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Properties of System W and Its Relationships to Other Inductive Inference Operators

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Book cover Foundations of Information and Knowledge Systems (FoIKS 2022)

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Abstract

System W is a recently introduced inference method for conditional belief bases with some notable properties like capturing system Z and thus rational closure and, in contrast to system Z, fully satisfying syntax splitting. This paper further investigates properties of system W. We show how system W behaves with respect to postulates put forward for nonmonotonic reasoning like rational monotony, weak rational monotony, or semi-monotony. We develop tailored postulates ensuring syntax splitting for any inference operator based on a strict partial order on worlds. By showing that system W satisfies these axioms, we obtain an alternative and more general proof that system W satisfies syntax splitting. We explore how syntax splitting affects the strict partial order underlying system W and exploit this for answering certain queries without having to determine the complete strict partial order. Furthermore, we investigate the relationships among system W and other inference methods, showing that, for instance, lexicographic inference extends both system W and c-inference, and leading to a full map of interrelationships among various inductive inference operators.

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Acknowledgement

We thank the anonymous reviewers for their detailed and helpful comments. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant BE 1700/10-1 awarded to Christoph Beierle as part of the priority program “Intentional Forgetting in Organizations” (SPP 1921).

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  1. Faculty of Mathematics and Computer Science, FernUniversität in Hagen, 58084, Hagen, Germany

    Jonas Haldimann & Christoph Beierle

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  1. Jonas Haldimann
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  2. Christoph Beierle
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Correspondence to Christoph Beierle .

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  1. Université d'Artois and CNRS, Lens, France

    Ivan Varzinczak

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Haldimann, J., Beierle, C. (2022). Properties of System W and Its Relationships to Other Inductive Inference Operators. In: Varzinczak, I. (eds) Foundations of Information and Knowledge Systems. FoIKS 2022. Lecture Notes in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-11321-5_12

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  • DOI: https://doi.org/10.1007/978-3-031-11321-5_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-11320-8

  • Online ISBN: 978-3-031-11321-5

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