Temat: bounded lattice - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Minimal bounded lattices with an antitone involution the complemented elements of which do not form a sublattice
Autorzy:: Chajda, Ivan
Länger, Helmut
Powiązania:: https://bibliotekanauki.pl/articles/728776.pdf
Data publikacji:: 2008
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: bounded lattice
antitone involution
complemented element
Opis:: Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.
Źródło:: Discussiones Mathematicae - General Algebra and Applications; 2008, 28, 2; 251-259
1509-9415
Pojawia się w:: Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Distributivity of bounded lattices with sectionally antitone involutions
Autorzy:: Chajda, Ivan
Powiązania:: https://bibliotekanauki.pl/articles/729093.pdf
Data publikacji:: 2005
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: sectionally antitone involution
bounded lattice
distributive lattice
MV-algebra
Opis:: We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.
Źródło:: Discussiones Mathematicae - General Algebra and Applications; 2005, 25, 2; 155-163
1509-9415
Pojawia się w:: Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Four-valued expansions of Dunn-Belnaps logic (I): Basic characterizations
Autorzy:: Pynko, Alexej P.
Powiązania:: https://bibliotekanauki.pl/articles/1023300.pdf
Data publikacji:: 2020-12-30
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: propositional logic
logical matrix
Dunn-Belnap's logic
expansion
[bounded] distributive/De Morgan lattice
equality determinant
Opis:: Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique (up to isomorphism) conjunctive matrix ℳ4 with exactly two distinguished values over an expansion 4 of a De Morgan non-Boolean four-valued diamond, but by no matrix with either less than four values or a single [non-]distinguished value, and has no proper extension satisfying Variable Sharing Property (VSP). We then characterize L4's having a theorem / inconsistent formula, satisfying VSP and being [inferentially] maximal / subclassical / maximally paraconsistent, in particular, algebraically through ℳ4|4's (not) having certain submatrices|subalebras. Likewise, [providing 4 is regular / has no three-element subalgebra] L4 has a proper consistent axiomatic extension if[f] ℳ4 has a proper paraconsistent / two-valued submatrix [in which case the logic of this submatrix is the only proper consistent axiomatic extension of L4 and is relatively axiomatized by the Excluded Middle law axiom]. As a generic tool (applicable, in particular, to both classically-negative and implicative expansions of DB4), we also prove that the lattice of axiomatic extensions of the logic of an implicative matrix ℳ with equality determinant is dual to the distributive lattice of lower cones of the set of all submatrices of ℳ with non-distinguished values.
Źródło:: Bulletin of the Section of Logic; 2020, 49, 4; 401-437
0138-0680
2449-836X
Pojawia się w:: Bulletin of the Section of Logic
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: PC-lattices: A Class of Bounded BCK-algebras
Autorzy:: Shoar, Sadegh Khosravi
Borzooei, Rajab Ali
Moradian, R.
Radfar, Atefe
Powiązania:: https://bibliotekanauki.pl/articles/749890.pdf
Data publikacji:: 2018
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Tematy:: PC-lattice
BCK-lattice
Involutory BCK-algebras
Bounded commutative BCK-algebras
Opis:: In this paper, we define the notion of PC-lattice, as a generalization of finite positive implicative BCK-algebras with condition (S) and bounded commutative BCK-algebras. We investiate some results for Pc-lattices being a new class of BCK-lattices. Specially, we prove that any Boolean lattice is a PC-lattice and we show that if X is a PC-lattice with condition S, then X is an involutory BCK-algebra if and only if X is a commutative BCK-algebra. Finally, we prove that any PC-lattice with condition (S) is a distributive BCK-algebra.
Źródło:: Bulletin of the Section of Logic; 2018, 47, 1
0138-0680
2449-836X
Pojawia się w:: Bulletin of the Section of Logic
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: A reduction theorem for ring varieties whose subvariety lattice is distributive
Autorzy:: Volkov, Mikhail
Powiązania:: https://bibliotekanauki.pl/articles/729065.pdf
Data publikacji:: 2010
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: variety of rings
subvariety lattice
distributive lattice
torsion-bounded variety
Mal'tsev product
Opis:: We prove a theorem (for arbitrary ring varieties and, in a stronger form, for varieties of associative rings) which basically reduces the problem of a description of varieties with distributive subvariety lattice to the case of algebras over a finite prime field.
Źródło:: Discussiones Mathematicae - General Algebra and Applications; 2010, 30, 1; 119-132
1509-9415
Pojawia się w:: Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:: Biblioteka Nauki

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