共查询到20条相似文献,搜索用时 31 毫秒
1.
C. J. van Alten 《Studia Logica》2006,83(1-3):425-445
A biresiduation algebra is a 〈/,\,1〉-subreduct of an integral residuated lattice. These algebras arise as algebraic models of the implicational fragment
of the Full Lambek Calculus with weakening. We axiomatize the quasi-variety B of biresiduation algebras using a construction for integral residuated lattices. We define a filter of a biresiduation algebra
and show that the lattice of filters is isomorphic to the lattice of B-congruences and that these lattices are distributive. We give a finite basis of terms for generating filters and use this
to characterize the subvarieties of B with EDPC and also the discriminator varieties. A variety generated by a finite biresiduation algebra is shown to be a subvariety
of B. The lattice of subvarieties of B is investigated; we show that there are precisely three finitely generated covers of the atom.
Mathematics Subject Classification (2000): 03G25, 06F35, 06B10, 06B20
Dedicated to the memory of Willem Johannes Blok 相似文献
2.
This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q
3
of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q
3
and we construct the lattice of subvarieties (Q
3
) of the variety Q
3
. 相似文献
3.
Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK-lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK-lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK. Finally, we describe invariants determining a twist-structure over a modal algebra. 相似文献
4.
5.
Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K
S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular. 相似文献
6.
This paper is the concluding part of [1] and [2], and it investigates the inner structure of the lattice (MHA) of all varieties of monadic Heyting algebras. For every n , we introduce and investigate varieties of depth n and cluster n, and present two partitions of (MHA), into varieties of depth n, and into varieties of cluster n. We pay a special attention to the lower part of (MHA) and investigate finite and critical varieties of monadic Heyting algebras in detail. In particular, we prove that there exist exactly thirteen critical varieties in (MHA) and that it is decidable whether a given variety of monadic Heyting algebras is finite or not. The representation of (MHA) is also given. All these provide us with a satisfactory insight into (MHA). Since (MHA) is dual to the lattice NExtMIPC of all normal extensions of the intuitionistic modal logic MIPC, we also obtain a clearer picture of the lattice structure of intuitionistic modal logics over MIPC. 相似文献
7.
In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4— our formulation has several important metatheoretic properties. In addition, we study models of IS4— not in the framework of Kirpke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models but also a means of modelling proofs as well as provability. 相似文献
8.
An algebra A is said to be congruence coherent if every subalgebra of A that contains a class of some congruence on A is a union of -classes. This property has been investigated in several varieties of lattice-based algebras. These include, for example,
de Morgan algebras, p-algebras, double p-algebras, and double MS-algebras. Here we determine precisely when the property holds in the class of symmetric extended
de Morgan algebras.
Presented by M.E. Adams 相似文献
9.
Bruno Teheux 《Studia Logica》2007,87(1):13-36
In this paper, we develop a duality for the varieties of a Łukasiewicz
n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived
and we propose some ideas for future research.
Presented by Daniele Mundici 相似文献
10.
H. P. Sankappanavar 《Studia Logica》2011,98(1-2):27-81
This paper is a contribution toward developing a theory of expansions of semi-Heyting algebras. It grew out of an attempt to settle a conjecture we had made in 1987. Firstly, we unify and extend strikingly similar results of [48] and [50] to the (new) equational class DHMSH of dually hemimorphic semi-Heyting algebras, or to its subvariety BDQDSH of blended dual quasi-De Morgan semi-Heyting algebras, thus settling the conjecture. Secondly, we give a criterion for a unary expansion of semi-Heyting algebras to be a discriminator variety and give an algorithm to produce discriminator varieties. We then apply the criterion to exhibit an increasing sequence of discriminator subvarieties of BDQDSH. We also use it to prove that the variety DQSSH of dually quasi-Stone semi- Heyting algebras is a discriminator variety. Thirdly, we investigate a binary expansion of semi-Heyting algebras, namely the variety DblSH of double semi-Heyting algebras by characterizing its simples, and use the characterization to present an increasing sequence of discriminator subvarieties of DblSH. Finally, we apply these results to give bases for ??small?? subvarieties of BDQDSH, DQSSH, and DblSH. 相似文献
11.
Given a variety we study the existence of a class such that S1 every A can be represented as a global subdirect product with factors in and S2 every non-trivial A is globally indecomposable. We show that the following varieties (and its subvarieties) have a class satisfying properties S1 and S2: p-algebras, distributive double p-algebras of a finite range, semisimple varieties of lattice expansions such that the simple members form a universal class (bounded distributive lattices, De Morgan algebras, etc) and arithmetical varieties in which the finitely subdirectly irreducible algebras form a universal class (f-rings, vector groups, Wajsberg algebras, discriminator varieties, Heyting algebras, etc). As an application we obtain results analogous to that of Nachbin saying that if every chain of prime filters of a bounded distributive lattice has at most length 1, then the lattice is Boolean.We wish to thank Lic. Alfredo Guerin and Dr. Daniel Penazzi for helping us with linguistics aspects. We are indebted to the referee for several helpful suggestions. We also wish to thank Professor Mick Adams for providing us with several reprints and useful e-mail information on the subject.Suported by CONICOR and SECyT (UNC). 相似文献
12.
The lattices of varieties were studied in many works (see [4], [5], [11], [24], [31]). In this paper we describe the lattice
of all subvarieties of the variety defined by so called externally compatible identities of Abelian groups and the identity x
n
≈ y
n
.
The notation in this paper is the same as in [2].
Presented by W. Dziobiak 相似文献
13.
Adam Přenosil 《Studia Logica》2016,104(3):389-415
We introduce a novel expansion of the four-valued Belnap–Dunn logic by a unary operator representing reductio ad contradictionem and study its algebraic semantics. This expansion thus contains both the direct, non-inferential negation of the Belnap–Dunn logic and an inferential negation akin to the negation of Johansson’s minimal logic. We formulate a sequent calculus for this logic and introduce the variety of reductio algebras as an algebraic semantics for this calculus. We then investigate some basic algebraic properties of this variety, in particular we show that it is locally finite and has EDPC. We identify the subdirectly irreducible algebras in this variety and describe the lattice of varieties of reductio algebras. In particular, we prove that this lattice contains an interval isomorphic to the lattice of classes of finite non-empty graphs with loops closed under surjective graph homomorphisms. 相似文献
14.
Wiesław Dziobiak 《Studia Logica》1981,40(3):249-252
We prove that each intermediate or normal modal logic is strongly complete with respect to a class of finite Kripke frames
iff it is tabular, i.e. the respective variety of pseudo-Boolean or modal algebras, corresponding to it, is generated by a
finite algebra.
The author wishes to thank the Editors for calling his attention to the fact that the result of this paper concerning the
intermediate logics was announced earlier by A. Wroński at the conference “Logical calculi”, Wrocław, October 5–7, 1975, though
without proof. Wroński's result has not been published. 相似文献
15.
Krystyna Mruczek-Nasieniewska 《Studia Logica》2010,95(1-2):21-35
In the present paper we give syntactical and semantical characterization of the class of algebras defined by P-compatible identities of modular ortholattices. We also describe the lattice of some subvarieties of the variety MOL Ex defined by so called externally compatible identities of modular ortholattices. 相似文献
16.
Bronisław Tembrowski 《Studia Logica》1983,42(4):389-405
This paper deals with Boolean algebras supplied with an additional binary operation, calledB-algebras for short.The aim of the paper is to generalize some theorems concerning topological Boolean algebras to more comprehensive classes ofB-algebras, to formulate fundamental properties ofB-algebras, and to find more important relationships of these algebras to other known algebras.The paper consists of two parts. At the beginning of the first one, several subclasses ofB-algebras are distinguished, and then, their basic properties, connections between them as well as certain relationships with other algebras, are investigated. In particular, it is shown that the class of Boolean algebras together with an arbitrary unary operation is polynomially equivalent to the class ofB
1-algebras.The second part of the paper is concerned with the theory of filters and congruences inB-algebras. 相似文献
17.
In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation ${\tau(a) \leq b \vee (b \rightarrow a)}$ , for all ${a, b \in A}$ . These operators were studied from an algebraic, logical and topological point of view by Leo Esakia in [10]. We will study frontal operators in weak Heyting algebras and we will consider two examples of them. We will give a Priestley duality for the category of frontal weak Heyting algebras in terms of relational spaces ${\langle X, \leq, T, R \rangle}$ where ${\langle X, \leq, T \rangle}$ is a WH-space [6], and R is an additional binary relation used to interpret the modal operator. We will also study the WH-algebras with successor and the WH-algebras with gamma. For these varieties we will give two topological dualities. The first one is based on the representation given for the frontal weak Heyting algebras. The second one is based on certain particular classes of WH-spaces. 相似文献
18.
In the present paper we continue the investigation of the lattice of subvarieties of the variety of ${\sqrt{\prime}}$ quasi-MV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for the same variety. 相似文献
19.
Averaging the truth-value in Łukasiewicz logic 总被引:3,自引:0,他引:3
Daniele Mundici 《Studia Logica》1995,55(1):113-127
Chang's MV algebras are the algebras of the infinite-valued sentential calculus of ukasiewicz. We introduce finitely additive measures (called states) on MV algebras with the intent of capturing the notion of average degree of truth of a proposition. Since Boolean algebras coincide with idempotent MV algebras, states yield a generalization of finitely additive measures. Since MV algebras stand to Boolean algebras as AFC*-algebras stand to commutative AFC*-algebras, states are naturally related to noncommutativeC*-algebraic measures. 相似文献
20.
The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL
ew
of the substructural logic FL
ew
. The main result of Part I of this series [41] shows that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL
ew
(namely, a certain variety of FL
ew
-algebras) are term equivalent. In this paper, the term equivalence result of Part I [41] is lifted to the setting of deductive
systems to establish the definitional equivalence of the logics N and NFL
ew
. It follows from the definitional equivalence of these systems that constructive logic with strong negation is a substructural
logic.
Presented by Heinrich Wansing 相似文献