Displaying similar documents to “Многообразия логических матриц”

Interrelation of algebraic, semantical and logical properties for superintuitionistic and modal logics

Larisa Maksimova (1999)

Banach Center Publications

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We consider the families 𝓛 of propositional superintuitionistic logics (s.i.l.) and NE(K) of normal modal logics (n.m.l.). It is well known that there is a duality between 𝓛 and the lattice of varieties of pseudo-boolean algebras (or Heyting algebras), and also NE(K) is dually isomorphic to the lattice of varieties of modal algebras. Many important properties of logics, for instance, Craig's interpolation property (CIP), the disjunction property (DP), the Beth property (BP), Hallden-completeness...

Modal Boolean Connexive Logics: Semantics and Tableau Approach

Tomasz Jarmużek, Jacek Malinowski (2019)

Bulletin of the Section of Logic

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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...

On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1

Andrzej Pietruszczak (2017)

Bulletin of the Section of Logic

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This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and(T) and (altn) have no common atom. We generalize Pollack’s result from [12],where he...

On Theses without Iterated Modalities of Modal Logics Between C1 and S5. Part 2

Andrzej Pietruszczak (2017)

Bulletin of the Section of Logic

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This is the second, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics can be divided into certain groups. Each such group depends only on which of the following formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨☐q⌝, and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and (T) and (altn) have no common atom. We generalize Pollack’s result from [1], where...