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In this paper we investigate splitting notions for conditional belief bases that allow us to localize reasoning and computations to only the relevant parts of a belief base. The focus of our investigations lies on splitting notions for c-representations, which are special kinds of Spohn’s ranking models for belief bases and which can be specified via a constraint satisfaction problem. We extend the notion of constraint splittings for c-representations to conditional constraint splittings, covering also cases where the subbases may share conditionals. Inspired by conditional syntax splittings, we identify the subclass of safe conditional constraint splittings, allowing us to solve the constraint systems of the subbases independently from each other. We elaborate the relationships of constraint and safe conditional constraint splittings to safe and generalized safe conditional syntax splittings and also to safe covers, which have been proposed for localized computation of c-representations. Additionally, we generalize solution splittings for c-representations to safe conditional c-solution splittings and show how they relate to conditional constraint splittings.

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Conditional Constraint and Solution Splittings of Belief Bases in the Context of c-Representations

  • 会议论文

  • 发表日期：

    2026年

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  • Lars-Phillip Spiegel,
  • Christoph Beierle,
  • Gabriele Kern-Isberner,
  • Alexander Hahn

摘要

In this paper we investigate splitting notions for conditional belief bases that allow us to localize reasoning and computations to only the relevant parts of a belief base. The focus of our investigations lies on splitting notions for c-representations, which are special kinds of Spohn’s ranking models for belief bases and which can be specified via a constraint satisfaction problem. We extend the notion of constraint splittings for c-representations to conditional constraint splittings, covering also cases where the subbases may share conditionals. Inspired by conditional syntax splittings, we identify the subclass of safe conditional constraint splittings, allowing us to solve the constraint systems of the subbases independently from each other. We elaborate the relationships of constraint and safe conditional constraint splittings to safe and generalized safe conditional syntax splittings and also to safe covers, which have been proposed for localized computation of c-representations. Additionally, we generalize solution splittings for c-representations to safe conditional c-solution splittings and show how they relate to conditional constraint splittings.