Expansion and Contraction of Finite States

We present a theory that copes with the dynamics of inconsistent information. A method is set forth to represent possibly inconsistent information by a finite state. Next, finite operations for expansion and contraction of finite states are given. No extra-logical element — a choice function or an ordering over (sets of) sentences — is presupposed in the definition of contraction. Moreover, expansion and contraction are each other's duals. AGM-style characterizations of these operations follow.

[1]  Peter Gärdenfors,et al.  Knowledge in Flux , 1988 .

[2]  Newton C. A. da Costa,et al.  Belief change and inconsistency , 1998 .

[3]  Peter Jackson,et al.  Partial monotonicity and a new version of the Ramsey test , 1992, Stud Logica.

[4]  André Fuhrmann,et al.  Theory contraction through base contraction , 1991, J. Philos. Log..

[5]  Renata Wassermann Resource Bounded Belief Revision , 1999 .

[6]  David Makinson,et al.  On the status of the postulate of recovery in the logic of theory change , 1987, J. Philos. Log..

[7]  SVEN OVE HANSSON,et al.  Reversing the Levi identity , 1993, J. Philos. Log..

[8]  Sven Ove Hansson,et al.  Levi Contractions and AGM Contractions: a Comparison , 1995, Notre Dame J. Formal Log..

[9]  Sven Ove Hansson Editorial: Belief Revision Theory Today , 1998, J. Log. Lang. Inf..

[10]  Richard Routley,et al.  The Semantics of First Degree Entailment , 1972 .

[11]  Nicholas Rescher,et al.  The logic of inconsistency , 1979 .

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

[13]  Rohit Parikh,et al.  Relevance sensitive belief structures , 2000, Annals of Mathematics and Artificial Intelligence.

[14]  Edwin D. Mares,et al.  A Paraconsistent Theory Of Belief Revision , 2002 .

[15]  Koji Tanaka,et al.  A Natural Deduction System for First Degree Entailment , 1999, Notre Dame J. Formal Log..

[16]  Peter Gärdenfors,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985, Journal of Symbolic Logic.

[17]  J. Dunn,et al.  Intuitive semantics for first-degree entailments and ‘coupled trees’ , 1976 .

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

[19]  John K. Slaney,et al.  Realistic Belief Revision , 1995, WOCFAI.

[20]  Gustav Bergmann,et al.  PHILOSOPHICAL STUDIES , 1927, Philosophy.

[21]  Allard Tamminga,et al.  Belief Dynamics: (Epistemo)logical Investigations , 2001 .

[22]  W. Salmon,et al.  Knowledge in Flux , 1991 .