Bulletin of the Section of Logic 49/3 (2020)
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Equality Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)In this paper, we introduce and study a corresponding logic to equalityalgebras and obtain some basic properties of this logic. We prove the soundness and completeness of this logic based on equalityalgebras and local ... 
Module Structure on Effect Algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)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. ... 
New Modification of the Subformula Property for a Modal Logic
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)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 ... 
Empirical Negation, Conegation and Contraposition Rule I: Semantical Investigations
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as conegation, corresponds to different logics under different semantics. We then ... 
Proof Compression and NP Versus PSPACE II
(Wydawnictwo Uniwersytetu Łódzkiego, 20201104)We upgrade [3] to a complete proof of the conjecture NP = PSPACE that is known as one of the fundamental open problems in the mathematical theory of computational complexity; this proof is based on [2]. Since minimal ...