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1.
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
2.
L. L. Maksimova 《Algebra and Logic》2009,48(1):33-53
The restricted interpolation property IPR in modal and superintuitionistic logics is investigated. It is proved that in superintuitionistic
logics of finite slices and in finite-slice extensions of the Grzegorczyk logic, the property IPR is equivalent to the projective
Beth property PB2.
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).
Translated from Algebra i Logika, Vol. 48, No. 1, pp. 54-89, January-February, 2009. 相似文献
3.
4.
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
5.
L. L. Maksimova 《Algebra and Logic》2009,48(6):426-448
Propositional modal and positive logics are considered as well as extensions of Johansson’s minimal logic. It is proved that
basic versions of the interpolation property and of the Beth definability property, and also the Hallden property, are decidable
on the class of tabular logics, i.e., logics given by finitely many finite algebras. Algorithms are described for constructing
counterexamples to each of the properties mentioned in handling cases where the logic under consideration does not possess
the required property. 相似文献
6.
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
7.
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
8.
We deal with logics based on lattices with an additional unary operation. Interrelations of different versions of interpolation,
the Beth property, and amalgamation, as they bear on modal logics and varieties of modal algebras, superintuitionistic logics
and varieties of Heyting algebras, positive logics and varieties of implicative lattices, have been studied in many works.
Sometimes these relations can and sometimes cannot be extended to the logics without implication considered in the paper.
Supported by INTAS (grant No. 04-77-7080) and by RFBR (grant No. 06-01-00358).
Supported by INTAS grant No. 04-77-7080.
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Translated from Algebra i Logika, Vol. 47, No. 3, pp. 307–334, May–June, 2008. 相似文献
9.
Vladimir V. Rybakov Vladimir R. Kiyatkin Tahsin Oner 《Mathematical Logic Quarterly》1999,45(4):505-520
Our investigation is concerned with the finite model property (fmp) with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown (Theorem 4.3) that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics (which is equipotent to all these λ extend a certain subframe logic defined over S4 by omission of four special frames) have fmp w.r.t. admissibility. 相似文献
10.
D. E. Tishkovskii 《Algebra and Logic》2001,40(2):122-134
Algebraic counterparts are found for the Beth, projective Beth, interpolation, disjunction, and existential properties of superintuitionistic first-order logics. 相似文献
11.
L. L. Maksimova 《Siberian Mathematical Journal》2014,55(1):118-124
We consider versions of the interpolation property stronger than the Craig interpolation property and prove the Lyndon interpolation property for the Grzegorczyk logic and some of its extensions. We also establish the Lyndon interpolation property for most extensions of the intuitionistic logic with Craig interpolation property. For all modal logics over the Grzegorczyk logic as well as for all superintuitionistic logics, the uniform interpolation property is equivalent to Craig’s property. 相似文献
12.
L. L. Maksimova 《Algebra and Logic》2001,40(3):159-165
Previously, we proved that there are only finitely many varieties of Heyting algebras possessing the projective Beth property and gave an exhaustive list of these. The projective Beth property is equivalent to strong epimorphisms surjectivity (SES). Here, we prove that the projective Beth property and SES are base-decidable on a class of varieties of Heyting algebras. 相似文献
13.
14.
Olivier Gasquet 《Mathematical Logic Quarterly》1998,44(1):45-49
The problem of completeness for predicate modal logics is still under investigation, although some results have been obtained in the last few years (cf. [2, 3, 4, 7]). As far as we know, the case of multimodal logics has not been addressed at all. In this paper, we study the combination of modal logics in terms of combining their semantics. We demonstrate by a simple example that in this sense predicate modal logics are not so easily manipulated as propositional ones: mixing two Kripke-complete predicate modal logics (one with the Barcan formula, and the other without) results in a Kripke-incomplete system. 相似文献
15.
L. L. Maksimova 《Algebra and Logic》2003,42(6):398-406
Interconnections between syntactic and categorical properties of equational theories are established. The notions of restricted interpolation and of restricted amalgamation are introduced and their equivalence proved; interrelations of the above-mentioned properties and the projective Beth property, interpolation, and amalgamation are studied. 相似文献
16.
Martin Lück 《Annals of Pure and Applied Logic》2018,169(9):928-969
In a modular approach, we lift Hilbert-style proof systems for propositional, modal and first-order logic to generalized systems for their respective team-based extensions. We obtain sound and complete axiomatizations for the dependence-free fragment FO(~) of Väänänen's first-order team logic TL, for propositional team logic PTL, quantified propositional team logic QPTL, modal team logic MTL, and for the corresponding logics of dependence, independence, inclusion and exclusion.As a crucial step in the completeness proof, we show that the above logics admit, in a particular sense, a semantics-preserving elimination of modalities and quantifiers from formulas. 相似文献
17.
We give a criterion for inheritance of the admissible inference rules of the modal logic K4 by the finitely approximable modal logics extending K4. We give a negative solution to the question of inheritance of the admissible rules of K4 by tabular logics. We exhibit a series of examples of modal logics which inherit or fail to inherit the admissible inference rules of K4. 相似文献
18.
Intuitionistic propositional logicInt and its extensions, known as intermediate or superintuitionistic logics, in many respects can be regarded as just fragments
of classical modal logics containingS4. The main aim of this paper is to construct a similar correspondence between intermediate logics augmented with modal operators—we
call them intuitionistic modal logics—and classical polymodal logics We study the class of intuitionistic polymodal logics
in which modal operators satisfy only the congruence rules and so may be treated as various sorts of □ and ◇.
Supported by the Alexander von Humboldt Foundation.
Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 121–155, March–April, 1997. 相似文献
19.
Edwin D. Mares 《Mathematical Logic Quarterly》1993,39(1):165-177
A variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule γ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them “classically complete”. MSC: 03B45, 03B46. 相似文献
20.
We look into methods which make it possible to determine whether or not the modal logics under examination are residually finite w.r.t. admissible inference rules. A general condition is specified which states that modal logics over K4 are not residually finite w.r.t. admissibility. It is shown that all modal logics over K4 of width strictly more than 2 which have the co-covering property fail to be residually finite w.r.t. admissible inference rules; in particular, such are K4, GL, K4.1, K4.2, S4.1, S4.2, and GL.2. It is proved that all logics over S4 of width at most 2, which are not sublogics of three special table logics, possess the property of being residually finite w.r.t. admissibility. A number of open questions are set up. 相似文献