排序方式: 共有71条查询结果,搜索用时 15 毫秒
51.
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
52.
Continuing work initiated by Jónsson, Daigneault, Pigozzi and others; Maksimova proved that a normal modal logic (with a single unary modality) has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property (cf. [Mak 91], [Mak 79]). The aim of this paper is to extend the latter result to a large class of logics. We will prove that the characterization can be extended to all algebraizable logics containing Boolean fragment and having a certain kind of local deduction property. We also extend this characterization of the interpolation property to arbitrary logics under the condition that their algebraic counterparts are discriminator varieties. We also extend Maksimova's result to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with modalities of ranks smaller than 2, too.The problem of extending the above characterization result to no n-normal non-unary modal logics remains open.Related issues of universal algebra and of algebraic logic are discussed, too. In particular we investigate the possibility of extending the characterization of interpolability to arbitrary algebraizable logics. 相似文献
53.
Tarek Sayed Ahmed 《Studia Logica》2007,85(2):139-151
SC, CA, QA and QEA denote the class of Pinter’s substitution algebras, Tarski’s cylindric algebras, Halmos’ quasi-polyadic
and quasi-polyadic equality algebras, respectively. Let . and . We show that the class of n dimensional neat reducts of algebras in K
m
is not elementary. This solves a problem in [2]. Also our result generalizes results proved in [1] and [2].
Presented by Robert Goldblatt 相似文献
54.
de Freitas Renata P. Viana Jorge P. Benevides Mario R. F. Veloso Sheila R. M. Veloso Paulo A. S. 《Journal of Philosophical Logic》2003,32(4):343-355
In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. 相似文献
55.
The complexity of the satisfiability problems of various arrow logics and cylindric modal logics is determined. As is well known, relativising these logics makes them decidable. There are several parameters that can be set in such a relativisation. We focus on the following three: the number of variables involved, the similarity type and the kind of relativised models considered. The complexity analysis shows the importance and relevance of these parameters. 相似文献
56.
Marta A. Zander 《Studia Logica》2008,88(2):233-246
In this paper we prove that, for n > 1, the n-generated free algebra in any locally finite subvariety of HoRA can be written in a unique nontrivial way as Ł2 × A′, where A′ is a directly indecomposable algebra in . More precisely, we prove that the unique nontrivial pair of factor congruences of is given by the filters and , where the element is recursively defined from the term introduced by W. H. Cornish. As an additional result we obtain a characterization of minimal irreducible filters of in terms of its coatoms.
Presented by Daniele Mundici 相似文献
57.
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
58.
Ivor Grattan-Guinness 《Theology & Science》2013,11(1):137-147
An important feature of mathematics, both pure and applied, during the nineteenth century was the widening from its common form to a proliferation, where the “objects” studied were not numbers or geometrical magnitudes but operations such as functions and differentiation and integration, abstract ones (as we now call them), linear algebras of vectors, matrices and determinants, and algebras in logic. In this article the author considers several of them, including the contributions of Hermann Grassmann and Benjamin Peirce. A notable feature of these developments was analogising from one algebra to another by adopting some of the same laws, such as associativity, commutativity and distributivity. In the final section we consider the normally secular character of these algebras. 相似文献
59.
We study ranges of algebraic functions in lattices and in algebras, such as Łukasiewicz-Moisil algebras which are obtained
by extending standard lattice signatures with unary operations.We characterize algebraic functions in such lattices having
intervals as their ranges and we show that in Artinian or Noetherian lattices the requirement that every algebraic function
has an interval as its range implies the distributivity of the lattice.
Presented by Daniele Mundici 相似文献
60.
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