2 research outputs found
Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus
The Distributional Compositional Categorical (DisCoCat) model is a
mathematical framework that provides compositional semantics for meanings of
natural language sentences. It consists of a computational procedure for
constructing meanings of sentences, given their grammatical structure in terms
of compositional type-logic, and given the empirically derived meanings of
their words. For the particular case that the meaning of words is modelled
within a distributional vector space model, its experimental predictions,
derived from real large scale data, have outperformed other empirically
validated methods that could build vectors for a full sentence. This success
can be attributed to a conceptually motivated mathematical underpinning, by
integrating qualitative compositional type-logic and quantitative modelling of
meaning within a category-theoretic mathematical framework.
The type-logic used in the DisCoCat model is Lambek's pregroup grammar.
Pregroup types form a posetal compact closed category, which can be passed, in
a functorial manner, on to the compact closed structure of vector spaces,
linear maps and tensor product. The diagrammatic versions of the equational
reasoning in compact closed categories can be interpreted as the flow of word
meanings within sentences. Pregroups simplify Lambek's previous type-logic, the
Lambek calculus, which has been extensively used to formalise and reason about
various linguistic phenomena. The apparent reliance of the DisCoCat on
pregroups has been seen as a shortcoming. This paper addresses this concern, by
pointing out that one may as well realise a functorial passage from the
original type-logic of Lambek, a monoidal bi-closed category, to vector spaces,
or to any other model of meaning organised within a monoidal bi-closed
category. The corresponding string diagram calculus, due to Baez and Stay, now
depicts the flow of word meanings.Comment: 29 pages, pending publication in Annals of Pure and Applied Logi
A framework for analyzing changes in health care lexicons and nomenclatures
Ontologies play a crucial role in current web-based biomedical applications for capturing contextual knowledge in the domain of life sciences. Many of the so-called bio-ontologies and controlled vocabularies are known to be seriously defective from both terminological and ontological perspectives, and do not sufficiently comply with the standards to be considered formai ontologies. Therefore, they are continuously evolving in order to fix the problems and provide valid knowledge. Moreover, many problems in ontology evolution often originate from incomplete knowledge about the given domain. As our knowledge improves, the related definitions in the ontologies will be altered. This problem is inadequately addressed by available tools and algorithms, mostly due to the lack of suitable knowledge representation formalisms to deal with temporal abstract notations, and the overreliance on human factors. Also most of the current approaches have been focused on changes within the internal structure of ontologies, and interactions with other existing ontologies have been widely neglected. In this research, alter revealing and classifying some of the common alterations in a number of popular biomedical ontologies, we present a novel agent-based framework, RLR (Represent, Legitimate, and Reproduce), to semi-automatically manage the evolution of bio-ontologies, with emphasis on the FungalWeb Ontology, with minimal human intervention. RLR assists and guides ontology engineers through the change management process in general, and aids in tracking and representing the changes, particularly through the use of category theory. Category theory has been used as a mathematical vehicle for modeling changes in ontologies and representing agents' interactions, independent of any specific choice of ontology language or particular implementation. We have also employed rule-based hierarchical graph transformation techniques to propose a more specific semantics for analyzing ontological changes and transformations between different versions of an ontology, as well as tracking the effects of a change in different levels of abstractions. Thus, the RLR framework enables one to manage changes in ontologies, not as standalone artifacts in isolation, but in contact with other ontologies in an openly distributed semantic web environment. The emphasis upon the generality and abstractness makes RLR more feasible in the multi-disciplinary domain of biomedical Ontology change management