Franz Baader and Bernhard Hollunder. How to prefer more specific defaults in terminological default logic. In Ruzena Bajcsy, editor, Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pages 669--674, San Mateo, California, 1993. Morgan Kaufmann.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....ordered program ( that is a strict partial order. The static concept of preference corresponds to most previous approaches to preference handling in logic programming and nonmonotonic reasoning, where the preference information is specified as a fixed relation at the meta level (cf. [Baader and Hollunder, 1993; Brewka, 1994; Zhang and Foo, 1997; Brewka and Eiter, 1999; Wang et al. 2000] The idea behind our methodology for compiling preferences is straightforward. Given a preference handling strategy , our approach provides a mapping T that transforms an ordered logic program into a standard ....

....been applied or found to be blocked. This is important to guarantee the selection among existing answer sets, since otherwise not all rules of the original program are considered (cf. Proposition 4.2 and 5. 3) Let us illustrate this by means of the following statically ordered program taken from [Baader and Hollunder, 1993] : r 1 = f p; not f r 2 = w b; not :w r 3 = f w; not :f r 4 = b p r 5 = p r 2 r 1 : 7) Program 7 = fr 1 ; r 5 g has two answer sets: X 1 = fp; b; w; fg and X 2 = fp; b; w; fg. Letters b; p; f; w stand, as usual, for birds, penguins, flies, and wings, respectively. Baader ....

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F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In R. Bajcsy, editor, Proceedings of the International Joint

....in human s commonsense reasoning. In fact, the famous example of whether penguins fly because they are birds [23] in default reasoning is an example of reasoning with specificity. Reasoning with specificity also constitutes a difficult problem which has been studied extensively in the literature [1, 5, 7, 14, 16, 29, 31, 38]. Formally a default theory T could be defined as a pair (E; K) where E is a set of evidence or facts representing what we call the concrete context of T , and K = D; B) constitutes the domain knowledge consisting of a set of default rules D and a first order theory B representing the background ....

....T could be defined as a pair (E; K) where E is a set of evidence or facts representing what we call the concrete context of T , and K = D; B) constitutes the domain knowledge consisting of a set of default rules D and a first order theory B representing the background knowledge. In the literature [1, 5, 7, 14, 16, 29] the principle of reasoning with specificity is enforced by first determining a set of priority orders between defaults in D using the information given by the domain knowledge K. Based on these priorities between defaults and following some sensible and intuitive criteria, the semantics of T is ....

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Baader, F. and Hollunder, B.: How to prefer more specific defaults in terminological default logic, Proc. IJCAI'93.

....method. This applies also to the approach in [Sakama and Inoue, 1996] where preferences on literals are investigated. While the approach of [Gelfond and Son, 1997] remains within NP, it advocates strategies that are non selective. Approaches that can be addressed within this framework include [Baader and Hollunder, 1993; Brewka, 1994] that were originally proposed for default logic. 2 Definitions and notation We assume a basic familiarity with logic programming under answer set semantics [Gelfond and Lifschitz, 1991] An extended logic program is a finite set of rules of the form L 0 L 1 ; Lm ; not ....

....rules. That is, once the negative body body (r) is eliminated there is no way to detect whether head (r 0 ) 2 body (r) holds in case of r r 0 . Such an approach is pursued in [Wang et al. 2000] for characterizing preferred answer sets. Following earlier approaches based on default logic [Baader and Hollunder, 1993; Brewka, 1994] this approach is based on the concept of activeness: Let X;Y Lit be two sets of literals in an ordered logic program ( A rule r in is active wrt the pair (X; Y ) if body (r) X and body (r) Y = Definition 1 (Wang et al. 2000) Let ( be an ordered logic ....

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F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In Proc. IJCAI'93, p 669--674, 1993.

....applying all maximal defaults at each step. In contrast we translate priorities into standard default theories. As a first distinguishing example, consider the normal default rules ffi 1 : A A ; ffi 2 : B B ; ffi 3 : B : C C ; ffi 4 : A : C :C along with ffi 4 ffi 3 ; taken from [Baader and Hollunder, 1993b] With no facts Baader and Hollunder obtain one extension containing fA; B;Cg: Curiously, Brewka obtains an additional extension containing fA; B; Cg: In our approach, the resultant default theory yields only the first extension containing fA; B;Cg: So here our approach yields the same result as ....

....containing fA; B;Cg: Curiously, Brewka obtains an additional extension containing fA; B; Cg: In our approach, the resultant default theory yields only the first extension containing fA; B;Cg: So here our approach yields the same result as Baader and Hollunder s. As a second example, again from [Baader and Hollunder, 1993b] consider the rules ffi 1 : A A ; ffi 2 : B : A :A ; ffi 3 : B B ; ffi 4 : A : B :B along with ffi 1 ffi 2 ; ffi 3 ffi 4 : Baader and Hollunder show that in Brewka s approach two extensions are obtained, one containing fA; Bg and another containing f:A;Bg: However an ....

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. Technical Report RR-92-58, DFKI, December 1993. 46

....i i i2I of default rules is grounded in a set of formulas W , if we have for every i 2 I that W [ Conseq(fffi 0 ; ffi i Gamma1 g) Prereq(ffi i ) For adding preferences among default rules, a default theory is usually extended with an ordering on the set of default rules. In analogy to [Baader and Hollunder, 1993a; Brewka, 3 1994a] an ordered default theory (D; W; is a finite set D of default rules, a finite set W of formulas, and a strict partial order D Theta D on the default rules. That is, is a binary irreflexive and transitive relation on D. For simplicity in the following development we ....

....arguably they in fact implement the (distinct) notion of preference, described following. 2 This isn t intended as a cut and dried distinction, but rather as an often useful classification. For example, Brewka and Eiter, 2000 ] contains elements of both. 3 This is for instance obtained in [ Baader and Hollunder, 1993a; Brewka, 1994a; Marek and Truszczy nski, 1993 ] the approach presented in Section 4 yields no preferred extension. 5 least preferred default, the most preferred default can be applied; this yields an extension containing fA; Bg. This has led some researchers to advocate systems based on the ....

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F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 669--674, 1993.

....Another conditional approach which is also equivalent to System Z is Lamarre s normal big model (Lamarre, 1992) He shows how conditional logic can deal with exceptional rules. He gives a theorem prover based on a construction of a particular Lewis system of spheres called big normal model . Baader and Hollunder (1993) propose a way to modify terminological 34 default logic such that more specific defaults will be preferred. Concepts in terminological logic are described by a first order formula OE(x) with one free variable x. The subsumption hierarchy between concepts is defined as: OE is subsumed by iff 8 ....

....x OE(x) x) Terminological default rules are defaults rules where antecedents and consequents are concepts. Given two terminological default rules d 1 : ff 1 fi 1 and d 2 : ff 2 fi 2 then d 1 is said to be more specific than d 2 if and only if ff 1 subsumes ff 2 but not conversely. Lastly, Baader and Hollunder (1993) define a class of extensions in the sense of Reiter which takes in consideration the specificity ordering. Lastly, specificity is also used in the context of logic programming (Geerts and Vermeir, 1993; Gregoire, 1989) Often, a translation of inheritance networks into the language of logic ....

F. Baader and B. Hollunder(1993), How to prefer more specific defaults in terminological default logic. Proc. of the 13th Inter. Joint Conf. on Artificial Intelligence (IJCAI'93), Aug. 28-Sept. 23, pp.669-674.

....exceptions or of default or typical characteristics. 1 We argue that in many applications what one wants is a notion of individuals being recognised as members of a concept, based on having a sufficient number of a cluster of 1 Some work has been done on extending DLs to include defaults (e.g. [Baader and Hollunder, 1993, Padgham and Nebel, 1993, Padgham and Zhang, 1993] but this is primarily directed towards default reasoning, rather than the issue of using defaults for recognition as is being explored here. typical characteristics (plus possibly some necessary characteristics) rather than simply a fixed set ....

Franz Baader and Bernhard Hollunder. How to prefer more specific defaults in terminological default logic. In Proc. of the 13th Int. Joint Conf. on Artificial Intelligence (IJCAI-93), pages 669--674, 1993.

....normal defaults. 1 An al 1 According to [Brewka,1994] the approach given in [Brewka,1991, Section 3] leads to reasonable results for prerequisite free normal defaults only, although it applies to normal defaults, too. ternative approach to prioritized default theories is proposed in [ Baader Hollunder,1993 ] In fact, it is shown in [ Baader Hollunder,1993 ] that both approaches are orthogonal to each other even though they share many common intuitions. According to [ Brewka,1994 ] the basic idea is as follows: during the generation of an extension defaults with higher priorities whose ....

...., the approach given in [Brewka,1991, Section 3] leads to reasonable results for prerequisite free normal defaults only, although it applies to normal defaults, too. ternative approach to prioritized default theories is proposed in [ Baader Hollunder,1993 ] In fact, it is shown in [ Baader Hollunder,1993 ] that both approaches are orthogonal to each other even though they share many common intuitions. According to [ Brewka,1994 ] the basic idea is as follows: during the generation of an extension defaults with higher priorities whose prerequisite has been derived are always considered before ....

F. Baader & B. Hollunder. How to prefer more specific defaults in terminological default logic. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 669--674, 1993.

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Franz Baader and Bernhard Hollunder. How to prefer more specific defaults in terminological default logic. In Ruzena Bajcsy, editor, Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pages 669--674, San Mateo, California, 1993. Morgan Kaufmann.

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In R. Bajcsy, editor, Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pages 669--674, San Mateo, California, 1993. Morgan Kaufmann.

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Franz Baader and Bernhard Hollunder. How to prefer more specific defaults in terminological default logic. Technical Report RR-92-58, 1992.

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Baader, F., and Hollunder, B. 1993b. How to prefer more specific defaults in terminological default logic. Technical Report RR92 -58, DFKI.

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Baader, F., and Hollunder, B. 1993a. How to prefer more specific defaults in terminological default logic. In Bajcsy, R., ed., Proceedings of the International Joint Conference on Artificial Intelligence, 669--674. Morgan Kaufmann Publishers.

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In R. Bajcsy, editor, Proceedings of the International Joint Conference on Artificial Intelligence, pages 669--674. Morgan Kaufmann Publishers, 1993.

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. Technical Report RR-92-58, DFKI, December 1993.

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In R. Bajcsy, editor, Proceedings of the International Joint Conference on Artificial Intelligence, pages 669--674. Morgan Kaufmann Publishers, 1993.

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 669--674, 1993.

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In R. Bajcsy, editor, Proceedings of the International Joint Conference on Artificial Intelligence, pages 669--674. Morgan Kaufmann Publishers, 1993.

No context found.

F. Baader and B. Hollunder, `How to prefer more specific defaults in terminological default logic', in Proc. IJCAI, pp. 669--674, (1993).

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F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. Technical Report RR-92-58, DFKI, December 1993. 46

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 669--674, 1993.

No context found.

Franz Baader and Bernhard Hollunder. How to prefer more specific defaults in terminological default logic. In Ruzena Bajcsy, editor, Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pages 669--674, San Mateo, California, 1993. Morgan Kaufmann.

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In Proc. IJCAI'93, p 669--674, 1993.

No context found.

Franz Baader and Bernhard Hollunder. How to prefer more specific defaults in terminological default logic. In Ruzena Bajcsy, editor, Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pages 669--674, San Mateo, California, 1993. Morgan Kaufmann.

No context found.

F. Baader and B. Hollunder. How to prefer more specific defaults in terminological default logic. In R. Bajcsy, editor, Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, pages 669--674, San Mateo, California, 1993. Morgan Kaufmann.

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