Tomasz Imielinski. Results on translating defaults to circumscription. Arti cial Intelligence, 32(1):131-146, April 1987.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sense: 8x( b(x) ab(x) f (x) The idea is to minimize abnormality to only those objects which are known to be abnormal. The relationships between default logic and circumscription as well as between autoepistemic logic and circumscription have been investigated by a number of researchers [25, 26, 47, 74, 63]. Imielinski [47] points out that default rules cannot not be translated modularly into circumscription. This due to the fact that circumscription cannot capture the notion of provability or logical consequence required to translate a default rule. We show that Imielinski s [47] argument applies ....

....The idea is to minimize abnormality to only those objects which are known to be abnormal. The relationships between default logic and circumscription as well as between autoepistemic logic and circumscription have been investigated by a number of researchers [25, 26, 47, 74, 63] Imielinski [47] points out that default rules cannot not be translated modularly into circumscription. This due to the fact that circumscription cannot capture the notion of provability or logical consequence required to translate a default rule. We show that Imielinski s [47] argument applies also to ....

[Article contains additional citation context not shown here]

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32:131--146, 1987.

....for translations that depend globally on the theory under translation so that a local modication to the theory changes the translation totally. However, it is possible to introduce further constraints for translation functions. A very promising requirement modularity is introduced by Imielinski [10] and then used by Gottlob [9] and Niemel# [23] Roughly speaking, a modular translation function is in a sense systematic: local changes in a theory cause only local changes in its translation. Most importantly, it has been shown that a modular translation function between certain non monotonic ....

....are exhibited in this section in order to classify non monotonic logics by their expressive power. Moreover, counter examples are provided to show that such translations are not possible in certain cases. Such non equivalence proofs have already been devised for non monotonic logics by Imielinski [10], Gottlob [9] and Niemel# [23] In the forthcoming subsections, we perform a pairwise comparison of non monotonic logics in the following order: CIRC, AEL, SAEL, DL and PL. But as a starter, we relate classical propositional logic (CL) with CIRC. This result is supported by other complexity and ....

[Article contains additional citation context not shown here]

T. Imielinski. Results on translating defaults to circumscription. Articial Intelligence, 32:131146, 1987.

.... strong autoepistemic logic by Marek and Truszczyski [16] and syntactically restricted forms of default logic such as normal default logic and prerequisite free default logic (see e.g. 4] Naturally, the interconnections of these variants to their predecessors have also been analyzed (see e.g. [1, 5, 6, 8, 15, 16, 20, 23]) The translation functions proposed in the literature provide means to measure the expressive power of non monotonic logics involved: a non monotonic logic can capture expressions of another non monotonic logic via a translation function. The tightness of this relationship depends on the ....

....We have adopted three requirements from earlier approaches namely polynomiality, faithfulness and modularity (PFM) as the basis of our framework. In particular, the modularity requirement has turned out to be useful when one wants to di erentiate non monotonic logics by their expressive power [5, 6, 9]. The author has used PFM translation functions systematically for classifying non monotonic logics on the basis of their expressive power. So far, our analysis [10] has covered eight non monotonic logics giving rise to a hierarchy (EPH) on page 3. In this paper, we analyze the expressive powers ....

T. Imielinski. Results on translating defaults to circumscription. Articial Intelligence, 32:131146, 1987.

.... construction to de ne the level of an atom a 2 Mm(P ) denoted by l(a) which is the least natural number i such that a 2 TP i ( 3 Translations The author has analyzed the expressive powers of non monotonic logics in a systematic fashion [9, 10] extending previous work by Imielinski [8] and Gottlob [7] Roughly speaking, the comparison is performed for any pair of non monotonic logics by analyzing the existence of certain kinds of translation functions between the logics. As a result of such pairwise comparisons, we have gradually constructed the expressive power hierarchy (EPH) ....

T. Imielinski. Results on translating defaults to circumscription. Articial Intelligence, 32:131146, 1987.

.... provides the key challenge [48, 61, 1, 2] Circumscription has been used to capture, e.g. semantics of logic programs [60] The relationships between default logic and circumscription as well as between autoepistemic logic and circumscription have been investigated by a number of researchers [24, 25, 41, 62, 52]. Etherington s [25] and Brewka s [13] books are good sources on circumscription. 3 Decidability and Complexity In default logic possible sets of correct conclusions from a default theory are given in terms of extensions of the default theory and in nonmonotonic modal logics (and in Niemel# and ....

....modal logics and default logics have been studied intensively [71, 118, 119] These results show that default logic can be embedded into nonmonotonic modal logics using local translations in the sense that extensions of a default theory are expansions of the translated theory. Imielinski [41] points out that default rules cannot not be translated modularly into circumscription. This due to the fact that circumscription cannot capture the notion of provability or logical consequence required to translate a default rule. As an example we consider a particular intuitively appealing ....

T. Imielinski. Results on translating defaults to circumscription. Articial Intelligence, 32:131146, 1987.

.... to study the relationship between prioritized argumentation and default reasoning (in the sense of Reiter [41] as Reiter s default logic is perhaps the most extensively studied nonmonotonic reasoning formalism, and its relationships with other formalisms have often been investigated deeply (cf. [18, 23, 32]) Thus the technical ideas in establishing the main results of this paper could be useful in studying how prioritized argumentation is related to other forms of nonmonotonic reasoning. We first show that defaults can be expressed adequately by priority among rules. This is achieved by a ....

....use of rule labels in priority logic. Abnormality symbols are semantic entities. Whether they can be embedded in the original 19 Before answering this question, let s define the notion of modular transformation within the same language. The concept of modularity was first introduced by Imielinski [23] and later used by Gottlob [21] in the study of translation between two different formal systems. Here we adopt their definition for the context of priority logic programs. Definition 4.5 (modular translation) Suppose L is a propositional language. A translation Delta from priority logic ....

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32:131--146, 1987.

....formalism will conclude that Tweety is not a bird, while the more conventional one will not. Thus the default rule does not contrapose in the original formulation. I am indebted to Karen Myers for pointing this out to me. Imielinski also discusses this and related issues at some length in [28]; his results appear to indicate that it is only seminormal defaults without preconditions that can be captured in a multivalued setting. r r r r r r r r r r Phi Phi Phi Phi Phi Phi Phi Phi PhiH H H H H H H H H H H H H H H H H H Phi Phi Phi Phi Phi Phi Phi Phi Phi A A A A A A A ....

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32:131--146, 1987.

....a great variety of different approaches to nonmonotonic reasoning have been introduced, of which none seems to be the best approach. A very positive development is the fact that recently several results clarifying the connection between different approaches have been obtained (see, e.g. [61, 64, 65, 71, 66]) In the following, we briefly introduce the four most important types of approaches. Consistency based approaches, of which Reiter s Default Logic [97] is a typical example, consider nonmonotonic rules of the form A normally implies B. Such a rule can be applied (i.e. B is inserted in the ....

T. Imielinski. Results on translating defaults to circumscription. Journal of Artificial Intelligence, 32(1):131--146, 1987.

....reasoning. In the past decade, variations and extensions to the circumscriptive formalism has been studied by several researchers Bidoit , Bossu , Etherington , Gelfond , Hull , Imielinski , Li , Lifschitz , Minker , Moinard , Perlis , Przymusinska , Przymusinski , Reiter , Siegel and You . [40, 24, 25, 3, 5, 2, 13, 12, 23, 2, 7, 9, 11, 15, 14, 21, 32, 35, 8, 31, 10, 16, 30, 36, 33, 34, 43]. One of the major concerns in the field has been the computational aspect of circumscription. The problem of answering queries using circumscription can be stated as follows [6] Given a finite set of axioms A, a circumscriptive policy C, and a formula F, does F follow from A by the ....

T. Imielinski. Results on Translating Defaults to Circumscription. Artificial Intelligence, 32:131--146, 1986.

....There are at least three important reasons for choosing these two formalisms to demonstrate the generality of priority logic. First, default logic is perhaps the most prominent nonmonotonic reasoning formalism, and its relationship with other nonmonotonic formalisms has been studied extensively [13, 16, 21]. Secondly, default logic and logic programming with negation are often related at the level of literals (e.g. 20] The fact that default logic is syntactically richer often makes it unclear whether an idea in logic programming can be successfully applied to default reasoning. Thirdly, in view ....

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32:131--146, 1987.

....sense: 8x( b(x) ab(x) f (x) The idea is to minimize abnormality to only those objects which are known to be abnormal. The relationships between default logic and circumscription as well as between autoepistemic logic and circumscription have been investigated by a number of researchers [25, 26, 47, 74, 63]. Imielinski [47] points out that default rules cannot not be translated modularly into circumscription. This due to the fact that circumscription cannot capture the notion of provability or logical consequence required to translate a default rule. We show that Imielinski s [47] argument applies ....

....(x) The idea is to minimize abnormality to only those objects which are known to be abnormal. The relationships between default logic and circumscription as well as between autoepistemic logic and circumscription have been investigated by a number of researchers [25, 26, 47, 74, 63] Imielinski [47] points out that default rules cannot not be translated modularly into circumscription. This due to the fact that circumscription cannot capture the notion of provability or logical consequence required to translate a default rule. We show that Imielinski s [47] argument applies also to ....

[Article contains additional citation context not shown here]

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32:131--146, 1987.

.... provides the key challenge [48, 61, 1, 2] Circumscription has been used to capture, e.g. semantics of logic programs [60] The relationships between default logic and circumscription as well as between autoepistemic logic and circumscription have been investigated by a number of researchers [24, 25, 41, 62, 52]. Etherington s [25] and Brewka s [13] books are good sources on circumscription. 3 Decidability and Complexity In default logic possible sets of correct conclusions from a default theory are given in terms of extensions of the default theory and in nonmonotonic modal logics (and in Niemela and ....

....modal logics and default logics have been studied intensively [71, 118, 119] These results show that default logic can be embedded into nonmonotonic modal logics using local translations in the sense that extensions of a default theory are expansions of the translated theory. Imielinski [41] points out that default rules cannot not be translated modularly into circumscription. This due to the fact that circumscription cannot capture the notion of provability or logical consequence required to translate a default rule. As an example we consider a particular intuitively appealing ....

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32:131--146, 1987.

....inference algorithm for such networks. Lobo and Subrahmanian [LS92] show that given any disjunctive logic program P , the minimal Herbrand models of P are in a precise 1 1 correspondence with the default logic theory 1P obtained by adding to P the default logic schema : A :A . See Imielinski [Imi87] for connections between default logic and circumscription. Selman [Sel90] in an excellent thesis, explores three default reasoning formalisms. He obtains the first characterization of tractable forms of default reasoning. He also gives a high level characterization of the main factors ....

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32:131--146, 1987.

....Same goes if we chose to represent our default in Default Logic: p :p . Since defaults are represented differently in different nonmonotonic frameworks, we proceed by restricting ourselves to circumscription, and only note the following two results. For the propositional case, it was shown in (Imielinski, 1987) that Default Logic is translatable to Circumscription in the case of open semi normal defaults (i.e. defaults of the form :fffi fi ) Second, Konolige (Konolige, 1988) showed that Autoepistemic Logic and Default logic are formally equivalent. The following is an account of defaults and ....

Imielinski, T. (1987). Results on translating defaults to circumscription. Artificial Intelligence, 32(1):131--146.

....It is worth noticing that those reductions have been studied with the primary goal of comparing semantics and expressiveness and were not intended for complexity analysis. In particular, transformations are usually required to fulfill some abstract criteria. Modularity, defined by Imielinski in [72] in the context of translations from default logic into circumscription, is one of these criteria. Loosely speaking, a translation is modular if the introduction of new facts does not require recomputation of the whole translation from the beginning. Grosof [69] Imielinski [72] and Etherington ....

....by Imielinski in [72] in the context of translations from default logic into circumscription, is one of these criteria. Loosely speaking, a translation is modular if the introduction of new facts does not require recomputation of the whole translation from the beginning. Grosof [69] Imielinski [72] and Etherington [50, 51] addressed the issue of translating default theories into circumscriptive ones. Transformation for some restricted classes of default theories, such as propositional semi normal defaults without prerequisites, are shown. Several authors have shown the relations within ....

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence Journal, 32:131--146, 1987.

No context found.

Tomasz Imielinski. Results on translating defaults to circumscription. Arti cial Intelligence, 32(1):131-146, April 1987.

No context found.

Tomasz Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32(1):131--146, April 1987.

No context found.

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32(1):131--146, Apr. 1987.

No context found.

T. Imielinski. Results on translating defaults to circumscription. Articial Intelligence, 32:131146, 1987.

No context found.

T. Imielinski. Results on translating defaults to circumscription. Artificial Intelligence, 32:131--146, 1987.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC