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From Forgetting Signature Elements to Forgetting Formulas in Epistemic States

by Kai Sauerwald, Gabriele Kern-Isberner, Alexander Becker, Christoph Beierle

Abstract: In this paper,we bring together marginalisation and forgetting of signature elements in the framework of epistemic states. Marginalisation of epistemic states is a specific approach to actively reduce signatures, also aiming at forgetting atoms which are very well known from probability theory. On the other hand, rooted in Boole’s variable elimination, Delgrande’s knowledge level account of forgetting provides a general approach to forgetting syntax elements from sets of formulas with links to many other forgetting operations. We generalize Delgrande’s axioms to epistemic states and show that marginalisation is the most specific and informative forgetting operator that satisfies these axioms. Moreover, we propose rephrasing Delgrande’s postulates suitable for forgetting formulas by transferring the basic ideas of the axioms to forgetting formulas in epistemic states.

A Comparison of ASP-Based and SAT-Based Algorithms for the Contension Inconsistency Measure

by Isabelle Kuhlmann, Anna Gessler, Vivien Laszlo, Matthias Thimm

Abstract: We propose an algorithm based on satisfiability problem (SAT) solving for determining the contension inconsistency degree in propositional knowledge bases. In addition, we present a revised version of an algorithm based on answer set programming (ASP), which serves the same purpose. In an experimental analysis, we compare the two algorithms to each other, as well as to a naive baseline method. Our results demonstrate that both the SAT and the ASP approach expectedly outperform the baseline algorithm. Further, the revised ASP method is not only superior to the SAT approach, but also to its predecessors from the literature. Hence, it poses a new state of the art.

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