Skip Navigation

Journal of Logic and Computation 2001 11(2):229-256; doi:10.1093/logcom/11.2.229
© 2001 by Oxford University Press
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (8)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Lehmann, D.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Original Article

Nonmonotonic Logics and Semantics

Daniel Lehmann1

1 School of Engineering and Computer Science, Hebrew University Jerusalem, 91904 Israel. E-mail: lehmann{at}cs.huji.ac.il

Tarski gave a general semantics for deductive reasoning: a formula {alpha} may be deduced from a set A of formulas iff {alpha} holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula {alpha} may be deduced from a set A of formulas iff {alpha} holds in all of the preferred models in which all the elements of A hold. Shoham proposed that the notion of preferred models be defined by a partial ordering on the models of the underlying language. A more general semantics is described in this paper, based on a set of natural properties of choice functions. This semantics is here shown to be equivalent to a semantics based on comparing the relative importance of sets of models, by what amounts to a qualitative probability measure. The consequence operations defined by the equivalent semantics are then characterized by a weakening of Tarski's properties in which the monotonicity requirement is replaced by three weaker conditions. Classical propositional connectives are characterized by natural introduction-elimination rules in a nonmonotonic setting. Even in the nonmonotonic setting, one obtains classical propositional logic, thus showing that monotonicity is not required to justify classical propositional connectives.

Keywords: Nonmonotonic logics; nonmonotonic reasoning; choice functions; qualitative probability measures

Received 18 June 1999.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.