Advanced search
1 file | 301.40 KB

An adaptive logic for rational closure

Author
Organization
Project
Contextual and formal-logical approach to scientific problem solving processes
Abstract
In [12] Lehmann and Magidor study a strong nonmonotonic, so-called rational consequence relation, which extends the preferential consequence relation of [10] by also validating the rule of rational monotonicity. Every rational consequence relation can be semantically represented by a ranked model, and vice versa. To answer for a conditional assertion a→b the question whether it is entailed by a set of conditional assertions K, it is not sufficient to check if it is derivable by the rules for rational consequence relations, or semantically, to check if it is valid in all ranked models of K, as it can be shown that the intersection of all ranked models does not in general satisfy rational monotonicity. The authors therefore define a semantic selection in order to obtain the so-called rational closure. However, a proof theory for rational closure is missing. This paper will fill the syntactical gap for a finite language by defining an adaptive logic ARCs such that an assertion a→b is derivable from a knowledge base K containing conditional assertions and negated conditional assertions iff it is in the rational closure of K.
Keywords
rational closure, KLM, adaptive logics, default reasoning, nonmonotonic reasoning

Downloads

    • full text
    • |
    • UGent only
    • |
    • PDF
    • |
    • 301.40 KB

Citation

Please use this url to cite or link to this publication:

Chicago
Strasser, Christian. 2009. “An Adaptive Logic for Rational Closure.” In The Many Sides of Logic, ed. Walter Carnielli, Marcello E Coniglio, and Itala M Loffredo D’Ottaviano, 21:47–67. London, UK: College Publications.
APA
Strasser, C. (2009). An adaptive logic for rational closure. In Walter Carnielli, M. E. Coniglio, & I. M. Loffredo D’Ottaviano (Eds.), The many sides of logic (Vol. 21, pp. 47–67). London, UK: College Publications.
Vancouver
1.
Strasser C. An adaptive logic for rational closure. In: Carnielli W, Coniglio ME, Loffredo D’Ottaviano IM, editors. The many sides of logic. London, UK: College Publications; 2009. p. 47–67.
MLA
Strasser, Christian. “An Adaptive Logic for Rational Closure.” The Many Sides of Logic. Ed. Walter Carnielli, Marcello E Coniglio, & Itala M Loffredo D’Ottaviano. Vol. 21. London, UK: College Publications, 2009. 47–67. Print.
@incollection{1101388,
  abstract     = {In [12] Lehmann and Magidor study a strong nonmonotonic, so-called rational consequence relation, which extends the preferential consequence relation of [10] by also validating the rule of rational monotonicity. Every rational consequence relation can be semantically represented by a ranked model, and vice versa. To answer for a conditional assertion a{\textrightarrow}b the question whether it is entailed by a set of conditional assertions K, it is not sufficient to check if it is derivable by the rules for rational consequence relations, or semantically, to check if it is valid in all ranked models of K, as it can be shown that the intersection of all ranked models does not in general satisfy rational monotonicity. The authors therefore define a semantic selection in order to obtain the so-called rational closure. However, a proof theory for rational closure is missing. This paper will fill the syntactical gap for a finite language by defining an adaptive logic ARCs such that an assertion a{\textrightarrow}b is derivable from a knowledge base K containing conditional assertions and negated conditional assertions iff it is in the rational closure of K.},
  author       = {Strasser, Christian},
  booktitle    = {The many sides of logic},
  editor       = {Carnielli, Walter and Coniglio, Marcello E and Loffredo D'Ottaviano, Itala M},
  isbn         = {9781904987789},
  keyword      = {rational closure,KLM,adaptive logics,default reasoning,nonmonotonic reasoning},
  language     = {eng},
  pages        = {47--67},
  publisher    = {College Publications},
  series       = {Studies in Logic},
  title        = {An adaptive logic for rational closure},
  volume       = {21},
  year         = {2009},
}