Hector J. Levesque and Ronald J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of these two aspects. In particular, starting with [14] the research on the computational complexity of the reasoning tasks associated with description logics has shown that in order to ensure decidability and or efficiency of reasoning in all cases, one must renounce some of the expressive power [76, 81, 83, 82, 47, 48, 49]. These results have led to a debate on the trade off between expressive power of representation formalisms and worst case efficiency of the associated reasoning tasks. Recently, this issue has been one of the main themes in the area of description logics, and has led to at least four different ....

H. J. Levesque and R. J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987. 130

....Smo89] is a decidable logic that generalizes Ait Kaci s formalism by adding negation and quantification. Feature Logic makes explicit that Ait Kaci s terms, the feature descriptions developed by computational linguists [KB82, RK86, Joh88] and the knowledge representation language KL ONE [BS85, LB87, Neb89, SSS91, NS90] are all closely related members of the same family of logics. These logics offer attributive concept descriptions that are interpreted as sets and are built from sorts and binary relations (called attributes, roles or features) using set operations such as intersection, union ....

....Smo89] a decidable logic that generalizes Ait Kaci s formalism by adding negation and quantification. Feature Logic makes explicit that Ait Kaci s terms, the feature descriptions developed by computational linguists [KB82, RK86, Joh88] and the knowledge representation language KL ONE [BS85, LB87, Neb89, SSS91, NS90] are all closely related members of the same family of logics. These logics offer attributive concept descriptions that are interpreted as sets and are built from sorts and binary relations (called attributes, roles or features) using set operations such as intersection, union ....

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Hector J. Levesque and Ronald J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

....studied in this paper is probably too expressive since general negation is not needed. 20 Thus it would be interesting to find out whether satisfiability of feature terms built from the forms a, A, p#q, 9L(S) and S u S is decidable. Feature logics are closely related to terminological logics [4, 13, 14, 19], which are employed in knowledge representation and grew out of research in semantic networks and frame systems. The essential difference between these two formalisms is that in terminological logics attributes can be nonfunctional while they must be functional in feature logics. Baader [1] ....

H. J. Levesque and R. J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

....in F . 2 7 Sorts In this section we extend our logic to include sorts. For our purposes, a sort is simply a symbol denoting a subset of the domain of a feature algebra. Equivalently, one can regard a sort as a unary predicate. Our sorts correspond to the concepts of terminological languages [28, 33, 34] and to the templates of the PATR II system [46] They are different from sorts in sorted logics in that we don t exploit sorts to impose a well sortedness discipline on formulas. From now on we assume an additional alphabet whose symbols are called sorts. Furthermore, we assume that the ....

H. J. Levesque and R. J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

....ourselves to unqualified existential quantification, the satisfiability problem becomes trivial as all formulas in are satisfiable. More interesting is the fact that deciding subsumption (given two formulas #, # # FL decide whether # # is a theorem) is solvable in polynomial time [6]. We refer the reader to [8] for further discussion on the computational aspects and its extensions. In [12] Halpern shows that finiteness restrictions (both on the number of propositional symbols and on the nesting of operators) also lowers the complexity of the inference tasks. ....

R. Brachman and H. Levesque. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

.... ) and by restricting to unquali ed existential quanti cation, the satis ability problem becomes trivial as all formulas in FL are satis able. More interesting is the fact that deciding subsumption (given two formulas ; 2 FL decide whether is a theorem) is solvable in polynomial time [5]. We refer the reader to [7] for further discussion on the computational aspects of FL and its extensions. In [11] Halpern shows that niteness restrictions (both on number of propositional symbols and on nesting of operators) also lowers the complexity of the inference tasks. Satis ability of ....

R. Brachman and H. Levesque. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, (3):78-93, 1987.

....ourselves to unqualified existential quantification, the satisfiability problem becomes trivial as all formulas in are satisfiable. More interesting is the fact that deciding subsumption (given two formulas 213 decide whether 4 1 is a theorem) 4 is solvable in polynomial time [5]. We refer the reader to [7] for further discussion on the computational aspects of and its extensions. In [11] Halpern shows that finiteness restrictions (both on the number of propositional symbols and on the nesting of operators) also lowers the complexity of the inference tasks. ....

R. Brachman and H. Levesque. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

....these two aspects. In particular, starting with [9] the research on the computational complexity of the reasoning tasks associated with Description Logics has shown that in order to ensure decidability and or efficiency of reasoning in all cases, one must renounce to some of the expressive power [43, 45, 47, 46, 25, 26, 27]. These results have led to a debate on the trade off between expressive power of representation formalisms and worst case efficiency of the associated reasoning tasks. This issue has been one of the main themes in the area of Description Logics, and has led to at least four different approaches ....

H. J. Levesque and R. J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

....of the inference problem for first order logic and by the intention to preserve the structure of knowledge to be represented. The ontological basis of description logics is again set theory, in particular the semantics of first order predicate calculus. But, in addition, as formulated in [35], the language has to be restricted to formulas of a certain form. This philosophy behind this is called in [16] the restricted language thesis. One argument in [35] is that general purpose knowledge representation systems should restrict 22 their languages by omitting constructs which require ....

....logics is again set theory, in particular the semantics of first order predicate calculus. But, in addition, as formulated in [35] the language has to be restricted to formulas of a certain form. This philosophy behind this is called in [16] the restricted language thesis. One argument in [35] is that general purpose knowledge representation systems should restrict 22 their languages by omitting constructs which require non polynomial (or otherwise unacceptably long) worst case response time for the correct classification of concepts. In [16] the position is taken that the restricted ....

Levesque,H.J., R.J.Brachman. Expressiveness and tractability in knowledge representation and reasoning. Comp. Intell., 3 , 78-93 30

....mentioned inferences and for the subsumption problem were only known for rather trivial languages which explains the use of incomplete algorithms in existing kl one systems. Another argument in favour of incomplete algorithms was that for many languages the subsumption problem is at least NP hard [LB87, Neb88] Consequently, complete algorithms have to be intractable, whereas incomplete algorithms may still be polynomial. However, one should keep in mind that these complexity results are worst case results. It is not at all clear how complete algorithms may behave for typical knowledge bases. ....

H. J. Levesque, R. J. Brachman. \Expressiveness and tractability in knowledge representation and reasoning." Computational Intelligence, 3:78-93, 1987.

....of the inference problem for first order logic and by the intention to preserve the structure of the knowledge to be represented. The ontological basis of description logics is again set theory, in particular the semantics of the first order predicate calculus. But in addition, as formulated in [18], the language has to be restricted to formulas of a certain form. The philosophy behind this is called in [11] the restricted language thesis. One argument is that general purpose knowledge representation systems should restrict their languages by omitting constructs which lead to the ....

Levesque,H.J., R.J.Brachman. Expressiveness and tractability in knowledge representation and reasoning. Comp. Intell., 3 , 78-93

.... complexity results: even in the propositional case, inference in classical logic is NP complete [24] nonmonotonic logic is # # # complete [47, 35] and probabilistic inference is ## complete [79] In response the KR community developed various tractable knowledge representation systems [54], but their limited expressive power meant that complexity was simply shifted from the KR system itself to some larger problemsolving system that used it. Despite these worst case results general reasoning algorithms are becoming remarkably fast and finding practical applications. In this section ....

H. J. Levesque and R. J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3(2):78--93, 1987.

....accurately and efficiently with combined information. In the context of related work, our study was mainly inspired from two currently disjoint research fields. The first is concerned by tractable approaches of knowledge representation. Standard techniques such as language restriction (e.g. [23]) or knowledge compilation (e.g. 28] are ill suited in this setting. Notably, they use classical logic and thus become fragile when contradictions appear within a pool of combined information. Furthermore, the technique of language restriction is not adequate for modeling agents that need at ....

H. J. Levesque and R. J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3(2):78--93, 1987.

....for this application. Unsurprisingly, the more expressive power a DL provides, the more complex the reasoning algorithms for this DL are. As a consequence, a variety of DLs were introduced together with investigations of the complexity of the corresponding reasoning algorithms problems (see, e.g. [26, 34, 13]) In 1991, Schild described the close relationship between DLs and modal logics or dynamic logics [32] For example, it turned out that ALC is a notational variant of multi modal K. Following that, numerous new DLs with corresponding complexity results emerged by (extensions of) translations ....

H. Levesque and R. J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3, 1987.

....Therefore, subsumption is usually defined to be independent of these contingent assertions. As we shall see below, the use of individual properties in description subsumption also leads to intractability. 3. 1 Complex Subsumption Reasoning: An Example Traditional proofs of intractability (e.g. (Levesque Brachman, 1987)) have occasionally left users of DLs puzzled over the intuitive aspects of a language which make reasoning difficult. For this reason we present an example that illustrates the complexity of reasoning with the set description. Suppose that we have the concept of JADED PERSON as being one who ....

Levesque, H. J., & Brachman, R. J. (1987). Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3 (2), 78--93.

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Hector J. Levesque and Ronald J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

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Hector J. Levesque and Ronald J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

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H. Levesque, R. Brachman. Expressiveness and Tractability in Knowledge Representation and Reasoning. Computational Intelligence, 3: 7893, 1987.

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Levesque, H.J. and R.J. Brachman, Expressiveness and Tractability in Knowledge Representation and Reasoning. Computational Intelligence, 1987. 3(2): p. 78-93.

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Levesque, H.J. and R.J. Brachman, Expressiveness and Tractability in Knowledge Representation and Reasoning. Computational Intelligence, 1987. 3(2): p. 78-93.

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R. Brachman and H. Levesque. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78-93, 1987.

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H.Levesque and R.Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78--93, 1987.

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Hector J. Levesque and Ron J. Brachman. Expressiveness and tractability in knowledge representation and reasoning. Computational Intelligence, 3:78-93, 1987.

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H. Levesque, R. Brachman. Expressiveness and Tractability in Knowledge Representation and Reasoning. Computational Intelligence, 3: 7893, 1987.

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H.J. Levesque and R.J. Brachman. Expressiveness and tractability in knowledge representation. Computational Intelligence, 3(2):78--93, 1987.

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