# Computation and comparison of nonmonotonic skeptical inference relations induced by sets of ranking models for the realization of intelligent agents

## Abstract

Skeptical inference of an intelligent agent in the context of a knowledge base \(\mathcal {R}\) containing conditionals of the form *If A then usually B* can be defined with respect to a set of models of \(\mathcal {R}\). For the semantics of ranking functions that assign a degree of surprise to each possible world, we develop a method for comparing the inference relations induced by different sets of ranking models. Using this method, we address the problem of ensuring the correctness of approximating skeptical c-inference for \(\mathcal {R}\) by constraint satisfaction problems (CSPs) over finite domains. Skeptical c-inference is defined by taking the set of all c-representations into account, where c-representations are ranking functions induced by impact vectors encoding the conditional impact on each possible world. By setting a bound for the maximal impact value, c-inference can be approximated by a resource-bounded inference operation. We investigate the concepts of regular and sufficient upper bounds for conditional impacts and how they can be employed for implementing c-inference as a finite domain constraint solving problem. While in general, determining a sufficient upper bound for these CSPs is an open problem, for a sequence of simple knowledge bases investigated only experimentally before, we prove that using the number of conditionals in \(\mathcal {R}\) as an upper bound correctly captures skeptical c-inference. The ideas presented in this paper are implemented in a software platform that realizes the core reasoning component of an intelligent agent.

## Keywords

Conditional logic Ranking functions Nonmonotonic reasoning Skeptical inference c-inference Constraint satisfaction problem## Notes

### Acknowledgements

We thank the anonymous reviewers for their detailed and helpful comments that helped us to improve the article.

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