Nonmonotonic reasoning from conditional knowledge bases with system W
type: Item
instance of: scholarly article
title: Nonmonotonic reasoning from conditional knowledge bases with system W
author: Christian Komo
author: C. Beierle
published in: Annals of Mathematics and Artificial Intelligence
publication date: 2022-02-14T00:00:00Z
review text: This is an article in the context of defeasible reasoning. Intuitively, knowledge bases comprise conditional axioms to express that truth of an expression ``usually'' implies truth of another expression, leaving anyhow the possibility for the second expression to not hold. A preference over the possible interpretations, or worlds, for such knowledge bases is usually employed to define a meaningful form of reasoning, as intuitively is expected that worlds satisfying more conditional axioms are more plausible than others. The specific preference relation that is adopted actually characterizes the resulting reasoning system, as for example one may opt for several different types of quantitative or qualitative preference relations. The first part of this article focuses on ranking functions, which essentially assign a natural number, called rank, to each model of the knowledge base's input, so that models with the lowest rank are preferred over the others. In such a context, an interesting question to gain insight into the complexity of the problem, and therefore to understand what can be a reasonable solving strategy, is \textit{what can be an upper bound on the rank to consider?} An interesting result in this direction is shown in Section 7, where the authors present a construction obtaining a knowledge base for which a ranking function presented in the literature needs rank values exponential with respect to the number of conditional axioms in the input knowledge base. I found such a result interesting in the light that the upper bound was actually conjectured to be linear, and some experimental assessment was confirming the conjecture. In the second part of the article, the authors come up with a different semantics for knowledge bases comprising conditional axioms, which is named \textit{system W} and is not based on ranking functions. Actually, the authors formally prove that the inference system W cannot be characterized by any ranking function. At the same level…
reviewed by: M. Alviano
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 68T30
Mathematics Subject Classification ID: 68T37
zbMATH DE Number: 7473196
zbMATH Keywords: conditional
zbMATH Keywords: conditional knowledge base
zbMATH Keywords: nonmonotonic inference
zbMATH Keywords: system P
zbMATH Keywords: system Z
zbMATH Keywords: C-representation
zbMATH Keywords: C-inference
zbMATH Keywords: constraint satisfaction problem
zbMATH Keywords: system W
describes a project that uses: InfOCF-Web
MaRDI profile type: Publication
full work available at URL: s10472-021-09777-9
OpenAlex ID: W4200057034
cites work: The logic of conditionals. An application of probability to deductive logic
cites work: Skeptical Inference Based on C-Representations and Its Characterization as a Constraint Satisfaction Problem
cites work: Q4576240
cites work: Properties of skeptical c-inference for conditional knowledge bases and its realization as a constraint satisfaction problem
cites work: Properties and interrelationships of skeptical, weakly skeptical, and credulous inference induced by classes of minimal models
cites work: Semantical investigations into nonmonotonic and probabilistic logics
cites work: Compilation of static and evolving conditional knowledge bases for computing induced nonmonotonic inference relations
cites work: Conditional objects as nonmonotonic consequence relationships
cites work: On the consistency of defeasible databases
cites work: Qualitative probabilities for default reasoning, belief revision, and causal modeling
cites work: The quantitative/qualitative watershed for rules of uncertain inference
cites work: Conditionals in nonmonotonic reasoning and belief revision. Considering conditionals as agents
cites work: A thorough axiomatization of a principle of conditional preservation in belief revision
cites work: Structural inference from conditional knowledge bases
cites work: Nonmonotonic reasoning, preferential models and cumulative logics
cites work: Semantic classification of qualitative conditionals and calculating closures of nonmonotonic inference relations
cites work: What does a conditional knowledge base entail?
cites work: Counterfactuals.
cites work: Q4518818
cites work: Relevance in belief revision
cites work: Nonmonotonic Inferences with Qualitative Conditionals Based on Preferred Structures on Worlds
DOI: 10.1007/S10472-021-09777-9
description: scientific article; zbMATH DE number 7473196