A procedural criterion for final derivability in inconsistency-adaptive logics

Abstract This paper concerns a (prospective) goal directed proof procedure for the propositional fragment of the inconsistency-adaptive logic ACLuN1. At the propositional level, the procedure forms an algorithm for final derivability. If extended to the predicative level, it provides a criterion for final derivability. This is essential in view of the absence of a positive test. The procedure may be generalized to all flat adaptive logics.

[1]  Friedrich Stadler,et al.  Induction and Deduction in the Sciences , 2004 .

[2]  Joke Meheus,et al.  Erotetic Arguments from Inconsistent Premises. , 1999 .

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

[4]  Graham Priest,et al.  Paraconsistent Logic: Essays on the Inconsistent , 1990 .

[5]  Guido Vanackere,et al.  HL2, an Inconsistency-adaptive and Inconsistency-resolving Logic for General Statements that might have Exceptions , 2000, J. Appl. Non Class. Logics.

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

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

[8]  Gerhard Brewka,et al.  Nonmonotonic Reasoning: Logical Foundations of Commonsense By Gerhard Brewka (Cambridge University Press, 1991) , 1991, SGAR.

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

[10]  Guido Vanackere Preferences as inconsistency-resolvers: an Inconsistency-adaptive Tool , 2001 .

[11]  Diderik Batens A Strengthening of the Rescher--Manor Consequence Relations , 2003 .

[12]  George Boolos,et al.  Computability and logic , 1974 .

[13]  Diderik Batens Frontiers of Paraconsistent Logic , 2000 .

[14]  Newton C. A. da Costa,et al.  The Logic of Pragmatic Truth , 1998, J. Philos. Log..

[15]  Didier Dubois,et al.  Some Syntactic Approaches to the Handling of Inconsistent Knowledge Bases: A Comparative Study Part 1: The Flat Case , 1997, Stud Logica.

[16]  Nicholas Rescher,et al.  On Inferences from Inconsistent Premises , 1970 .

[17]  J. Meheus Adaptive Logics and the Integration of Induction and Deduction , 2004 .

[18]  Joseph C. Pitt,et al.  Change and Progress in Modern Science , 1984 .

[19]  Diderik Batens,et al.  Zero logic adding up to classical logic , 1999 .

[20]  Diderik Batens,et al.  Direct Dynamic Proofs for the Rescher–Manor Consequence Relations: The Flat Case , 2002, J. Appl. Non Class. Logics.

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

[22]  Torsten Schaub,et al.  Signed Systems for Paraconsistent Reasoning , 1998, Journal of Automated Reasoning.

[23]  Joke Meheus An adaptive logic for pragmatic truth , 2002 .

[24]  D. Batens TOWARDS THE UNIFICATION OF INCONSISTENCY HANDLING MECHANISMS , 2004 .

[25]  T. Kuipers From Instrumentalism to Constructive Realism: On Some Relations between Confirmation, Empirical Progress, and Truth Approximation , 2000 .

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

[27]  N. Rescher,et al.  On inference from inconsistent premisses , 1970 .

[28]  R. Smullyan First-Order Logic , 1968 .

[29]  Grigoris Antoniou,et al.  Nonmonotonic reasoning , 1997 .

[30]  Joke Meheus,et al.  Empirical progress and ampliative adaptive logics. , 2005 .

[31]  Anthony Hunter,et al.  Paraconsistent logics , 1998 .

[32]  Andrzej Wiśniewski,et al.  The posing of questions , 1995 .

[33]  Vito F. Sinisi,et al.  Entailment: The Logic of Relevance and Necessity , 1996 .

[34]  H. Rasiowa,et al.  Logic at work : essays dedicated to the memory of Helena Rasiowa , 1999 .

[35]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[36]  P. Damerow,et al.  Exploring the limits of preclassical mechanics , 1991 .

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

[38]  Arnon Avron,et al.  A Formula-Preferential Base for Paraconsistent and Plausible Reasoning Systems , 2001 .

[39]  Liza Verhoeven Proof Theories for Some Prioritized Consequence Relations , 2003 .

[40]  Witold Łukaszewicz Non-monotonic reasoning : formalization of commonsense reasoning , 1990 .

[41]  Newton C. A. da Costa,et al.  Pragmatic truth and approximation to truth , 1986, Journal of Symbolic Logic.

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

[43]  Diderik Batens Inconsistency-Adaptive Logics , 1999 .

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

[45]  J. Meheus Adaptive logic in scientific discovery: the case of Clausius , 1993 .

[46]  Dov M. Gabbay,et al.  Handbook of defeasible reasoning and uncertainty management systems: Volume 4 abductive reasoning and learning , 2000 .

[47]  Joke Meheus Adaptive Logics for Question Evocation , 2001 .

[48]  Kristof de Clercq,et al.  Two new strategies for inconsistency-adaptive logics , 2004 .

[49]  D. Batens MEANING, ACCEPTANCE AND DIALECTICS* , 1985 .

[50]  Lorenzo Magnani,et al.  Logical and Computational Aspects of Model-Based Reasoning , 2002 .

[51]  L. R. Harris Hypothetical reasoning , 1989 .

[52]  Itala M. Loffredo D'Ottaviano,et al.  Paraconsistency: The Logical Way to the Inconsistent , 2002 .

[53]  Andrzej Wiśniewski,et al.  The posing of questions : logical foundations of erotetic inferences , 1995 .

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

[55]  Nuel D. Belnap,et al.  Entailment : the logic of relevance and necessity , 1975 .

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

[57]  Diderik Batens Inconsistency-adaptive logies and the foundation of non-monotonic logic , 1994 .

[58]  Guido Vanackere,et al.  Preferences as inconsistency-resolvers: The Inconsistency-adaptive Logic PRL , 2004 .