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Fellow (1 September 2004 - 30 June 2005)
The main aim of my project at NIAS was to investigate the structure of human reasoning. The topic was divided into three parts: (i) Semiotic dimension: the structure of signs and codes,(ii) Pragmatics dimension: the distinction Semantics - Pragmatics, (iii) Logical dimension: the hierarchy of reasoning.
Work on parts (i) and (ii) is almost finished and has resulted in a manuscript with the provisional title "Logic in Semiotics and Communication". Part (iii) is intended to present the many different types of unfeasible reasoning in a form of generalisation of a logical consequence operation. The results of my research on this subject are presented in a series of papers. I investigate the probabilistic inference "support" of the form: A supports B if and only if the fact that A in this case increases the probability of B. It appears that this relation could be equivalently defined as A supports B if and only if probability of B is higher when A is true, than when A is false. This relationship formalises the accepted notions of corroboration used by philosophers of science as a tool for testing scientific hypotheses. I give its syntactic as well as semantic characterisation. I also present some counter-examples showing that this relation does not satisfy as typical properties for logical consequence operation.
Another paper contains an analysis of the Simpson paradox - an amazing phenomenon of statistics in terms of 'support' relation.
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