KR2020Proceedings of the 17th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning

Rhodes, Greece. September 12-18, 2020.

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ISSN: 2334-1033
ISBN: 978-0-9992411-7-2

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Copyright © 2020 International Joint Conferences on Artificial Intelligence Organization

Syntax Splitting = Relevance + Independence: New Postulates for Nonmonotonic Reasoning From Conditional Belief Bases

  1. Gabriele Kern-Isberner(TU Dortmund)
  2. Christoph Beierle(University of Hagen)
  3. Gerhard Brewka(Leipzig University)


  1. Nonmonotonic logics, default logics, conditional logics-General


Syntax splitting, first introduced by Parikh in 1999, is a natural and desirable property of KR systems. Syntax splitting combines two aspects: it requires that the outcome of a certain epistemic operation should only depend on relevant parts of the underlying knowledge base, where relevance is given a syntactic interpretation (relevance). It also requires that strengthening antecedents by irrelevant information should have no influence on the obtained conclusions (independence). In the context of belief revision the study of syntax splitting already proved useful and led to numerous new insights. In this paper we analyse syntax splitting in a different setting, namely nonmonotonic reasoning based on conditional knowledge bases. More precisely, we analyse inductive inference operators which, like system P, system Z, or the more recent c-inference, generate an inference relation from a conditional knowledge base. We axiomatize the two aforementioned aspects of syntax splitting, relevance and independence, as properties of such inductive inference operators. Our main results show that system P and system Z, whilst satisfying relevance, fail to satisfy independence. C-inference, in contrast, turns out to satisfy both relevance and independence and thus fully complies with syntax splitting.