Download or read book Tractable Reasoning in Incomplete First-order Knowledge Bases written by Yongmei Liu and published by . This book was released on 2006 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to specify a limited reasoning service for proper+ KBs, we propose a new logic of limited belief called the subjective logic SL . SL supports unit resolution, but only does case analysis in a limited way. We give a sound and complete axiomatization for propositional SL . Reasoning based on SL is classically sound and is also classically complete in some simple cases. We show that SL -based reasoning with proper+ KBs is decidable in general, and tractable when both the KB and the query use a bounded number of variables. This thesis proposes a general methodology to establish tractable (by "tractable" we mean "solvable in polynomial time") limited reasoning services for incomplete first-order knowledge bases (KBs). It consists of defining a logic that is weaker than classical logic and has two properties: first, the entailment problem can be reduced to the model checking problem for a characteristic model; and second, the model checking problem is tractable for formulas with a bounded number of variables. We show this methodology in action for two forms of incomplete first-order KBs proposed by Levesque and Lakemeyer. One is called proper KBs, and is used for open-world reasoning. The other is called proper+ KBs, and is used for reasoning with disjunctive information. Levesque has proposed a reasoning scheme called V for proper KBs that is classically sound and is also classically complete when the query is in a certain normal form called NF . We prove that V is tractable for queries with a bounded number of variables. We also settle the open problems concerning the expressiveness and succinctness of NF . Then we extend V to reasoning in dynamic systems, and propose a tractable, sound, and sometimes complete solution to the projection problem, that is, determining whether a formula holds after a sequence of actions is performed.