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1
Content available On the lattice of tolerances for a finite chain
Górnicka A., Grygiel J., Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2016
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Vol. 21
25--30
EN
We provide some description of the lattice of tolerances for a finite chain, pointing to the skeleton tolerance as a special element of this lattice. In particular, we prove that the lattice of all glued tolerances of an n-element chain is isomorphic to the lattice of all tolerances of an n- 1-element chain nad at the same time is a principal filter of the lattice of an n-element chain.
2
Content available Sparingly glued tolerances
Górnicka A., Grygiel J., Tyrala I.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2015
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Vol. 20
49--54
EN
We introduce the notion of sparingly glued tolerances for lattices and then count their numbers in case of finite chains. We also estimate the density of sparingly glued tolerances among all glued tolerances on finite chains.
3
Content available Some dual logic without tautologies
Górnicka A., Bryll A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2015
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Vol. 20
39--47
EN
On this paper we consider a logic dual to the logic CRA and prove that it does not contain tautologies.
4
Content available The logic dual to Sobociński's n-valued logic
Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2010
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Vol. 15
35--42
EN
In this paper, we describe the logic dual to n-valued Sobociński logic. According to the idea presented by Malinowski and Spasowski [1], we introduce the consequence dual to the consequence of n-valued Sobociński logic in two ways: by a logical matrix and by a set of rules of inference. Then we prove that both approaches are equivalent and the consequence is dual in Wójcicki sense (see [3]).
5
Content available remote Special partial orderings in simple graphs
Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2007
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Vol. 12
37-40
EN
We show an algorithm checking whether in a given simple graph G it la possible to introduce a partial ordering whose covering relation agrees with the adjacency relation in G.
6
Content available remote Formalization of the Sentential Logic Dual to Łukasiewicz’s Three-valued Logic
Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2006
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Vol. 11
41--50
EN
Dual logics with respect to Łukasiewicz’s logics were investigated by G. Malinowski, M. Spasowski and R. Wójcicki in [4,5]. Our aim is to discuss the generalized method of natural deduction for the logic which is dual to Łukasiewicz’s three-valued logic.
7
Content available remote Rachunek refutacyjny a rachunek dualny
Bryll G., Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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1999
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Vol. 7
23--29
8
Content available remote Dwie formalizacje rachunku dualnego względem systemu W.
Bryll G., Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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1999
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Vol. 7
9--22
9
Content available remote Aksjomatyzacja rachunku zdaniowego dualnego względem klasycznego implikacyjno-negacyjnego rachunku zdań
Górnicka A.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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1999
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Vol. 7
30--36
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