A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with Bialgebras

Categorical 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, 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

Derivational Event Semantics for Pregroup Grammars

The focus of this research project is the development of a derivational system for event semantics over pregroup grammars. More concretely, it is shown how by extending the usual pregroup framework with a semantic layer and by assigning explicit event variables to the basic syntactic types of an expression, one can get semantic extraction from pregroup derivations without too many complications. The resulting meaning is neo-davidsonian and conjunctivist in form, that is, the meaning is analysed in terms of events, and a single logical operator is used for meaning combination: the conjunction ∧. Using conjunctions as sole mean of meaning combination makes it harder at first to analyse certain constructions, but this is a small price to pay for the level of generality and overall derivational simplicity that is obtained in the end by equating syntactic combination — pregroup contractions — with meaning conjunction. The issue of having non-functional types in this work is circumvented by using a unification operation over event and entity variables rather than abstraction/application operations à la λ- calculus, usually used in formal semantics

Semantic Vector Models and Functional Models for Pregroup Grammars.

We show that vector space semantics and functional semantics in two-sorted first order logic are equivalent for pregroup grammars. We present an algorithm that translates functional expressions to vector expressions and vice-versa. The semantics is compositional, variable free and invariant under change of order or multiplicity. It includes the semantic vector models of Information Retrieval Systems and has an interior logic admitting a comprehension schema. A sentence is true in the interior logic if and only if the 'usual' first order formula translating the sentence holds. The examples include negation, universal quantifiers and relative pronouns. © 2011 Springer Science+Business Media B.V

Сучасні тенденції розвитку готельно-ресторанного господарства в Україні

У статті аналізуються питання щодо актуальних методів дослідження тенденцій розвитку готельно-ресторанного господарства. Розглянуто проблематику державного стимулювання даної галузі. Наведено загальні заходи підвищення об’єктивності результатів