Semantic Splitting of Conditional Belief Bases

Beierle, Christoph; Haldimann, Jonas; Kern-Isberner, Gabriele

doi:10.1007/978-3-030-76020-5_5

Cited by 3 publications

(5 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We address this issue by following ideas from (Beierle, Haldimann, and Kern-Isberner 2021;Wilhelm et al 2023) before we develop our framework on localizing the calculation of c-representations in the next sections. Constraint reductions are not mandatory for our further investigations but usually lead to much more fine-grained localizations.…”

Section: Constraint Reductionsmentioning

confidence: 99%

“…∆ and ϕ. In (Beierle, Haldimann, and Kern-Isberner 2021;Wilhelm et al 2023) the authors suggest rewriting rules for constraint sets which satisfy the requirements of spcrs. The following rules R1-R4 yield natural reductions of CSP(∆):…”

Section: Constraint Reductionsmentioning

confidence: 99%

“…In (Beierle, Haldimann, and Kern-Isberner 2021) spcrs where studied in the context of so-called constraint splittings where CSP ϕ (∆) decomposes into a set of smaller independent constraint satisfaction problems. Constraint splittings subsume many splitting techniques such as syntax splitting (Parikh 1999; Kern-Isberner and Brewka 2017; Kern-Isberner, Beierle, and Brewka 2020; Beierle and Kern-Isberner 2021), safe conditional syntax splitting (Heyninck, Kern-Isberner, and Meyer 2022), and case splitting (Sezgin, Kern-Isberner, and Beierle 2021).…”

Section: Constraint Reductionsmentioning

confidence: 99%

“…Constraint splittings (Beierle, Haldimann, and Kern-Isberner 2021) constitute a specific sub-class of safe covers for which the sub-bases and, thus, the edges of the corresponding hypergraph are pairwise disjoint. Definition 5 (Constraint Splitting (adapted from (Beierle, Haldimann, and Kern-Isberner 2021))). Let ∆ be a consistent belief base.…”

Section: Safe Coversmentioning

confidence: 99%

“…With constraint networks it is possible to solve the constraints referring to the sub-bases in O(∆) locally and propagate calculated penalty points through the network in order to comply with the c-consistency condition. Constraint networks generalize the socalled constraint splittings (Beierle, Haldimann, and Kern-Isberner 2021) and, therewith, subsume all common splitting techniques for conditional belief bases such as the already addressed syntax splitting. Besides the computation of c-representations, we show that drawing skeptical c-inferences can be localized based on safe sub-bases.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Decomposing Constraint Networks for Calculating c-Representations

Wilhelm,

Kern-Isberner

2024

AAAI

View full text Add to dashboard Cite

It is well-known from probability theory that network-based methods like Bayesian networks constitute remarkable frameworks for efficient probabilistic reasoning. In this paper, we focus on qualitative default reasoning based on Spohn’s ranking functions for which network-based methods have not yet been studied satisfactorily. With constraint networks, we develop a framework for iterative calculations of c-representations, a family of ranking models of conditional belief bases which show outstanding properties from a commonsense and formal point of view, that are characterized by assigning possible worlds a degree of implausibility via penalizing the falsification of conditionals. Constraint networks unveil the dependencies among these penalty points (and hence among the conditionals) and make it possible to compute the penalty points locally on so-called safe sub-bases. As an application of our framework, we show that skeptical c-inferences can be drawn locally from safe sub-bases without losing validity.

show abstract

Section: Constraint Reductionsmentioning

confidence: 99%

Section: Constraint Reductionsmentioning

confidence: 99%