Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
What does a conditional knowledge base entail?
Artificial Intelligence
Conditional entailment: bridging two approaches to default reasoning
Artificial Intelligence
Nonmonotonic reasoning, conditional objects and possibility theory
Artificial Intelligence
Conceptual Spaces: The Geometry of Thought
Conceptual Spaces: The Geometry of Thought
System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
Reasoning about categories in conceptual spaces
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
SUM'11 Proceedings of the 5th international conference on Scalable uncertainty management
Interpolation of fuzzy data: Analytical approach and overview
Fuzzy Sets and Systems
Preferential semantics for the logic of comparative similarity over triangular and metric models
JELIA'12 Proceedings of the 13th European conference on Logics in Artificial Intelligence
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Default reasoning and interpolation are two important forms of commonsense rule-based reasoning. The former allows us to draw conclusions from incompletely specified states, by making assumptions on normality, whereas the latter allows us to draw conclusions from states that are not explicitly covered by any of the available rules. Although both approaches have received considerable attention in the literature, it is at present not well understood how they can be combined to draw reasonable conclusions from incompletely specified states and incomplete rule bases. In this paper, we introduce an inference system for interpolating default rules, based on a geometric semantics in which normality is related to spatial density and interpolation is related to geometric betweenness. We view default rules and information on the betweenness of natural categories as particular types of constraints on qualitative representations of Gärdenfors conceptual spaces. We propose an axiomatization, extending the well-known System P, and show its soundness and completeness w.r.t. the proposed semantics. Subsequently, we explore how our extension of preferential reasoning can be further refined by adapting two classical approaches for handling the irrelevance problem in default reasoning: rational closure and conditional entailment.