Computational complexity of polyadic lifts of generalized quantifiers in natural language

Computational complexity of polyadic lifts of generalized quantifiers in natural language

We study the computational complexity of polyadic quantifiers in natural language. This type of quantification is widely used in formal semantics to model the meaning of multi-quantifier sentences. First, we show that the standard constructions that turn simple determiners into complex quantifiers, namely Boolean operations, iteration, cumulation, and resumption, are tractable. Then, we provide...

Deenability of Polyadic Lifts of Generalized Quantiiers

We study generalized quantiiers on nite structures. With every function f : ! ! ! we associate a quantiier Q f by letting Q f x' say \there are at least f(n) elements x satisfying ', where n is the size of the universe". This is the general form of what is known as a monotone quantiier of type h1i. We study so called polyadic lifts of such quantiiers. The particular lifts we consider are Ramsey...

Deafault logic, natural language and generalized quantifiers

Default logic [Reiter 80] is now commonly used in artificial intelligence systems and turns out to be one of the major research fields in knowledge representation. One of the first motivations of default logic wan to give a more accurate semantic represem tation to natural language statements of the form: Birds fl~: Mos t birds fly. or~ arguably: Typicall2o; birds lty~ The idea was to define a ...

Computational Complexity in Natural Language

We have become so used to viewing natural language in computational terms that we need occasionally to remind ourselves of the methodological commitment this view entails. That commitment is this: we assume that to understand linguistic tasks—tasks such as recognizing sentences, determining their structure, extracting their meaning, and manipulating the information they contain—is to discover t...

Fuzzy quantifiers in natural language:: semantics and computational models