For a Data-Driven Interpretation of Rules wrt GMP Conclusions in Abductive Problems

International audienceAbductive reasoning is an explanatory process in which potential causes of an observation are unearthed. In its classical – crisp – version it offers little lattitude for discovery of new knowledge. Placed in a fuzzy context, abduction can explain observations which did not, originally, exactly match the expected conclusions. Studying the effects of slight modifications through the use of linguistic modifiers was, therefore , of interest in order to describe the extent to which observations can be modified yet still explained and, possibly, create new knowledge. We will concentrate on the formal definition of fuzzy abduction given by Mellouli and Bouchon-Meunier. Our results will be shown to be incompatible with established theories. We will show where this incompatibility comes from and derive from it a selection of fuzzy implication , based on observable data

Interpolative and extrapolative reasoning in propositional theories using qualitative knowledge about conceptual spaces

International audienceMany logical theories are incomplete, in the sense that non-trivial conclusions about particular situations cannot be derived from them using classical deduction. In this paper, we show how the ideas of interpolation and extrapolation, which are of crucial importance in many numerical domains, can be applied in symbolic settings to alleviate this issue in the case of propositional categorization rules. Our method is based on (mainly) qualitative descriptions of how different properties are conceptually related, where we identify conceptual relations between properties with spatial relations between regions in Gärdenfors conceptual spaces. The approach is centred around the view that categorization rules can often be seen as approximations of linear (or at least monotonic) mappings between conceptual spaces. We use this assumption to justify that whenever the antecedents of a number of rules stand in a relationship that is invariant under linear (or monotonic) transformations, their consequents should also stand in that relationship. A form of interpolative and extrapolative reasoning can then be obtained by applying this idea to the relations of betweenness and parallelism respectively. After discussing these ideas at the semantic level, we introduce a number of inference rules to characterize interpolative and extrapolative reasoning at the syntactic level, and show their soundness and completeness w.r.t. the proposed semantics. Finally, we show that the considered inference problems are PSPACE-hard in general, while implementations in polynomial time are possible under some relatively mild assumptions

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Analyzing The Impact Of Social Factors On Homelessness: A Fuzzy Cognitive Map Approach

Background The forces which affect homelessness are complex and often interactive in nature. Social forces such as addictions, family breakdown, and mental illness are compounded by structural forces such as lack of available low-cost housing, poor economic conditions, and insufficient mental health services. Together these factors impact levels of homelessness through their dynamic relations. Historic models, which are static in nature, have only been marginally successful in capturing these relationships. Methods Fuzzy Logic (FL) and fuzzy cognitive maps (FCMs) are particularly suited to the modeling of complex social problems, such as homelessness, due to their inherent ability to model intricate, interactive systems often described in vague conceptual terms and then organize them into a specific, concrete form (i.e., the FCM) which can be readily understood by social scientists and others. Using FL we converted information, taken from recently published, peer reviewed articles, for a select group of factors related to homelessness and then calculated the strength of influence (weights) for pairs of factors. We then used these weighted relationships in a FCM to test the effects of increasing or decreasing individual or groups of factors. Results of these trials were explainable according to current empirical knowledge related to homelessness. Results Prior graphic maps of homelessness have been of limited use due to the dynamic nature of the concepts related to homelessness. The FCM technique captures greater degrees of dynamism and complexity than static models, allowing relevant concepts to be manipulated and interacted. This, in turn, allows for a much more realistic picture of homelessness. Through network analysis of the FCM we determined that Education exerts the greatest force in the model and hence impacts the dynamism and complexity of a social problem such as homelessness. Conclusions The FCM built to model the complex social system of homelessness reasonably represented reality for the sample scenarios created. This confirmed that the model worked and that a search of peer reviewed, academic literature is a reasonable foundation upon which to build the model. Further, it was determined that the direction and strengths of relationships between concepts included in this map are a reasonable approximation of their action in reality. However, dynamic models are not without their limitations and must be acknowledged as inherently exploratory