Compilation of static and evolving conditional knowledge bases for computing induced nonmonotonic inference relations

Beierle, Christoph; Kutsch, Steven; Sauerwald, Kai

doi:10.1007/s10472-019-09653-7

Cited by 12 publications

(1 citation statement)

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“…We are currently working on investigating system W with respect to further properties put forward for nonmonotonic reasoning, e.g., regarding syntax splitting [21,22,32,34]. We are also empirically evaluting system W with the reasoning platform InfOCF [6,28] and investigating to what extent compilation techniques developed for implementing c-inference [10] can be employed for system W. The problem of establishing an upper bound for knowledge bases that is sufficient to realize skeptical c-inference remains and will be addressed in future work.…”

Section: Discussionmentioning

confidence: 99%

Nonmonotonic reasoning from conditional knowledge bases with system W

Komo

Beierle

2021

Ann Math Artif Intell

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For nonmonotonic reasoning in the context of a knowledge base $\mathcal {R}$ R containing conditionals of the form If A then usually B, system P provides generally accepted axioms. Inference solely based on system P, however, is inherently skeptical because it coincides with reasoning that takes all ranking models of $\mathcal {R}$ R into account. System Z uses only the unique minimal ranking model of $\mathcal {R}$ R , and c-inference, realized via a complex constraint satisfaction problem, takes all c-representations of $\mathcal {R}$ R into account. C-representations constitute the subset of all ranking models of $\mathcal {R}$ R that are obtained by assigning non-negative integer impacts to each conditional in $\mathcal {R}$ R and summing up, for every world, the impacts of all conditionals falsified by that world. While system Z and c-inference license in general different sets of desirable entailments, the first major objective of this article is to present system W. System W fully captures and strictly extends both system Z and c-inference. Moreover, system W can be represented by a single strict partial order on the worlds over the signature of $\mathcal {R}$ R . We show that system W exhibits further inference properties worthwhile for nonmonotonic reasoning, like satisfying the axioms of system P, respecting conditional indifference, and avoiding the drowning problem. The other main goal of this article is to provide results on our investigations, underlying the development of system W, of upper and lower bounds that can be used to restrict the set of c-representations that have to be taken into account for realizing c-inference. We show that the upper bound of n − 1 is sufficient for capturing c-inference with respect to $\mathcal {R}$ R having n conditionals if there is at least one world verifying all conditionals in $\mathcal {R}$ R . In contrast to the previous conjecture that the number of conditionals in $\mathcal {R}$ R is always sufficient, we prove that there are knowledge bases requiring an upper bound of 2n− 1, implying that there is no polynomial upper bound of the impacts assigned to the conditionals in $\mathcal {R}$ R for fully capturing c-inference.

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