Abstract
The present research project consists of three large interrelated spheres, called `tasks'. These three tasks will support the main issues to be addressed, related to the notions of consistency, contradiction and evidence, which, together with their probabilistic interpretations, aim at reaching a more solid position on the general philosophy of paraconsistency, its understanding, its impact and its importance in the philosophy of science and in the philosophy of mathematics. Task I: Evidence, Probability and Logic intends to investigate probabilistic and possibilistic semantics, emphasizing some specially designed new logical systems, including the generalization of such ideas towards plausibility measures (\cite{fried-halpner:1995}) and (\cite{halpern:2001}). Task II: Non-Deterministic Methods: Hyperalgebraic Structures, Modalities, and Extensions of Probabilities aims to develop and apply results obtained from a multialgebra theory to specific logical systems and to the theory of probabilities;Task III: Contradictions, Evidence and Truth: Towards a Global Philosophy of Paraconsistency seeks to investigate technical and philosophical aspects of an epistemic approach to paraconsistency. The three tasks will support the general objectives of the present project, which are the study of the various aspects of formal rationality, logic and probability with special emphasis on new methods of algebra, semantics and probability theory, involving expansions of standard logic systems to non-classical logics. (AU)
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