2020-11-13T00:00:00Z

One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity Płaczek, Paweł Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek, we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTime complexity of the multiplicative fragment of NBL.

2020-11-13T00:00:00Z Tomova, Natalya http://hdl.handle.net/11089/35351 2021-05-06T01:12:56Z 2020-11-13T00:00:00Z

A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics Tomova, Natalya In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10-element upper semi-lattice with respect to the functional embeddinig one logic into another. The mechanism of variation of paraconsistency and paracompleteness properties in logics is demonstrated on the example of two four-element lattices included in the upper semi-lattice. Functional properties and sets of tautologies of corresponding literal-paraconsistent-paracomplete matrices are investigated. Among the considered matrices there are the matrix of Puga and da Costa's logic V and the matrix of paranormal logic P1I1, which is the part of a sequence of paranormal matrices proposed by V. Fernández.

2020-11-13T00:00:00Z