Bulletin of the Section of Logic 53/4 (2024)http://hdl.handle.net/11089/545152026-04-06T17:37:00Z2026-04-06T17:37:00Z\(\mathcal{L}\)−weakly 1−Absorbing Prime Ideals and FiltersAmare, Natnael Teshalehttp://hdl.handle.net/11089/545252025-02-06T02:18:41Z2024-11-14T00:00:00Z\(\mathcal{L}\)−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).
2024-11-14T00:00:00ZSome Additional Axioms for T-normal Logics. Defining K45, KB4, KD45 and S5 without Using Modal RulesPietruszczak, Andrzejhttp://hdl.handle.net/11089/545262025-02-06T02:18:37Z2024-06-24T00:00:00ZSome 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.
2024-06-24T00:00:00ZHilbert Algebras with Hilbert-Galois Connections IICelani, Sergio A.Montagie, Danielahttp://hdl.handle.net/11089/545272025-02-06T06:49:27Z2024-12-09T00:00:00ZHilbert 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.
2024-12-09T00:00:00ZD-complete Single Axioms for the Equivalential Calculus with the rules D and RCzakon, Marcinhttp://hdl.handle.net/11089/545242025-02-06T02:18:43Z2024-11-05T00:00:00ZD-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.
2024-11-05T00:00:00Z