http://hdl.handle.net/11089/35157 Mon, 06 Apr 2026 15:49:18 GMT 2026-04-06T15:49:18Z https://dspace.uni.lodz.pl:443/bitstream/id/6abec3ec-d2b6-4ce6-bf88-893c9f3a4403/ http://hdl.handle.net/11089/35157 http://hdl.handle.net/11089/35354 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. Wed, 30 Dec 2020 00:00:00 GMT http://hdl.handle.net/11089/35354 2020-12-30T00:00:00Z http://hdl.handle.net/11089/35353 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. Sun, 30 Aug 2020 00:00:00 GMT http://hdl.handle.net/11089/35353 2020-08-30T00:00:00Z http://hdl.handle.net/11089/35352 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. Fri, 13 Nov 2020 00:00:00 GMT http://hdl.handle.net/11089/35352 2020-11-13T00:00:00Z http://hdl.handle.net/11089/35351 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. Fri, 13 Nov 2020 00:00:00 GMT http://hdl.handle.net/11089/35351 2020-11-13T00:00:00Z