排序方式: 共有104条查询结果,搜索用时 15 毫秒
71.
A Dedekind algebra is an order pair (B, h) where B is a non-empty set and h is a similarity transformation on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are 0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type which occur in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. It is shown that configuration signatures can be used to characterize the homogeneous, universal and homogeneous-universal Dedekind algebras. This characterization is used to prove various results about these subclasses of Dedekind algebras. 相似文献
72.
Wojciech Buszkowski 《Studia Logica》2007,87(2-3):145-169
We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars.
The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system
of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid.
Special Issue Categorial Grammars and Pregroups Edited by
Wojciech Buszkowski and Anne Preller 相似文献
73.
74.
Mathematical modal logic: A view of its evolution 总被引:1,自引:0,他引:1
This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. It focuses on the interconnections between algebraic semantics using Boolean algebras with operators and relational semantics using structures often called Kripke models. It reviews the ideas of a number of people who independently contributed to the emergence of relational semantics, and compares them with the work of Kripke. It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science. 相似文献
75.
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
76.
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
77.
Thomas Vetterlein 《Studia Logica》2008,90(3):407-423
Fuzzy logics are in most cases based on an ad-hoc decision about the interpretation of the conjunction. If they are useful
or not can typically be found out only by testing them with example data. Why we should use a specific fuzzy logic can in
general not be made plausible. Since the difficulties arise from the use of additional, unmotivated structure with which the
set of truth values is endowed, the only way to base fuzzy logics on firm ground is the development of alternative semantics
to all of whose components we can associate a meaning.
In this paper, we present one possible approach to justify ex post Łukasiewicz Logic as well as Basic Logic. The notion of
ambiguity is central. Our framework consists of a Boolean or a Heyting algebra, respectively, endowed with an equivalence
relation expressing ambiguity. The quotient set bears naturally the structure of an MV- or a BL-algebra, respectively, and
thus can be used to interpret propositions of the mentioned logics. 相似文献
78.
79.
Although findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe, 2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on algebraic feature knowledge and solving quadratic equations. Middle school algebra students (N = 206) were randomly assigned to four conditions. Two errorful conditions either displayed errors and asked students to explain or displayed correct solutions and primed students to reflect on potential errors by problem type. A correct example condition and problem-solving control group were also included. Studying and explaining common errors displayed in incorrect examples improved equation-solving ability. An aptitude-by-treatment interaction revealed that learners with limited understandings of algebraic features demonstrated greater benefits. Theoretical implications about using examples to promote learning from errors are considered in addition to suggestions for educational practice. 相似文献
80.
In this paper we describe the Priestley space of a quasi-Stone algebra and use it to show that the class of finite quasi-Stone
algebras has the amalgamation property. We also describe the Priestley space of the free quasi-Stone algebra over a finite
set.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献