We define an inference system to capture explanations based on causal statements, using an ontology in the form of an IS-A hierarchy. We first introduce a simple logical language which makes it possible to express that a fact causes another fact and that a fact explains another fact. We present a set of formal inference patterns from causal statements to explanation statements. We introduce an elementary ontology which gives greater expressiveness to the system while staying close to propositional reasoning. We provide an inference system that captures the patterns discussed, firstly in a purely propositional framework, then in a datalog (limited predicate) framework. * This preprint of a paper published in Integrated Computer-Aided Engineering Journal (publisher: IOS Press, editor: Hojjat Adeli), 15(4), pp. [351][352][353][354][355][356][357][358][359][360][361][362][363][364][365][366][367] 2008) is an extended version of [BCM07].
Recently, the old logical notion of forgetting propositional symbols (or reducing the logical vocabulary) has been generalized to a new notion: forgetting literals. The aim was to help the automatic computation of various formalisms which are currently used in knowledge representation. We extend here this notion, by allowing propositional symbols to vary while forgetting literals. The definitions are not really more complex than for literal forgetting without variation. We describe the new notion, on the syntactical and the semantical side. Then, we show how to apply it to the computation of circumscription. This computation has been done before with standard literal forgetting, but here we show how introducing varying propositional symbols simplifies significantly the computation. We revisit a fifteen years old result about computing circumscription, showing that it can be improved in the same way. We provide hints in order to apply this forgetting method also to other logical formalisms.
This article presents the use of Answer Set Programming (ASP) to mine sequential patterns. ASP is a high-level declarative logic programming paradigm for high level encoding combinatorial and optimization problem solving as well as knowledge representation and reasoning. Thus, ASP is a good candidate for implementing pattern mining with background knowledge, which has been a data mining issue for a long time. We propose encodings of the classical sequential pattern mining tasks within two representations of embeddings (fill-gaps vs skip-gaps) and for various kinds of patterns: frequent, constrained and condensed. We compare the computational performance of these encodings with each other to get a good insight into the efficiency of ASP encodings. The results show that the fill-gaps strategy is better on real problems due to lower memory consumption. Finally, compared to a constraint programming approach (CPSM), another declarative programming paradigm, our proposal showed comparable performance.
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