Many Valued Generalised Quantifiers for Natural Language in the DisCoCat Model

DisCoCat refers to the Categorical compositional distributional model of natural language, which combines the statistical vector space models of words with the compositional logic-based models of grammar. It is fair to say that despite existing work on incorporating notions of entailment, quantification, and coordination in this setting, a uniform modelling of logical operations is still an open problem. In this report, we take a step towards an answer. We show how one can generalise our previous DisCoCat model of generalised quantifiers from category of sets and relations to category of sets and many valued rations. As a result, we get a fuzzy version of these quantifiers. Our aim is to extend this model to all other logical connectives and develop a fuzzy logic for DisCoCat. The main contributions are showing that category of many valued relations is compact closed, defining appropriate bialgebra structures over it, and demonstrating how one can compute within this setting many valued meanings for quantified sentences.EPSRC Career Acceleration Fellowship EP/J002607/

Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning

Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, the satisfaction of which is parametrized by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided.Comment: 36 page

A Bibliography on Fuzzy Automata, Grammars and Lanuages

This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing

Fuzzy Bigraphs: An Exercise in Fuzzy Communicating Agents

Bigraphs and their algebra is a model of concurrency. Fuzzy bigraphs are a generalization of birgraphs intended to be a model of concurrency that incorporates vagueness. More specifically, this model assumes that agents are similar, communication is not perfect, and, in general, everything is or happens to some degree.Comment: 11 pages, 3 figure

Neuro-fuzzy knowledge processing in intelligent learning environments for improved student diagnosis

In this paper, a neural network implementation for a fuzzy logic-based model of the diagnostic process is proposed as a means to achieve accurate student diagnosis and updates of the student model in Intelligent Learning Environments. The neuro-fuzzy synergy allows the diagnostic model to some extent "imitate" teachers in diagnosing students' characteristics, and equips the intelligent learning environment with reasoning capabilities that can be further used to drive pedagogical decisions depending on the student learning style. The neuro-fuzzy implementation helps to encode both structured and non-structured teachers' knowledge: when teachers' reasoning is available and well defined, it can be encoded in the form of fuzzy rules; when teachers' reasoning is not well defined but is available through practical examples illustrating their experience, then the networks can be trained to represent this experience. The proposed approach has been tested in diagnosing aspects of student's learning style in a discovery-learning environment that aims to help students to construct the concepts of vectors in physics and mathematics. The diagnosis outcomes of the model have been compared against the recommendations of a group of five experienced teachers, and the results produced by two alternative soft computing methods. The results of our pilot study show that the neuro-fuzzy model successfully manages the inherent uncertainty of the diagnostic process; especially for marginal cases, i.e. where it is very difficult, even for human tutors, to diagnose and accurately evaluate students by directly synthesizing subjective and, some times, conflicting judgments