Jacek Malinowski, born in Pabianice, Poland, in 1959. Ph.D. from the Institute of Philosophy and Sociology, Polish Academy of Sciences, Warsaw. Associate Professor at the Institute of Philosophy and Sociology at the Polish Academy of Sciences, Warsaw, and at the Department of Logic and Semiotics, Nicolas Copernicus University, Torun.
Fellow (1 September 2004 – 30 June 2005)
GENERALISED CONSEQUENCE OPERATIONS: A LOGICAL FRAMEWORK FOR COMMONSENSE REASONING
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.