Theory resolution constitutes a set of complete procedures for incorporating theories into a resolution theorem-proving program, thereby making it unnecessary to resolve directly upon axioms of the theory. This can greatly reduce the length of proofs and the size of the search space. Theory resolution effects a beneficial division of labor, improving the performance of the theorem prover and increasing the applicability of the specialized reasoning procedures. Total theory resolution utilizes a decision procedure that is capable of determining unsatisfiability of any set of clauses using predicates in the theory. Partial theory resolution employs a weaker decision procedure that can determine potential unsatisfiability of sets of literals. Applications include the building in of both mathematical and special decision procedures, e.g., for the taxonomic information furnished by a knowledge representation system. Theory resolution is a generalization of numerous previously known resolution refinements. Its power is demonstrated by comparing solutions of "Schubert's Steamroller" challenge problem with and without building in axioms through theory resolution. 1 1

Levesque and Brachman argue that in order to provide timely and correct responses in the most critical applications, general purpose knowledge representation systems should restrict their languages by omitting constructs which require non-polynomial worst-case response times for sound and complete classification. They also separate terminological and assertional knowledge, and restrict classification to purely terminological information. We demonstrate that restricting the terminological language and classifier in these ways limits these "general-purpose" facilities so severely that they are no longer generally applicable. We argue that logical soundness, completeness, and worst-case complexity are inadequate measures for evaluating the utility of representation services, and that this evaluation should employ the broader notions of utility and rationality found in decision theory. We suggest that general purpose representation services should provide fully expressive languages, classi...

Belief revision leads to temporal nonmonotonicity, i.e., the set of beliefs does not grow monotonically with time. Default reasoning leads to logical nonmonotonicity, i.e., the set of consequences does not grow monotonically with the set of premises. The connection between these forms of nonmonotonicity will be studied in this paper focusing on syntaxbased approaches. It is shown that a general form of syntax-based belief revision corresponds to a special kind of partial meet revision in the sense of the theory of epistemic change, which in turn is expressively equivalent to some variants of logics for default reasoning. Additionally, the computational complexity of the membership problem in revised belief sets and of the equivalent problem of derivability in default logics is analyzed, which turns out to be located at the lower end of the polynomial hierarchy. 1 INTRODUCTION Belief revision is the process of incorporating new information into a knowledge base while preserving consist...

this paper we survey recent results in knowledge compilation of propositional knowledge bases. We first define and limit the scope of such a technique, then we survey exact and approximate knowledge compilation methods. We include a discussion of compilation for non-monotonic knowledge bases. Keywords: Knowledge Representation, Efficiency of Reasoning

Hybrid inference systems are an important way to address the fact that intelligent systems have muiltifaceted representational and reasoning competence. KRYPTON is an experimental prototype that competently handles both terminological and assertional knowledge; these two kinds of information are tightly linked by having sentences in an assertional component be formed using structured complex predicates denned in a complementary terminological component. KRYPTON is unique in that it combines in a completely integrated fashion a frame-based description language and a first-order resolution theorem-prover. We give here both a formal Knowledge Level view of the user interface to KRYPTON and the technical Symbol Level details of the integration of the two disparate components, thus providing an essential picture of the abstract function that KRYPTON computes and the implementation technology needed to make it work. We also illustrate the kind of complex question the system can answer. I

The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of non-monotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge.

Several studies about computational complexity of non-monotonic reasoning (NMR) showed that non-monotonic inference is significantly harder than classical, monotonic inference. This contrasts with the general idea that NMR can be used to make knowledge representation and reasoning simpler, not harder. In this paper we show that, to some extent, NMR fulfills the representation goal. In particular, we prove that non-monotonic formalisms such as circumscription and default logic allow for a much more compact and natural representation of propositional knowledge than propositional calculus. Proofs are based on a suitable definition of compilable inference problem, and on non-uniform complexity classes. Some results about intractability of circumscription and default logic can therefore be interpreted as the price one has to pay for having such an extra-compact representation. On the other hand, intractability of inference and compactness of representation are not equivalent notions: we ex...

this paper, we adopt the former perspective. In order to distinguish operations on syntactic descriptions -- on belief bases -- from operations on belief sets, belief base changes are called base revision and base contraction.

The logic program formalism is commonly viewed as a modal or default logic. In this paper, we propose an alternative interpretation of the formalism as a terminological logic. A terminological logic is designed to represent two different forms of knowledge. A TBox represents definitions for a set of concepts. An ABox represents the assertional knowledge of the expert. In our interpretation, a logic program is a TBox providing definitions for all predicates; this interpretation is present already in Clark's completion semantics. We extend the logic program formalism such that some predicates can be left undefined and use classical logic as the language for the ABox. The resulting logic can be seen as an alternative interpretation of abductive logic program formalism. We study the expressivity of the formalism for representing uncertainty by proposing solutions for problems in temporal reasoning, with null values and open domain knowledge. 1 Introduction The logic program formalism is c...

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