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21.
Alejandro Petrovich 《Studia Logica》1996,56(1-2):205-224
It was shown in [3] (see also [5]) that there is a duality between the category of bounded distributive lattices endowed with a join-homomorphism and the category of Priestley spaces endowed with a Priestley relation. In this paper, bounded distributive lattices endowed with a join-homomorphism, are considered as algebras and we characterize the congruences of these algebras in terms of the mentioned duality and certain closed subsets of Priestley spaces. This enable us to characterize the simple and subdirectly irreducible algebras. In particular, Priestley relations enable us to characterize the congruence lattice of the Q-distributive lattices considered in [4]. Moreover, these results give us an effective method to characterize the simple and subdirectly irreducible monadic De Morgan algebras [7].The duality considered in [4], was obtained in terms of the range of the quantifiers, and such a duality was enough to obtain the simple and subdirectly irreducible algebras, but not to characterize the congruences.I would like to thank my research supervisor Dr. Roberto Cignoli for his helpful suggestions during the preparation of this paper and the referee for calling my attention to Goldblatt's paper [5]. 相似文献
22.
Roberto Cignoli 《Studia Logica》1996,56(1-2):23-29
The dual spaces of the free distributive lattices with a quantifier are constructed, generalizing Halmos' construction of the dual spaces of free monadic Boolean algebras. 相似文献
23.
The aim of this paper is to apply properties of the double dual endofunctor on the category of bounded distributive lattices
and some extensions thereof to obtain completeness of certain non-classical propositional logics in a unified way. In particular,
we obtain completeness theorems for Moisil calculus, n-valued Łukasiewicz calculus and Nelson calculus. Furthermore we show some conservativeness results by these methods.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
24.
A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR
+ and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices. 相似文献
25.
The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of
propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class
of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed
under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological
Kripke-style models for logics that are sound and complete with respect to varieties of distributive lattices with operators
in the above-mentioned classes.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
26.
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
27.
Jeffrey S. Olson 《Studia Logica》2006,83(1-3):393-406
CRS(fc) denotes the variety of commutative residuated semilattice-ordered monoids that satisfy (x ⋀ e)k ≤ (x ⋀ e)k+1. A structural characterization of the subdi-rectly irreducible members of CRS(k) is proved, and is then used to provide a
constructive approach to the axiomatization of varieties generated by positive universal subclasses of CRS(k).
Dedicated to the memory of Willem Johannes Blok 相似文献
28.
A simplified duality for implicative lattices and l-groups 总被引:1,自引:0,他引:1
Nestor G. Martinez 《Studia Logica》1996,56(1-2):185-204
A topological duality is presented for a wide class of lattice-ordered structures including lattice-ordered groups. In this new approach, which simplifies considerably previous results of the author, the dual space is obtained by endowing the Priestley space of the underlying lattice with two binary functions, linked by set-theoretical complement and acting as symmetrical partners. In the particular case of l-groups, one of these functions is the usual product of sets and the axiomatization of the dual space is given by very simple first-order sentences, saying essentially that both functions are associative and that the space is a residuated semigroup with respect to each of them.The author is supported at the Mathematical Institute of Oxford by a grant of the Argentinian Consejo de Investigations Cientificas y Tecnicas (CONICET). The author wishes to acknowledge the CONICET and the kind hospitality of the Mathematical Institute. 相似文献
29.
30.
A Proof of Standard Completeness for Esteva and Godo's Logic MTL 总被引:7,自引:0,他引:7
In the present paper we show that any at most countable linearly-ordered commutative residuated lattice can be embedded into a commutative residuated lattice on the real unit interval [0, 1]. We use this result to show that Esteva and Godo's logic MTL is complete with respect to interpretations into commutative residuated lattices on [0, 1]. This solves an open problem raised in. 相似文献