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/

A synthesis of logic and bio-inspired techniques in the design of dependable systems

Much of the development of model-based design and dependability analysis in the design of dependable systems, including software intensive systems, can be attributed to the application of advances in formal logic and its application to fault forecasting and verification of systems. In parallel, work on bio-inspired technologies has shown potential for the evolutionary design of engineering systems via automated exploration of potentially large design spaces. We have not yet seen the emergence of a design paradigm that effectively combines these two techniques, schematically founded on the two pillars of formal logic and biology, from the early stages of, and throughout, the design lifecycle. Such a design paradigm would apply these techniques synergistically and systematically to enable optimal refinement of new designs which can be driven effectively by dependability requirements. The paper sketches such a model-centric paradigm for the design of dependable systems, presented in the scope of the HiP-HOPS tool and technique, that brings these technologies together to realise their combined potential benefits. The paper begins by identifying current challenges in model-based safety assessment and then overviews the use of meta-heuristics at various stages of the design lifecycle covering topics that span from allocation of dependability requirements, through dependability analysis, to multi-objective optimisation of system architectures and maintenance schedules

On fuzzy reasoning schemes

In this work we provide a short survey of the most frequently used fuzzy reasoning schemes. The paper is organized as follows: in the first section we introduce the basic notations and definitions needed for fuzzy inference systems; in the second section we explain how the GMP works under Mamdani, Larsen and G¨odel implications, furthermore we discuss the properties of compositional rule of inference with several fuzzy implications; and in the third section we describe Tsukamoto’s, Sugeno’s and the simplified fuzzy inference mechanisms in multi-input-single-output fuzzy systems

Simulation of complex environments:the Fuzzy Cognitive Agent

The world is becoming increasingly competitive by the action of liberalised national and global markets. In parallel these markets have become increasingly complex making it difficult for participants to optimise their trading actions. In response, many differing computer simulation techniques have been investigated to develop either a deeper understanding of these evolving markets or to create effective system support tools. In this paper we report our efforts to develop a novel simulation platform using fuzzy cognitive agents (FCA). Our approach encapsulates fuzzy cognitive maps (FCM) generated on the Matlab Simulink platform within commercially available agent software. We firstly present our implementation of Matlab Simulink FCMs and then show how such FCMs can be integrated within a conceptual FCA architecture. Finally we report on our efforts to realise an FCA by the integration of a Matlab Simulink based FCM with the Jack Intelligent Agent Toolkit

Designing Software Architectures As a Composition of Specializations of Knowledge Domains

This paper summarizes our experimental research and software development activities in designing robust, adaptable and reusable software architectures. Several years ago, based on our previous experiences in object-oriented software development, we made the following assumption: ‘A software architecture should be a composition of specializations of knowledge domains’. To verify this assumption we carried out three pilot projects. In addition to the application of some popular domain analysis techniques such as use cases, we identified the invariant compositional structures of the software architectures and the related knowledge domains. Knowledge domains define the boundaries of the adaptability and reusability capabilities of software systems. Next, knowledge domains were mapped to object-oriented concepts. We experienced that some aspects of knowledge could not be directly modeled in terms of object-oriented concepts. In this paper we describe our approach, the pilot projects, the experienced problems and the adopted solutions for realizing the software architectures. We conclude the paper with the lessons that we learned from this experience

An artificial immune systems based predictive modelling approach for the multi-objective elicitation of Mamdani fuzzy rules: a special application to modelling alloys

In this paper, a systematic multi-objective Mamdani fuzzy modeling approach is proposed, which can be viewed as an extended version of the previously proposed Singleton fuzzy modeling paradigm. A set of new back-error propagation (BEP) updating formulas are derived so that they can replace the old set developed in the singleton version. With the substitution, the extension to the multi-objective Mamdani Fuzzy Rule-Based Systems (FRBS) is almost endemic. Due to the carefully chosen output membership functions, the inference and the defuzzification methods, a closed form integral can be deducted for the defuzzification method, which ensures the efficiency of the developed Mamdani FRBS. Some important factors, such as the variable length coding scheme and the rule alignment, are also discussed. Experimental results for a real data set from the steel industry suggest that the proposed approach is capable of eliciting not only accurate but also transparent FRBS with good generalization ability