http://hdl.handle.net/11089/54515 Mon, 06 Apr 2026 20:50:52 GMT 2026-04-06T20:50:52Z https://dspace.uni.lodz.pl:443/bitstream/id/09c071a1-7a5a-4f69-bdd3-7c0bc5afcc4d/ http://hdl.handle.net/11089/54515 http://hdl.handle.net/11089/54525 \(\mathcal{L}\)−weakly 1−Absorbing Prime Ideals and Filters Amare, Natnael Teshale In this manuscript, we have presented the concept of \(\mathcal{L}\)-weakly 1-absorbing prime ideals and \(\mathcal{L}\)-weakly 1-absorbing prime filters within an ADL. Mainly, we illustrate the connections between \(\mathcal{L}\)-weakly prime ideals (filters) and \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters), as well as between \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters) and \(\mathcal{L}\)-weakly 2-absorbing ideals (filters). Lastly, we have shown that both the image and inverse image of \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters) result in \(\mathcal{L}\)-weakly 1-absorbing prime ideals (filters). Thu, 14 Nov 2024 00:00:00 GMT http://hdl.handle.net/11089/54525 2024-11-14T00:00:00Z http://hdl.handle.net/11089/54526 Some Additional Axioms for T-normal Logics. Defining K45, KB4, KD45 and S5 without Using Modal Rules Pietruszczak, Andrzej The paper studies extensions of t-normal logics S0.5o and S0.5 obtained by means of some axioms of normal logics. We will prove determination theorems for these extensions by appropriate Kripke-style models. It will allow us to obtain the determinations of the logics K45, KB4 (= KB5), KD45 and S5 without using modal rules. Mon, 24 Jun 2024 00:00:00 GMT http://hdl.handle.net/11089/54526 2024-06-24T00:00:00Z http://hdl.handle.net/11089/54527 Hilbert Algebras with Hilbert-Galois Connections II Celani, Sergio A.; Montagie, Daniela Hilbert algebra with a Hilbert-Galois connection, or HilGC-algebra, is a triple \(\left(A,ƒ,g\right)\) where \(A\) is a Hilbert algebra, and \(f\) and \(g\) are unary maps on \(A\) such that \(f(a)\leq b\) iff \(a\leq g(b)\), and \(g(a\rightarrow b)\leq g(a)\rightarrow g(b)\) forall \(a,b\in A\). In this paper, we are going to prove that some varieties of HilGC-algebras are characterized by first-order conditions defined in the dual space and that these varieties are canonical. Additionally, we will also study and characterize the congruences of an HilGC-algebra through specific closed subsets of the dual space. This characterization will be applied to determine the simple algebras and subdirectly irreducible HilGC-algebras. Mon, 09 Dec 2024 00:00:00 GMT http://hdl.handle.net/11089/54527 2024-12-09T00:00:00Z http://hdl.handle.net/11089/54524 D-complete Single Axioms for the Equivalential Calculus with the rules D and R Czakon, Marcin Ulrich showed that most of the known axiomatisations of the classical equivalence calculus (EC) are D-incomplete, that is, they are not complete with the condensed detachment rule (D) as the primary rule of the proof procedure. He proved that the axiomatisation EEpEqrErEqp, EEEpppp by Wajsberg is D-complete and pointed out a number of D-complete single axioms, including one organic single axiom. In this paper we present new single axioms for EC with the condensed detachment and the reversed condensed detachment rules that form D-complete bases and are organic. Tue, 05 Nov 2024 00:00:00 GMT http://hdl.handle.net/11089/54524 2024-11-05T00:00:00Z