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All splitting logics in the lattice NEXT(KTB:30A)

Kostrzycka Z.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2016

Vol. 21

31--61

We examine a special modal logic which is a normal extension of the Brouwer modal logic. It is determined by linearly ordered chains of clusters and the relation between clusters is reflexive and symmetric. The appropriate axiomatization of this logic is proposed in the papers [11] and [12]. There is also proved that all normal extensions of the investigated logic are Kripke complete and have f.m.p. Unfortunately, the cardinality of this family is continuum [13]. One may imagine that the structure of the lattice of these extensions is immensely complex. Then we use the technics of splitting to characterize this lattice and to describe some quite simple fragments. We characterize all the logics that split the lattice.

A certain approach to Kripke semantics for normal modal logics

Bryll G., Sochacki R.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2009

Vol. 14

13-20

In this paper the authors propose a method of verifying formulae in normal modal logics. In order to show that a formula α is a thesis of a normal modal logic, a set of decomposition rules for any formula is given. These decomposition rules are based on the symbols of assertion and rejection of formulae.

Knowledge based optimization

Tran Ch.

Computer Assisted Mechanics and Engineering Sciences

2004

Vol. 11, No. 4

283-291

Optimization theory has advanced considerably during the last three decades, as illustrated by a vast number of published books, surveys, and papers concerning this subject. However, for optimization of complex systems that may not be modeled exactly by Ludwig von Bertalanffy's general system theory, we may need a new philosophy based on rather non-conventional logics. It is represented bellow.

Intuitionistic Models of Arithmetic

Połacik T.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

1999

Vol. 6

70--74

Extensions of the Grzegorczyk Logic Determined by Some Countable Boolean Algebras

Dzik W.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

1999

Vol. 6

8--20

It is shown that a chain of type of w + 1 of modal logics: Tr = Grz + B1 ⊃ Grz + B2 ⊃ Grz + B3 ⊃...⊃ Grz (all of them are extensions of the Grzegorczyk logic Grz), contains all and only such modal logics which can be obtained as sets of formulae that are valid in the Stone spaces of countable superatomic Boolean algebras. Some topological conditions which correspond to the Grzegorczyk logic are presented.