45,571 research outputs found
Conditional Ranking Revision - Iterated Revision with Sets of Conditionals
In the context of a general framework for belief dynamics which interprets revision as doxastic constraint satisfaction, we discuss a proposal for revising quasi-probabilistic belief measures with finite sets of graded conditionals. The belief states are ranking measures with divisible values (generalizing Spohn's epistemology), and the conditionals are interpreted as ranking constraints. The approach is inspired by the minimal information paradigm and based on the principle-guided canonical construction of a ranking model of the input conditionals. This is achieved by extending techniques known from conditional default reasoning. We give an overview of how it handles different principles for conditional and parallel revision and compare it with similar accounts
The lexicographic closure as a revision process
The connections between nonmonotonic reasoning and belief revision are
well-known. A central problem in the area of nonmonotonic reasoning is the
problem of default entailment, i.e., when should an item of default information
representing "if A is true then, normally, B is true" be said to follow from a
given set of items of such information. Many answers to this question have been
proposed but, surprisingly, virtually none have attempted any explicit
connection to belief revision. The aim of this paper is to give an example of
how such a connection can be made by showing how the lexicographic closure of a
set of defaults may be conceptualised as a process of iterated revision by sets
of sentences. Specifically we use the revision process of Nayak.Comment: 7 pages, Nonmonotonic Reasoning Workshop 2000 (special session on
belief change), at KR200
Space Efficiency of Propositional Knowledge Representation Formalisms
We investigate the space efficiency of a Propositional Knowledge
Representation (PKR) formalism. Intuitively, the space efficiency of a
formalism F in representing a certain piece of knowledge A, is the size of the
shortest formula of F that represents A. In this paper we assume that knowledge
is either a set of propositional interpretations (models) or a set of
propositional formulae (theorems). We provide a formal way of talking about the
relative ability of PKR formalisms to compactly represent a set of models or a
set of theorems. We introduce two new compactness measures, the corresponding
classes, and show that the relative space efficiency of a PKR formalism in
representing models/theorems is directly related to such classes. In
particular, we consider formalisms for nonmonotonic reasoning, such as
circumscription and default logic, as well as belief revision operators and the
stable model semantics for logic programs with negation. One interesting result
is that formalisms with the same time complexity do not necessarily belong to
the same space efficiency class
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