|Norvig I 456
Description logic/AI research/Russell/Norvig: Description logics are notations that are designed to make it easier to describe definitions and properties of categories. The principal inference tasks for description logics are subsumption (checking if one category is a subset of another by comparing their definitions) and classification (checking whether an object belongs to a category).
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VsDescription logics/Norvig: either hard problems cannot be stated at all, or they require exponentially large descriptions! ((s) For a solution see >Conceptual space/Gärdenfors; >Semantic Web/Gärdenfors. (GärdenforsVsRussell, Stuart/GärdenforsVsNorvig).
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Circumspription: The idea is to specify particular predicates that are assumed to be “as false as possible”—that is, false for every object except those for which they are known to be true. For example, suppose we want to assert the default rule that birds fly. We would introduce a predicate, say Abnormal 1(x), and write Bird(x) ∧¬Abnormal 1(x) ⇒ Flies(x) .
If we say that Abnormal 1 is to be circumscribed, a circumscriptive reasoner is entitled to assume ¬Abnormal 1(x) unless Abnormal 1(x) is known to be true. This allows the conclusion Flies(Tweety) to be drawn from the premise Bird(Tweety ), but the conclusion no longer holds if Abnormal 1(Tweety) is asserted. Circumscription can be viewed as an example of a model preference logic. In such logics, a sentence is entailed (with default status) if it is true in all preferred models of the knowledge base, as opposed to the requirement of truth in all models in classical logic.
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The development of description logics is the most recent stage in a long line of research aimed at finding useful subsets of first-order logic for which inference is computationally tractable. Hector Levesque and Ron Brachman (1987)(1) showed that certain logical constructs - notably, certain uses of disjunction and negation - were primarily responsible for the intractability of logical inference. Building on the KL-ONE system (Schmolze and Lipkis, 1983)(2), several researchers developed systems that incorporate theoretical complexity analysis, most notably KRYPTON (Brachman et al., 1983)(3) and Classic (Borgida et al., 1989)(4). The result has been a marked increase in the speed of inference and a much better understanding of the interaction between complexity and expressiveness in reasoning systems. Calvanese et al. (1999)(5) summarize the state of the art, and Baader et al. (2007)(6) present a comprehensive handbook of description logic. Against this trend, Doyle and Patil (1991)(7) have argued that restricting the expressiveness of a language either makes it impossible to solve certain problems or encourages the user to circumvent the language restrictions through nonlogical means. >Inference/AI research.
1. Levesque, H. J. and Brachman, R. J. (1987). Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3(2), 78–93.
2. Schmolze, J. G. and Lipkis, T. A. (1983). Classification in the KL-ONE representation system. In
IJCAI-83, pp. 330–332.
3. Brachman, R. J., Fikes, R. E., and Levesque, H. J. (1983). Krypton: A functional approach to knowledge representation. Computer, 16(10), 67–73.
4. Borgida, A., Brachman, R. J., McGuinness, D., and Alperin Resnick, L. (1989). CLASSIC: A structural data model for objects. SIGMOD Record, 18(2), 58-67.
5. Calvanese, D., Lenzerini, M., and Nardi, D. (1999). Unifying class-based representation formalisms. JAIR, 11, 199–240
6. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., and Patel-Schneider, P. (2007). The Description
Logic Handbook (2nd edition). Cambridge University Press.
7. Doyle, J. and Patil, R. (1991). Two theses of knowledge representation: Language restrictions, taxonomic classification, and the utility of representation services. AIJ, 48(3), 261–297._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. The note [Author1]Vs[Author2] or [Author]Vs[term] is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.
Stuart J. Russell
Artificial Intelligence: A Modern Approach Upper Saddle River, NJ 2010