共查询到20条相似文献,搜索用时 15 毫秒
1.
P. A. Shreiner 《Algebra and Logic》2007,46(1):62-70
We deal with some issues on automatic recognition of interpolation properties in modal calculi extending the logics S5 and
S4.3.
Supported by RFBR grant No. 06-01-00358 and by INTAS grant No. 04-77-7080.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 103–119, January–February, 2007. 相似文献
2.
L. L. Maksimova 《Algebra and Logic》2008,47(1):56-64
The notions of a weak interpolation property and of weak amalgamation are introduced. It is proved that in varieties with
the congruence extension property, the weak interpolation property is equivalent to the weak amalgamation property. In turn,
weak amalgamability of a variety is equivalent to amalgamability of a class of finitely generated simple algebras in this
variety.
Supported by RFBR (grant Nos. 06-01-00358 and 05-01-04003-NNIOa) and by INTAS (grant No. 04-77-7080).
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 94–107, January–February, 2008. 相似文献
3.
O. V. Zeevald 《Algebra and Logic》2006,45(6):415-430
We explore the basic fuzzy logic BL as well as propositional fuzzy logics with modalities □ and ◊ and a total accessibility relation. Formulations and proofs
are given to replacement theorems for BL. A basic calculus of modal fuzzy logic is introduced. For this calculus and its extensions, we prove replacement and deduction
theorems.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 45, No. 6, pp. 731–757, November–December, 2006. 相似文献
4.
L. L. Maksimova 《Algebra and Logic》2006,45(1):49-66
We look at the interplay between the projective Beth property in non-classical logics and interpolation. Previously, we proved
that in positive logics as well as in superintuitionistic and modal ones, the projective Beth property PB2 follows from Craig's interpolation property and implies the restricted interpolation property IPR. Here, we show that IPR and PB2 are equivalent in positive logics, and also in extensions of the superintuitionistic logic KC and of the modal logic Grz.2.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-2069.2003.1.
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Translated from Algebra i Logika, Vol. 45, No. 1, pp. 85–113, January–February, 2006. 相似文献
5.
L. L. Maksimova 《Algebra and Logic》2005,44(6):407-421
We study into the interpolation property and the projective Beth property in extensions of Johansson's minimal logic. A family
of logics of some special form is considered. Effective criteria are specified which allow us to verify whether an arbitrary
logic in this family has a given property.
Supported by RFBR grant No. 03-06-80178, by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-2069.2003.1, and by INTAS grant No. 04-77-7080.
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Translated from Algebra i Logika, Vol. 44, No. 6, pp. 726–750, November–December, 2005. 相似文献
6.
V. M. Murzina 《Algebra and Logic》2007,46(6):409-418
We study into the question whether calculi associated with Ershov topological spaces possess Craig’s interpolation property.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 46, No. 6, pp. 745–762, November–December, 2007. 相似文献
7.
L. L. Maksimova 《Algebra and Logic》2007,46(5):341-353
The interpolation property in extensions of Johansson’s minimal logic is investigated. The construction of a matched product
of models is proposed, which allows us to prove the interpolation property in a number of known extensions of the minimal
logic. It is shown that, unlike superintuitionistic, positive, and negative logics, a sum of J-logics with the interpolation property CIP may fail to possess CIP, nor even the restricted interpolation property.
Supported by RFBR grant No. 06-01-00358, by INTAS grant No. 04-77-7080, and by the Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-4787.2006.1.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 627–648, September–October, 2007. 相似文献
8.
V. F. Murzina 《Algebra and Logic》2005,44(5):313-325
An axiomatization is furnished for a polymodal logic of strictly linearly ordered A-frames: for frames of this kind, we consider
a language of polymodal logic with two modal operators, □< and □≺. In the language, along with the operators, we introduce a constant β, which describes a basis subset. In the language with
the two modal operators and constant β, an Lα-calculus is constructed. It is proved that such is complete w.r.t. the class
of all strictly linearly ordered A-frames. Moreover, it turns out that the calculus in question possesses the finite-model
property and, consequently, is decidable.
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Translated from Algebra i Logika, Vol. 44, No. 5, pp. 560–582, September–October, 2005.
Supported by RFBR grant No. 03-06-80178, by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-2069.2003.1, and by INTAS grant No. 04-77-7080. 相似文献
9.
Let V be a variety of algebras. We specify a condition (the so-called generalized entropic property), which is equivalent to the
fact that for every algebra A ∈ V, the set of all subalgebras of A is a subuniverse of the complex algebra of the subalgebras of A. The relationship between the generalized entropic property and the entropic law is investigated. Also, for varieties with
the generalized entropic property, we consider identities that are satisfied by complex algebras of subalgebras.
Dedicated to George Gr?tzer on the occasion of his 70th birthday
Supported by INTAS grant No. 03-51-4110.
Supported by MŠMTČR (project MSM 0021620839) and by the Grant Agency of the Czech Republic (grant No. 201/05/0002).
Translated from Algebra i Logika, Vol. 47, No. 6, pp. 655–686, November–December, 2008. 相似文献
10.
A. G. Pinus 《Algebra and Logic》1996,35(6):398-402
We prove that there exist finitely generated, simple, rich algebras in discriminator varieties having continuum many finitely
generated mutually nonembeddable algebras, under some additional assumptions imposed on the varieties.
Supported by RFFR grant No. 93-011-1520.
Translated fromAlgebra i Logika, Vol. 35, No. 6, pp. 709–718, November–December, 1996. 相似文献
11.
L. L. Maksimova 《Algebra and Logic》1999,38(3):171-180
Projective Beth properties in superintuitionistic and normal modal logics are considered. Their interrelations and connections
with interpolation properties of the logics are established. Algebraic counterparts for the projective Beth properties are
found out.
Supported by the Russian Humanitarian Science Foundation, grant No. 97-03-04089.
Translated fromAlgebra i Logika, Vol. 38, No. 3, pp. 316–333, May–June, 1999. 相似文献
12.
Centers of universal envelopes for Mal’tsev algebras are explored. It is proved that the center of the universal envelope
for a finite-dimensional semisimple Mal’tsev algebra over a field of characteristic 0 is a ring of polynomials in a finite
number of variables equal to the dimension of its Cartan subalgebra, and that universal enveloping algebra is a free module
over its center. Centers of universal enveloping algebras are computed for some Mal’tsev algebras of small dimensions.
Supported by FAPESP grant No. 04/08537-4 and by SO RAN grant No. 1.9.
Supported by FAPESP grant Nos. 05/60142-7, 05/60337-2 and by CNPq grant No. 304991/2006-6.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 560–584, September–October, 2007. 相似文献
13.
We investigate differences in isomorphism types for Rogers semilattices of computable numberings of families of sets lying
in different levels of the arithmetical hierarchy.
Supported by RFBR grant No. 05-01-00819 and by INTAS grant No. 00-499.
Supported by NSFC grant No. 60310213.
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Translated from Algebra i Logika, Vol. 45, No. 6, pp. 637–654, November–December, 2006. 相似文献
14.
A class of varieties V (including all finitely based lattice varieties) is determined for which the elementary equivalence
of lattices of subalgebras of free V-algebras, Fv(X) and Fv(Y), is equivalent to sets X and Y being second-order equivalent.
Supported by RFFR grant No. 99-01-00571.
Supported by the National Research Foundation of the Republic of South Africa, and by the University of Cape Town Research
Committee.
Translated fromAlgebra i Logika, Vol. 39, No. 5, pp. 595–601, September–October, 2000. 相似文献
15.
A. G. Pinus 《Algebra and Logic》1998,37(4):245-259
We construct a conditional identity calculus (similar to the Birkhoff identity calculus), which complies with the concept
of truth for a conditional identity on a universal algebra. The relationship is studied between the isomorphism of embedding
categories of conditional varieties and the conditioned rational equivalence of these varieties. As applications, we describe
invariants for the relations ‘is conditional rational equivalent’ and ‘is similar’ on finite universal algebras.
Supported by RFFR grant No. 93-01-01520.
Translated fromAlgebra i Logika, Vol. 37, No. 4, pp. 432–459, July–August, 1998. 相似文献
16.
L. L. Maksimova 《Algebra and Logic》1999,38(6):374-382
It is proved that in superintuitionistic logics, the projective Beth property follows from the Craig interpolation property,
but the converse does not hold. A criterion is found which allows us to reduce the problem asking whether the projective Beth
property is valid in superintuitionistic logics to suitable properties of varieties of pseudoboolean algebras. It is shown
that the principle of variable separation follows from the projective Beth property. On the other hand, the interpolation
property in a logic L implies the projective Beth property in Δ(L).
Supported by RFFR grants No. 96-01-01552 and No. 99-01-00600.
Translated fromAlgebra i Logika, Vol. 38, No. 6, pp. 680–696, November–December, 1999. 相似文献
17.
D. E. Tishkovskii 《Algebra and Logic》1999,38(1):36-50
We construct a unified algebraic semantics for superintuitionistic predicate logics. Assigned to each predicate logic is some
deductive system of a propositional language which is kept fixed throughout all predicate superintuitionistic ones. Given
that system, we build up a variety of algebras w.r.t. which a given logic is proved to be strongly complete.
Supported by the Russian Arts Foundation (RAF), grant No. 97-03-04089a.
Translated fromAlgebra i Logika, Vol. 38, No. 1, pp. 68–95, January–February, 1999. 相似文献
18.
A. V. Karpenko 《Algebra and Logic》2008,47(6):395-404
Conditions are specified which are necessary and sufficient for a logic over K4 to possess the weak interpolation property.
For this goal to be met, simple transitive modal algebras are described, and we establish a criterion for the class of such
algebras to be amalgamable. For extensions of K4, the weak interpolation property is proved decidable.
Supported by RFBR (project No. 06-01-00358) and by the Council for Grants (under RF President) and State Aid of Leading Scientific
Schools (grant NSh-335.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 6, pp. 705–722, November–December, 2008. 相似文献
19.
Miroslav Ploščica 《Mathematica Slovaca》2009,59(2):221-230
In [PLOŠČICA, M.: Separation in distributive congruence lattices, Algebra Universalis 49 (2003), 1–12] we defined separable sets in algebraic lattices and showed a close connection between the types of non-separable
sets in congruence lattices of algebras in a finitely generated congruence distributive variety
and the structure of subdirectly irreducible algebras in
. Now we generalize these results using the concept of separable mappings (defined on some trees) and apply them to some lattice
varieties.
Supported by VEGA Grants 2/4134/24, 2/7141/27, and INTAS Grant 03-51-4110. 相似文献
20.
M. V. Zaitsev 《Algebra and Logic》1998,37(4):223-233
A variety of Lie algebras over a field of characteristic 0 has a finite superrank if it is generated by the Grassmann envelope
of a finitely generated Lie superalgebra. We prove that every commutator variety not in NcA has infinite superrank. Consequently, infinite are superranks of all polynilpotent varieties of Lie algebras except Nc and NcA.
Supported by RFFR grant No. 96-01-00146.
Translated fromAlgebra i Logika, Vol. 37, No. 4, pp. 394–412, July–August. 1998. 相似文献