scholarly journals Axiomatization of Aristotelian Syllogistic Logic Based on Generalized Quantifier Theory

2018 ◽  
Vol 7 (3) ◽  
pp. 167
Author(s):  
Xiaojun Zhang
Keyword(s):  
Generalized Quantifier ◽  
Generalized Quantifier Theory ◽  
Quantifier Theory

Determiners

2018 ◽  
Author(s):  
Phoevos Panagiotidis
Keyword(s):  
Research Work ◽  
Point Of View ◽  
Generalized Quantifier ◽  
Word Classes ◽  
Generalized Quantifier Theory ◽  
Nominal Agreement ◽  
Categorial Status ◽  
Semantic Point ◽  
And Function ◽  
Quantifier Theory

Determiners are a nominal syntactic category distinct from both adjectives and nouns; they constitute a functional (aka closed or ‘minor’) category and they are typically located high inside the nominal phrasal structure. From a syntactic point of view, the category of determiners is commonly understood to comprise the word classes of article, demonstrative, and quantifier, as well as non-adjectival possessives and some nominal agreement markers. From a semantic point of view, determiners are assumed to function as quantifiers, especially within research informed by Generalized Quantifier Theory. However, this is a one-way entailment: although determiners in natural language are quantificational, their class contains only a subset of the logically possible quantifiers; this class is restricted by conservativity and other factors. The tension between the ‘syntactic’ and the ‘semantic’ perspective on determiners results to a degree of terminological confusion: it is not always clear which lexical items the Determiner category includes or what the function of determiners is; moreover, there exists a tendency among syntacticians to view ‘Determiner’ as naming not a class, but a fixed position within a nominal phrasal template. The study of determiners rose to prominence within grammatical theory during the ’80s both due to advances in semantic theorizing, primarily Generalized Quantifier Theory, and due to the generalization of the X' phrasal schema to functional (minor) categories. Some issues in the nature and function of determiners that have been addressed in theoretical and typological work with considerable success include the categorial status of determiners, their (non-)universality, their structural position and feature makeup, their role in argumenthood and their interaction with nominal predicates, and their relation to pronouns. Expectedly, issues in (in)definiteness, quantification, and specificity also figure prominently in research work on determiners.

scholarly journals Directions in generalized quantifier theory

Studia Logica ◽  
1995 ◽  
Vol 55 (3) ◽  
pp. 389-419 ◽  
Author(s):  
Johan van Benthem ◽  
Dag Westerståhl
Keyword(s):  
Generalized Quantifier ◽  
Generalized Quantifier Theory ◽  
Quantifier Theory

An axiomatization of the logic with the rough quantifier

1991 ◽  
Vol 56 (2) ◽  
pp. 608-617 ◽  
Author(s):  
Michał Krynicki ◽  
Hans-Peter Tuschik
Keyword(s):  
Equivalence Relation ◽  
Equivalence Relations ◽  
Order Structure ◽  
Partition Model ◽  
Weak Model ◽  
First Order ◽  
Basic Properties ◽  
Generalized Quantifier ◽  
Order Language ◽  
The Right

We consider the language L(Q), where L is a countable first-order language and Q is an additional generalized quantifier. A weak model for L(Q) is a pair 〈, q〉 where is a first-order structure for L and q is a family of subsets of its universe. In case that q is the set of classes of some equivalence relation the weak model 〈, q〉 is called a partition model. The interpretation of Q in partition models was studied by Szczerba [3], who was inspired by Pawlak's paper [2]. The corresponding set of tautologies in L(Q) is called rough logic. In the following we will give a set of axioms of rough logic and prove its completeness. Rough logic is designed for creating partition models.The partition models are the weak models arising from equivalence relations. For the basic properties of the logic of weak models the reader is referred to Keisler's paper [1]. In a weak model 〈, q〉 the formulas of L(Q) are interpreted as usual with the additional clause for the quantifier Q: 〈, q〉 ⊨ Qx φ(x) iff there is some X ∊ q such that 〈, q〉 ⊨ φ(a) for all a ∊ X.In case X satisfies the right side of the above equivalence we say that X is contained in φ(x) or, equivalently, φ(x) contains X.

scholarly journals A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras

2019 ◽  
Vol 29 (06) ◽  
pp. 783-809
Author(s):  
Jules Hedges ◽  
Mehrnoosh Sadrzadeh
Keyword(s):  
Natural Language ◽  
Vector Space ◽  
Generative Grammar ◽  
Distributional Semantics ◽  
Compositional Semantics ◽  
Finite Dimensional ◽  
Linear Maps ◽  
First Time ◽  
Quantifier Theory ◽  
Compositional Distributional Semantics

AbstractCategorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, and then instantiate the abstract setting to sets and relations and to finite-dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics.

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