Compactness properties of nonmonotonic inference operations

2005 ◽  
pp. 19-33 ◽  
Author(s):  
Heinrich Herre
Keyword(s):  
Nonmonotonic Inference

scholarly journals Revision and Conditional Inference for Abstract Dialectical Frameworks

2021 ◽  
Author(s):  
Jesse Heyninck ◽  
Gabriele Kern-Isberner ◽  
Tjitze Rienstra ◽  
Kenneth Skiba ◽  
Matthias Thimm
Keyword(s):  
Belief Revision ◽  
Research Topic ◽  
Conditional Inference ◽  
Ramsey Test ◽  
The One ◽  
Exact Relationship ◽  
Nonmonotonic Inference ◽  
Total Preorder

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

Belief contraction as nonmonotonic inference

2000 ◽  
Vol 65 (2) ◽  
pp. 605-626 ◽  
Author(s):  
Alexander Bochman
Keyword(s):  
Belief Change ◽  
Epistemic State ◽  
Belief Contraction ◽  
Nonmonotonic Inference

AbstractA notion of an epistemic state is introduced as a generalization of common representations suggested for belief change. Based on it, a new kind of nonmonotonic inference relation corresponding to belief contractions is defined. A number of representation results is established that cover both traditional AGM contractions and contractions that do not satisfy recovery.

scholarly journals InfOCF-Web: An Online Tool for Nonmonotonic Reasoning with Conditionals and Ranking Functions

2021 ◽  
Author(s):  
Steven Kutsch ◽  
Christoph Beierle
Keyword(s):  
Nonmonotonic Reasoning ◽  
Minimal Models ◽  
Ranking Functions ◽  
Online Tool ◽  
Ranking Models ◽  
Conditional Knowledge ◽  
System P ◽  
Nonmonotonic Inference

InfOCF-Web provides implementations of system P and system Z inference, and of inference relations based on c-representation with respect to various inference modes and different classes of minimal models. It has an easy-to-use online interface for computing ranking models of a conditional knowledge R, and for answering queries and comparing inference results of nonmonotonic inference relations induced by R.

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