Induction, complexity, and economic methodology

This paper focuses on induction, because the supposed weaknesses of that process are the main reason for favouring falsificationism, which plays an important part in scientific methodology generally; the paper is part of a wider study of economic methodology. The standard objections to, and paradoxes of, induction are reviewed, and this leads to the conclusion that the supposed ‘problem’ or ‘riddle’ of induction is a false one. It is an artefact of two assumptions: that the classic two-valued logic (CL) is appropriate for the contexts in which induction is relevant; and that it is the touchstone of rational thought. The status accorded to CL is the result of historical and cultural factors. The material we need to reason about falls into four distinct domains; these are explored in turn, while progressively relaxing the restrictions that are essential to the valid application of CL. The restrictions include the requirement for a pre-existing, independently-guaranteed classification, into which we can fit all new cases with certainty; and non-ambiguous relationships between antecedents and consequents. Natural kinds, determined by the existence of complex entities whose characteristics cannot be unbundled and altered in a piecemeal, arbitrary fashion, play an important part in the review; so also does fuzzy logic (FL). These are used to resolve two famous paradoxes about induction (the grue and raven paradoxes); and the case for believing that conventional logic is a subset of fuzzy logic is outlined. The latter disposes of all questions of justifying induction deductively. The concept of problem structure is used as the basis for a structured concept of rationality that is appropriate to all four of the domains mentioned above. The rehabilitation of induction supports an alternative definition of science: that it is the business of developing networks of contrastive, constitutive explanations of reproducible, inter-subjective (‘objective’) data. Social and psychological obstacles ensure the progress of science is slow and convoluted; however, the relativist arguments against such a project are rejected.induction; economics; methodology; complexity

CBR and MBR techniques: review for an application in the emergencies domain

The purpose of this document is to provide an in-depth analysis of current reasoning engine practice and the integration strategies of Case Based Reasoning and Model Based Reasoning that will be used in the design and development of the RIMSAT system. RIMSAT (Remote Intelligent Management Support and Training) is a European Commission funded project designed to: a.. Provide an innovative, 'intelligent', knowledge based solution aimed at improving the quality of critical decisions b.. Enhance the competencies and responsiveness of individuals and organisations involved in highly complex, safety critical incidents - irrespective of their location. In other words, RIMSAT aims to design and implement a decision support system that using Case Base Reasoning as well as Model Base Reasoning technology is applied in the management of emergency situations. This document is part of a deliverable for RIMSAT project, and although it has been done in close contact with the requirements of the project, it provides an overview wide enough for providing a state of the art in integration strategies between CBR and MBR technologies.Postprint (published version

A comparison of techniques for learning and using mathematics and a study of their relationship to logical principles

Various techniques exist for learning mathematical concepts, like experimentation and exploration, respectively using mathematics, like modelling and simulation. For a clear application of such techniques in mathematics education, there should be a clear distinction between these techniques. A recently developed theory of fuzzy concepts can be applied to analyse the four mentioned concepts. For all four techniques one can pose the question of their relationship to deduction, induction and abduction as logical principles. An empirical study was conducted with 12-13 aged students, aiming at checking the three reasoning processes

Retraction and Generalized Extension of Computing with Words

Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input alphabet consists of all fuzzy subsets of a set of symbols, as a formal model of computing with all words. In this paper, we introduce a somewhat general formal model of computing with (some special) words. The new features of the model are that the input alphabet only comprises some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily. By employing the methodology of fuzzy control, we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with words. Some algebraic properties of retractions and generalized extensions are addressed as well.Comment: 13 double column pages; 3 figures; to be published in the IEEE Transactions on Fuzzy System

An annotation scheme and gold standard for Dutch-English word alignment

The importance of sentence-aligned parallel corpora has been widely acknowledged. Reference corpora in which sub-sentential translational correspondences are indicated manually are more labour-intensive to create, and hence less wide-spread. Such manually created reference alignments - also called Gold Standards - have been used in research projects to develop or test automatic word alignment systems. In most translations, translational correspondences are rather complex; for example word-by-word correspondences can be found only for a limited number of words. A reference corpus in which those complex translational correspondences are aligned manually is therefore also a useful resource for the development of translation tools and for translation studies. In this paper, we describe how we created a Gold Standard for the Dutch-English language pair. We present the annotation scheme, annotation guidelines, annotation tool and inter-annotator results. To cover a wide range of syntactic and stylistic phenomena that emerge from different writing and translation styles, our Gold Standard data set contains texts from different text types. The Gold Standard will be publicly available as part of the Dutch Parallel Corpus