A Formal Logic for Abductive Reasoning

This paper presents and illustrates a formal logic for the abduction of singular hypotheses. The logic has a semantics and a dynamic proof theory that is sound and complete with respect to the semantics. The logic presupposes that, with respect to a specific application, the set of explananda and the set of possible explanantia are disjoint (but not necessarily exhaustive). Where an explanandum can be explained by different explanantia, the logic allows only for the abduction of their disjunction.

[1]  Maarten Van Dyck,et al.  Ampliative Adaptive Logics and the Foundation of Logic-Based Approaches to Abduction , 2002 .

[2]  Jaakko Hintikka,et al.  What is Abduction? The Fundamental Problem of Contemporary Epistemology , 1999 .

[3]  D. Batens,et al.  Pushing the Search Paths in the Proofs. A Study in Proof Heuristics , 2003 .

[4]  Jon Williamson,et al.  Abduction, Reason, and Science: Processes of Discovery and Explanation , 2003 .

[5]  Diderik Batens,et al.  Blocks: the clue to dynamic aspects of logic , 1997 .

[6]  Diderik Batens.  A Dynamic Characterization of the Pure Logic of Relevant Implication , 2001, J. Philos. Log..

[7]  Diderik Batens,et al.  A Universal Logic Approach to Adaptive Logics , 2007, Logica Universalis.

[8]  Diderik Batens,et al.  Shortcuts and Dynamic Marking in the Tableau Method for Adaptive Logics , 2001, Stud Logica.

[9]  Diderik Batens,et al.  A survey of inconsistency-adaptive logics , 2000 .

[10]  D. Batens.  A General Characterization of Adaptive Logics , 2001 .

[11]  D. Batens,et al.  On Classical Adaptive Logics of Induction , 2003 .

[12]  P. Thagard,et al.  How Scientists Explain Disease , 1999 .

[13]  Atocha Aliseda-Llera,et al.  Seeking explanations: abduction in logic, philosophy of science and artificial intelligence , 1998 .

[14]  Lorenzo Magnani,et al.  Model-Based Creative Abduction , 1999 .

[15]  Jürg Kohlas,et al.  Handbook of Defeasible Reasoning and Uncertainty Management Systems , 2000 .

[16]  Diderik Batens.  A procedural criterion for final derivability in inconsistency-adaptive logics , 2005, J. Appl. Log..

[17]  Gabriele Paul,et al.  AI approaches to abduction , 2000 .

[18]  Diderik Batens,et al.  Recent results by the inconsistency-adaptive labourers. , 2007 .

[19]  Diderik Batens.  The Need for Adaptive Logics In Epistemology , 2004, Logic, Epistemology, and the Unity of Science.

[20]  P. Thagard,et al.  Computational Philosophy of Science , 1988 .

[21]  Diderik Batens,et al.  A Tableau Method for Inconsistency-Adaptive Logics , 2000, TABLEAUX.