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The Logic of Knowledge Bases: A Review

AI Magazine

As a result, they knowledge of an agent (that is, its epistemic coarse-grained level of abstraction, KBwould argue, it is not possible to discuss state) can be characterized as the Ss can be characterized in terms of two the knowledge of a system independently collection of all possible worlds that components: (1) a knowledge base, encoding of the task context in which are consistent with the knowledge the knowledge embodied by the system is meant to operate. I won't held by the agent. If the knowledge of the system, and (2) a reasoning engine, go into too many details here because the agent is complete, then the epistemic which is able to query the knowledge a detailed discussion of the declarative state contains only one world. A base, infer or acquire knowledge from versus the procedural argument is well nice feature of Levesque and Lakemeyer's external sources, and add new knowledge beyond the scope of this review. The treatment of epistemic logic is that to the knowledge base. Levesque important point to make is that in contrast to many other treatments and Lakemeyer's The Logic of Knowledge Levesque and Lakemeyer's approach is of modalities, the discussion is reasonably Bases deals with the "internal logic" of situated in a precise AI research easy to follow for people who are a KBS: It provides a formal account of paradigm, which considers knowledge not experts in the field. This is the result the interaction between a reasoning bases as declaratively specified, task-independent of two main features of this analysis: engine and a knowledge base.


A Knowledge Level Account of Forgetting

Journal of Artificial Intelligence Research

Forgetting is an operation on knowledge bases that has been addressed in different areas of Knowledge Representation and with respect to different formalisms, including classical propositional and first-order logic, modal logics, logic programming, and description logics. Definitions of forgetting have been expressed in terms of manipulation of formulas, sets of postulates, isomorphisms between models, bisimulations, second-order quantification, elementary equivalence, and others. In this paper, forgetting is regarded as an abstract belief change operator, independent of the underlying logic. The central thesis is that forgetting amounts to a reduction in the language, specifically the signature, of a logic. The main definition is simple: the result of forgetting a portion of a signature in a theory is given by the set of logical consequences of this theory over the reduced language. This definition offers several advantages. Foremost, it provides a uniform approach to forgetting, with a definition that is applicable to any logic with a well-defined consequence relation. Hence it generalises a disparate set of logic-specific definitions with a general, high-level definition. Results obtained in this approach are thus applicable to all subsumed formal systems, and many results are obtained much more straightforwardly. This view also leads to insights with respect to specific logics: for example, forgetting in first-order logic is somewhat different from the accepted approach. Moreover, the approach clarifies the relation between forgetting and related operations, including belief contraction.


The Logic of Knowledge Bases A Review

AI Magazine

Hence, at a coarse-grained level of abstraction, KB-Ss can be characterized in terms of two components: (1) a knowledge base, encoding the knowledge embodied by the system, and (2) a reasoning engine, which is able to query the knowledge base, infer or acquire knowledge from external sources, and add new knowledge to the knowledge base. A knowledge-level account of a KBS (that is, a competencecentered, implementation-independent description of a system), such as Clancey's (1985) analysis of first-generation rule-based systems, focuses on the task-centered competence of the system; that is, it addresses issues such as what kind of problems the KBS is designed to tackle, what reasoning methods it uses, and what knowledge it requires. In contrast with task-centered analyses, Levesque and Lakemeyer focus on the competence of the knowledge base rather than that of the whole system. Hence, their notion of competence is a task-independent one: It is the "abstract state of knowledge" (p. This is an interesting assumption, which the "proceduralists" in the AI community might object to: According to the procedural viewpoint of knowledge representation, the knowledge modeled in an application, its representation, and the associated knowledge-retrieval mechanisms have to be engineered as As a result, they would argue, it is not possible to discuss the knowledge of a system independently of the task context in which the system is meant to operate.


Implicitly learning to reason in first-order logic

Neural Information Processing Systems

We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed probability distribution. PAC semantics, introduced by Valiant, is one rigorous, general proposal for learning to reason in formal languages: although weaker than classical entailment, it allows for a powerful model theoretic framework for answering queries while requiring minimal assumptions about the form of the distribution in question. To date, however, the most significant limitation of that approach, and more generally most machine learning approaches with robustness guarantees, is that the logical language is ultimately essentially propositional, with finitely many atoms. Indeed, the theoretical findings on the learning of relational theories in such generality have been resoundingly negative. This is despite the fact that first-order logic is widely argued to be most appropriate for representing human knowledge.