http://hdl.handle.net/11089/35155 2026-04-06T20:39:18Z http://hdl.handle.net/11089/35379 Equality Logic Ghorbani, Shokoofeh In this paper, we introduce and study a corresponding logic to equality-algebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equality-algebras and local deduction theorem. We show that this logic is regularly algebraizable with respect to the variety of equality∆-algebras but it is not Fregean. Then we introduce the concept of (prelinear) equality∆-algebras and investigate some related properties. Also, we study ∆-deductive systems of equality∆-algebras. In particular, we prove that every prelinear equality ∆-algebra is a subdirect product of linearly ordered equality∆-algebras. Finally, we construct prelinear equality ∆ logic and prove the soundness and strong completeness of this logic respect to prelinear equality∆-algebras. 2020-11-04T00:00:00Z http://hdl.handle.net/11089/35378 Module Structure on Effect Algebras Saidi Goraghani, Simin; Borzooei, Rajab Ali In this paper, by considering the notions of effect algebra and product effect algebra, we define the concept of effect module. Then we investigate some properties of effect modules, and we present some examples on them. Finally, we introduce some topologies on effect modules.   2020-11-04T00:00:00Z http://hdl.handle.net/11089/35377 New Modification of the Subformula Property for a Modal Logic Takano, Mitio A modified subformula property for the modal logic KD with the additionalaxiom □ ◊(A ∨ B) ⊃ □ ◊ A ∨ □ ◊B is shown. A new modification of the notion of subformula is proposed for this purpose. This modification forms a natural extension of our former one on which modified subformula property for the modal logics K5, K5D and S4.2 has been shown ([2] and [4]). The finite model property as well as decidability for the logic follows from this. 2020-11-04T00:00:00Z http://hdl.handle.net/11089/35376 Empirical Negation, Co-negation and Contraposition Rule I: Semantical Investigations Niki, Satoru We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω. 2020-11-04T00:00:00Z