Peter F. Patel-Schneider. Decidable, Logic-Based Knowledge Representation. PhD thesis, Univ. Toronto, 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....level. We must resolve conflict among our desires . We must resolve conflict among our beliefs . The resolution of such conflicts is essential . 14, page 78] This move to the meta is the obvious thing to do. From AI researchers discussing metaplanning and metalevel inference [2, 7, 8, 17, 18, 19] to philosophers discussing basic mechanisms of mind the move to the meta has been found generally attractive. Assume some form of metalevel control for managing agents working on subproblems. How does the metalevel executive actually work Philosophers tend not to build systems, and the history ....

Peter Jackson, Han Reichgelt, and Frank van Harmalen (eds.). Logicbased Knowledge Representation. The MIT Press, Cambridge, MA, 1989.

....1975] and Dunn [Dunn, 1976] which make it amenable to the various extensions needed for modelling IR. Finally, the computational properties of E fde have been investigated. While deciding entailment in the general case is likely to be intractable (technically, the problem is co NPcomplete [Patel Schneider, 1987b] whenever ff and fi are formulae in Conjunctive Normal Form, there exists a O(jffj Delta jfij) algorithm that tests if ff fi holds [Levesque, 1984] Relevance TLs, i.e. four valued TLs based on some relevance logic, have already been used in Knowledge Representation and proven to have a ....

P.F. Patel-Schneider. Decidable, logic-based knowledge representation. Technical Report 201/87, Department of Computer Science, University of Toronto, Toronto, Ontario, 1987.

....the idea of Brink and Schmidt (1992) and formalize the language U in the context of Peirce algebra. To begin with we define the syntax of U . Our presentation is in line with that of Schmidt Schau and Smolka (1991) and Brink and Schmidt (1992) The syntax we use for U is essentially that of Patel Schneider (1987). The vocabulary of U consists of three disjoint sets of symbols: the set of primitive concepts, the set of primitive roles and the set of structural symbols. Primitive concepts and roles are also referred to as being atomic or generic . There are two designated concepts, the top concept ....

....C I , D I , and R I , S I , by C, D, and R, S, respectively. U abbreviates D I and Rb i abbreviates Rb i I . For expository purposes and without changing the expressive and deductive capabilities of U we have slightly adapted the original vocabulary in Patel Schneider (1987). The names of some of the operators have been changed; and, or and compose are here defined as binary operators; for some we use the more general definition given by Schmidt Schau and Smolka (1991) there denoted by 9R : C) and we Table 1: Algebraic Semantics of U Gamma Terminological ....

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Patel-Schneider, P. F. (1987), Decidable, Logic-Based Knowledge Representation, PhD thesis, University of Toronto.

....sd expression is equivalent to (not self) For this we need to establish that e ne 0 = e 0 . It follows by R11, R9 and R21 that e ne 0 = e ne 0 = ene 0 = e 0 = e 0 = e 0 . As a final example (which involves the all construct) consider the following expression from Patel Schneider [1990, p. 14] 4.28) and Persons (and (all has child Lawyers) all (restrict has child Lawyers) Doctors) v (and Persons (all has child Doctors) This is quite complicated. It is also not clear how to read this in English. Patel Schneider himself translates the subsumed term by the class of ....

Patel-Schneider, P.F. [1987a]. Decidable, Logic-Based Knowledge Representation. PhD Dissertation, University of Toronto.

....the idea to modify KL is as follows. We give existentially quantified variables within belief a constructive interpretation so that (roughly) an agent believes an existential only if he has a name for it. 8 More concretely, we restrict the semantics of belief in 8 This idea is used in [22, 13, 14] in order to obtain an efficient first order reasoner. These logics, in addition, also employ a four valued semantics, which is not necessary for our purposes. such a way that a sentence with existentially quantified variables is believed iff a corresponding sentence with all existentially ....

Patel-Schneider, P. F., Decidable, Logic-Based Knowledge Representation, Ph.D thesis, University of Toronto, 1987.

....about elements of concepts and roles. The different terminological representation languages distinguish themselves by the syntactic operators they provide for constructing complex concept and role descriptions. In column one of Figure 1 I list a subset of operators available in the language U of PatelSchneider (1987) and the language KL of Woods and Schmolze (1992) These are very expressive terminological languages. Most terminological languages like the AL languages provide only a selection of these operators. Concepts can be interrelated by the subsumption relation. Subsumption is interpreted as the ....

Patel-Schneider, P. F. (1987), Decidable, Logic-Based Knowledge Representation, PhD thesis, University of Toronto.

....representation; it should apply proactively to items not yet created. The privacy interface should make it easy to create, inspect, modify, and monitor such objects. To clarify this objective, we introduce the distinction between intensional and extensional representations of privacy policies [5]. An extensional representation describes a set by enumerating the items in it (such as a list of all private web pages) The record light interface creates an extensional privacy policy. In contrast, an intensional representation describes a set by characterizing the objects in the set. Consider, ....

Peter Jackson, Han Reichgelt, and Frank van Harmelen. Logic-Based Knowledge Representation, page 41. MIT Press, 1989.

....introduction and role value maps (another popular concept forming operator) Alternatively, instead of general number restrictions, a limited set of restricted operators could be used, e.g. some, none and unique 11 . Another way out of this dilemma, pursued by Patel Schneider in [17] and [18], could be to use a different semantics based on a four valued logic, for which a complete and tractable subsumption algorithm even for very expressive FDLs can be specified. Another view of this solution is that it provides a sound algorithm for standard semantics and gives a precise account a ....

Patel-Schneider, P. F., Decidable, Logic-Based Knowledge Representation, Ph.D. Thesis Draft, 1986.

....are not explicitly mentioned (or that cannot be inferred) are taken to be false. by V in exactly the same way as V does. In [ Schild, 1994b ] we investigated the computational complexity of answering such queries with respect to physical knowledge bases in the description logic U , introduced by Patel Schneider [ 1987 ] as a universal description logic. This concept language is universal in the sense that it encompasses all others considered in the literature, except for those which comprise nonstandard facilities like defaults, for instance. In addition to those of ALC, this language comprises number ....

....structuring primitives of U are the identity role ffl, Boolean operations u, t, on roles, the inverse R Gamma1 of a role, the composition R ffiS of two roles, as well as the transitive closure R and the reflexive transitive closure R of a role. For details cf. Schild, 1994b ] or [ Patel Schneider, 1987 ] Notably, it is known that there cannot exist any algorithm which is capable of deciding subsumption between two concepts (or two roles) of U , even with respect to empty terminologies [ Schild, 1988 ] The main result of [ Schild, 1994b ] is that even in this language V j= T Q can be decided ....

Peter F. Patel-Schneider. Decidable, Logic-Based Knowledge Representation. PhD thesis, University of Toronto, Toronto, Ont., 1987. Computer Science Department, Technical Report 201/87.

....a very small language in comparison with other DLs, and its implementation appeared to be evidently correct. To avoid such problems, it is necessary to produce convincing demonstrations that the algorithm is correct; several such proofs have in fact already appeared in the DL literature (e.g. (Patel Schneider, 1987; Hollunder Nutt, 1990; Donini et al. 1991) albeit only for languages that have not seen use in practical applications. 1.2 Outline The classic 1 2 system is a reasoner based on a moderately complicated DL. It is being used in commercial (Wright et al. 1993) and prototype applications at ....

Patel-Schneider, P. F. (1987). Decidable, Logic-Based Knowledge Representation. Ph.D.

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Peter F. Patel-Schneider. Decidable, Logic-Based Knowledge Representation. PhD thesis, Univ. Toronto, 1987.

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Peter Jackson, Han Reichgelt, and Frank van Harmalen (eds.). Logic-based Knowledge Representation. The MIT Press, Cambridge, MA, 1989.

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