Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge Base Combination

In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic and rule bases, have been proposed. They either cast rules into classical logic or limit the interaction between rules and ontologies. Autoepistemic logic (AEL) is an attractive formalism which allows to overcome these limitations, by serving as a uniform host language to embed ontologies and nonmonotonic logic programs into it. For the latter, so far only the propositional setting has been considered. In this paper, we present three embeddings of normal and three embeddings of disjunctive non-ground logic programs under the stable model semantics into first-order AEL. While the embeddings all correspond with respect to objective ground atoms, differences arise when considering non-atomic formulas and combinations with first-order theories. We compare the embeddings with respect to stable expansions and autoepistemic consequences, considering the embeddings by themselves, as well as combinations with classical theories. Our results reveal differences and correspondences of the embeddings and provide useful guidance in the choice of a particular embedding for knowledge combination.Comment: 52 pages, submitte

Basic characteristics to achieve common sense reasoning

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From here to human-level AI

AbstractHuman-level AI will be achieved, but new ideas are almost certainly needed, so a date cannot be reliably predicted—maybe five years, maybe five hundred years. I'd be inclined to bet on this 21st century.It is not surprising that human-level AI has proved difficult and progress has been slow—though there has been important progress. The slowness and the demand to exploit what has been discovered has led many to mistakenly redefine AI, sometimes in ways that preclude human-level AI—by relegating to humans parts of the task that human-level computer programs would have to do. In the terminology of this paper, it amounts to settling for a bounded informatic situation instead of the more general common sense informatic situation.Overcoming the “brittleness” of present AI systems and reaching human-level AI requires programs that deal with the common sense informatic situation—in which the phenomena to be taken into account in achieving a goal are not fixed in advance.We discuss reaching human-level AI, emphasizing logical AI and especially emphasizing representation problems of information and of reasoning. Ideas for reasoning in the common sense informatic situation include nonmonotonic reasoning, approximate concepts, formalized contexts and introspection

Dual Forgetting Operators in the Context of Weakest Sufficient and Strongest Necessary Conditions

Forgetting is an important concept in knowledge representation and automated reasoning with widespread applications across a number of disciplines. A standard forgetting operator, characterized in [Lin and Reiter'94] in terms of model-theoretic semantics and primarily focusing on the propositional case, opened up a new research subarea. In this paper, a new operator called weak forgetting, dual to standard forgetting, is introduced and both together are shown to offer a new more uniform perspective on forgetting operators in general. Both the weak and standard forgetting operators are characterized in terms of entailment and inference, rather than a model theoretic semantics. This naturally leads to a useful algorithmic perspective based on quantifier elimination and the use of Ackermman's Lemma and its fixpoint generalization. The strong formal relationship between standard forgetting and strongest necessary conditions and weak forgetting and weakest sufficient conditions is also characterized quite naturally through the entailment-based, inferential perspective used. The framework used to characterize the dual forgetting operators is also generalized to the first-order case and includes useful algorithms for computing first-order forgetting operators in special cases. Practical examples are also included to show the importance of both weak and standard forgetting in modeling and representation