Bulletin of the Section of Logic 48/3 (2019)
http://hdl.handle.net/11089/31213
2024-03-04T16:17:37ZModal Boolean Connexive Logics: Semantics and Tableau Approach
http://hdl.handle.net/11089/35363
Modal Boolean Connexive Logics: Semantics and Tableau Approach
Jarmużek, Tomasz; Malinowski, Jacek
In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication is weaker than the material one. In the final section, we present a tableau approach to the discussed modal logics.
2019-10-30T00:00:00ZA Note on Distributive Triples
http://hdl.handle.net/11089/35362
A Note on Distributive Triples
Łazarz, Marcin
Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note we provide some sufficient conditions for the distributivity of a given triple.
2019-10-30T00:00:00ZTopological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic
http://hdl.handle.net/11089/35361
Topological and Multi-Topological Frames in the Context of Intuitionistic Modal Logic
Witczak, Tomasz
We present three examples of topological semantics for intuitionistic modal logic with one modal operator □. We show that it is possible to treat neighborhood models, introduced earlier, as topological or multi-topological. From the neighborhood point of view, our method is based on differences between properties of minimal and maximal neighborhoods. Also we propose transformation of multitopological spaces into the neighborhood structures.
2019-10-30T00:00:00ZComplex Fuzzy Sets with Application in BCK/BCI-Algebras
http://hdl.handle.net/11089/35360
Complex Fuzzy Sets with Application in BCK/BCI-Algebras
Jun, Young Bae; Xin, Xiao Long
As a generation of fuzzy set, the notion of complex fuzzy set which is an innovative concept is introduced by Ramot, Milo, Friedman and Kandel. The purpose of this article is to apply complex fuzzy set to BCK/BCI-algebras. The notions of a complex subalgebra and a complex left (right) reduced ideal in a BCK/BCI- algebra are introduced, and related properties are investigated. Characterizations of a complex subalgebra are provided, and the homomorphic image (preimage) of a complex subalgebra and a complex left (right) reduced ideal.
2019-10-30T00:00:00Z