Basic Quantifier
نویسنده
چکیده
1 Preamble According to Lindstrr om 1966 a quantiier is a functor which assigns to each non-empty domain a relation among relations which is closed under isomorphisms. A simple instance of this notion is given by the quantiier`more than half of the', which for each domain E gives the relation between sets A; B E deened by: jfa 2 A : a 2 Bgj > jfa 2 A : a 6 2 Bgj In the present collection of articles the authors investigate several aspects of such quantiiers, also of quantiiers with relational arguments. This introduction presents some basic insights and techniques of quan-tiication theory. After a brief history, we pay attention to application of the theory in linguistics, and then to its more logical features. The linguistic topics include: denotational constraints, behaviour in certian linguistic contexts, and polyadic forms of quantiication. On the logical side, we discuss metaproperties of weak and of`real' quantiier logics. In particular, we concentrate on the tableau method for weak quantiier logics, and on decidability results. It is impossible to write an introduction to this eld which does not overlap with the comprehensive overviews in Westerst ahl 1989, van Eijck 1991, Keenan and Westerst ahl 1995, Westerst ahl 1995, and the reader is encouraged to study some of these as well. For surveys of recent work we recom-Aristotle was already aware that quantiiers play a key r^ ole in the process of making inferences, so ever since Aristotle's day quantiication is a central topic in logic. In his theory of the syllogism, Aristotle studied the following inferential pattern: Quantiier 1 Restriction 1 Body 1 Quantiier 2 Restriction 2 Body 2 Quantiier 3 Restriction 3 Body 3 As an example we give the valid syllogism FESTINO: No A are B Some C are B Some C are not A
منابع مشابه
Decidability Results for Classes of Ordered Abelian Groups in Logics with Ramsey-quantifiers
This paper is to contributive to the model theory of ordered abelian groups (o.a.g. for short). The basic elements to build up the algebraic structure of the o.a.g-s are the archimedean groups: By Hahn's embedding theorem every o.a.g. can be represented as a subgroup of the Hahn-product of archimedean o.a.g.s. Archimedean is not a first-order concept but there exists a first-order model theory ...
متن کاملTransfer Function Synthesis without Quantifier Elimination
Abstract. Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state. The net effect of a sequence of instructions, a basic block, can then be calculated by composi...
متن کاملCosubstitution, Derivational Locality, and Quantifier Scope
Quantifier scope challenges the mantra of Tree Adjoining Grammar (TAG) that all syntactic dependencies are local once syntactic recursion has been factored out. The reason is that on current TAG analyses, a quantifier and the furthest reaches of its scope domain are in general not part of any (unicomponent) elementary tree. In this paper, I consider a novel basic TAG operation called COSUBSTITU...
متن کاملModel Transformations in Decidability Proofs for Monadic Theories
We survey two basic techniques for showing that the monadic second-order theory of a structure is decidable. In the first approach, one deals with finite fragments of the theory (given for example by the restriction to formulas of a certain quantifier rank) and – depending on the fragment – reduces the model under consideration to a simpler one. In the second approach, one applies a global tran...
متن کاملBasic Properties of L-fuzzy Quantifiers of the Type <1> Determined by Fuzzy Measures
The aim of this paper is to study monadic L-fuzzy quantifiers of the type 〈1〉 determined by fuzzy measures. These fuzzy quantifiers are defined using a novel notion of ⊗-fuzzy integral. Several semantic properties of these L-fuzzy quantifiers are studied. Keywords— fuzzy integral, fuzzy logic, fuzzy measure, fuzzy quantifier, generalized quantifier
متن کامل