http://hdl.handle.net/11089/9983 2026-10-23T15:15:47Z http://hdl.handle.net/11089/59545 A Note on the Number of Subnormal Modal Logics Michalczenia, Patryk In the article we discuss the notion of a subnormal modal logic and, in particular, the notion of an intermediate subnormal modal logic. The goal of the article is to determine the cardinality of the set of all intermediate subnormal modal logics. Thus we define a set of certain formulas, such that each subset of the defined set determines a different intermediate subnormal modal logic. As we demonstrate, since the set in question is countable, the set of all intermediate subnormal modal logics has cardinality of the continuum. 2026-09-08T00:00:00Z http://hdl.handle.net/11089/59543 Valuation on L-Algebras Borzooei, Rajab Ali; Aaly Kologani, Mona; Mohseni Takallo, Mohammad; Xin, Xiao Long The purpose of this paper is to define the notion of valuation map on \(L\)-algebras and introduce its properties. For this, the concepts of  valuation and 1-valuation maps are introduced and some characterizations and related properties are investigated. Using a valuation map, a congruence relation is obtained and proved that this congruence relation is equivalent to the congruence relation made by an ideal. Also, showed that the image and inverse image of any valuation is a valuation. Finally, by using a 1-valuation map \(\xi\) on  \(L\)-algebra \(\mathcal{L}\), an \(L\)-algebra \((\widetilde{\mathcal{L}},\ast,\widetilde{\{1\}})\) and  a metric space \((\widetilde{\mathcal{L}}, \widetilde{d_\xi})\)  has been obtained. 2026-09-07T00:00:00Z http://hdl.handle.net/11089/59542 Perfect and Local Bounded Equality Algebras Niazian, Sogol; Aaly Kologani, Mona; Jun, Young Bae; Borzooei, Rajab Ali In this paper, by considering the notion of bounded equality algebra, we introduce the concepts of perfect, integral and local bounded equality algebras and we state and prove some related results. Specially, we define the notions of some filters such as primary and perfect filters and we get the relation between perfect filters with perfect bounded equality algebras and primary filters in the local bounded equality algebras. Finally, by defining the concepts of radical, locally finite, and peculiar bounded equality algebra, we give a representation for any bounded p-equality and local bounded equality algebras. 2026-09-07T00:00:00Z http://hdl.handle.net/11089/59544 Pre-Hilbert Algebras with Condition (GE3) Rezaei, Akbar; Borumand Saeid, Arsham GE-algebras are introduced as a generalization of Hilbert algebras in 2020. In this paper, we show that a self distributive GE-algebra is equivalent to the pimpl-RML algebra, and a transitive GE algebra is equivalent to the pi-pre-BBBCC algebra with condition (An). Further, we prove that pimpl-BE algebras are a subclass of pimpl-RML algebras and pre-Hilbert algebras with condition (GE3) are equivalent to the pi-pre-BBBCC algebras with condition (An). 2026-09-08T00:00:00Z