Etherington, D.W. : A Semantics for Default Logic, Proc. IJCAI-87, pp. 495-498; see also in: D.W. Etherington, Reasoning with Incomplete Information, Morgan Kaufmann, 1988  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... ff( x) fi( x) by the semi normal default: and to replace the semi normal default: by the normal default: fi( x) fl( x) The first is non controversial, but the second, despite being applicable for a large range of practically occurring defaults, has some rather alarming exceptions [30]. By using both translations sequentially, we can replace the eminently sensible: has motive(x ) guilty(x ) suspect(x ) by the rather unreasonable: has motive(x ) suspect(x ) guilty(x ) suspect(x ) guilty(x ) In a further paper, Lukaszewicz [55] generalises default logic, providing ....

D. W. Etherington. Reasoning with Incomplete Information. Pitman, London, UK, 1988.

....credulous one, in which a query is said to be derivable if it belongs to a single extension, and a skeptical one, in which one stipulates that a query lies in all extensions. So far, computational approaches to nonmonotonic logics have mainly focused on the computation of entire extensions, like [4, 22, 9, 25, 14], or credulous queryanswering, like [17, 21] 10] compute intersections of extensions in Autoepistemic Logic. Skeptical query answering has up to now been primarily studied in restricted nonmonotonic reasoning frameworks, like Theorist [15] corresponding to so called prerequisitefree default ....

D. Etherington. Reasoning with Incomplete Information. Research Notes in Artificial Intelligence. Pitman / Morgan Kaufmann, London, 1988.

..... The models of C(B;H;Z) are exactly those models of B[Z] that are most preferred with respect to vH . The circumscriptive theory is defined as the set of sentences satisfied in all models of C(B;H;Z) i.e. in all most preferred models of B, following [Lifschitz, 1988a] In general, however, as [Etherington, 1988] remarks, the existence of a model preference correspondent to a syntactically defined pre order is an open question. Notation: Let D E stand for 8x: D(x)oeE(x) where D and E are open formulas with the same arity (i.e. are sim One can express the fixing of a subset W of the predicates and ....

D. Etherington. Reasoning with Incomplete Information. Pitman, London, 1988.

....a single edition [37] From this work, default logic by Reiter [122] the family of circumscription type formalizations [92, 93] McDermott and Doyle style logics [96, 95] and autoepistemic logic [98] stand out as leading logical formalizations of nonmonotonic reasoning. The books of Etherington [26], Besnard [6] and Brewka [11] provide introductions to nonmonotonic reasoning. The aim of this work is to strengthen the theoretical foundations of symbolic nonmonotonic reasoning. For that purpose we strive for a framework where nonmonotonic reasoning can be analysed as sentences in some formal ....

....i=0 E i and 3. apply D;E ( i=0 E i . Furthermore, Reiter [122, Theorem 2.5] shows that if E is an extension of (D; W ) then E = Cn cl (W [ apply D;E (E) 7:6) Default logic is one of the most prominent formalizations of nonmonotonic reasoning. The books of Besnard [6] and Etherington [26] are good sources on default logic. There is a body of results indicating that default logic can capture a large number of different forms of nonmonotonic reasoning. Default logic is especially closely related to reasoning in logic programs and deductive databases [8, 9, 33] Default logic has ....

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D.W. Etherington. Reasoning with Incomplete Information. Pitman, London, 1988.

....Example 2 (Default Logic) Let D be a set of defaults. For X L let E( X, D ) denote the set of (Reiter) extensions of the default theory X, D . The following belief state operator and model operator can be defined for X L: G D (X) Mod(E) E D (X) fi Mod(E) E Compared to [Et87] (see also [Vo93] we have the following relation: G D (X) Mod(Th(M) M D minimal and D stable Default logic essentially gives a description at level 2 (and 3 as we shall see later) It does not abstract from these lower levels. 4 Reasoning Frames In the previous chapter we have seen ....

Etherington, D.W. : A Semantics for Default Logic, Proc. IJCAI-87, pp. 495-498; see also in: D.W. Etherington, Reasoning with Incomplete Information, Morgan Kaufmann, 1988

....same type, then P P is an abbreviation for: P 1 P 1 : P n P where P = P 1 ; P n and P = P 1 ; P n . P P stands for P P :P P. Here, we describe the model theoretic meaning of this circumscription. For a more comprehensive discussion refer to [36, 37, 26, 46, 13]. Let M 1 and M 2 be two arbitrary models of the theory Sigma in the language L with the tuples P and Z as before. We write M 1 M 2 if: 1. kM 1 k = kM 2 k. That is, M 1 and M 2 share the same domain. 2. M 1 and M 2 interpret every constant not in P; Z in the same way Later we write ....

....model of Sigma with respect to . B.2 Circumscribing Skolemized Theories It is well understood that existential theories are not logically equivalent to their skolemized versions. One of the consequences of this fact is that skolemization may change the set of minimal models of a theory [13]. On the positive side, we know that skolemization preserves satisfiability. Now, we would like to know if it is possible to retain this property by changing the circumscription policy. Thus, can we define a skolemized circumscription In this appendix we show that this is indeed possible. In ....

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Etherington, D. W. Reasoning with Incomplete Information, Investigations of NonMonotonic Reasoning. PhD thesis, The University of British Columbia, Apr. 1986. 117

.... and to replace the semi normal default: x) x) x) x) by the normal default: x) x) x) x) x) The rst is non controversial, but the second, despite being applicable for a large range of practically occurring defaults, has some rather alarming exceptions [30]. By using both translations sequentially, we can replace the eminently sensible: has motive(x ) guilty(x ) suspect(x ) by the rather unreasonable: has motive(x ) suspect(x ) guilty(x ) suspect(x ) guilty(x ) In a further paper, Lukaszewicz [55] generalises default logic, providing ....

D. W. Etherington. Reasoning with Incomplete Information. Pitman, London, UK, 1988.

....has also been proposed. Let us just mention some of these approaches: parallel circumscription by Lifschitz [13] 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 ....

.... T i is equivalent to Reiter s original de nition [21] De nition 2 (Marek and Truszczyski [17] A theory E L is an extension of a default theory hD; T i in L if and only if E = Cn DE (T ) Normality and semi normality are examples of syntactic restrictions proposed for defaults (see e.g. [4, 14]) Normal defaults have the form : while seminormal defaults are of the form : A default theory hD; T i is called normal if D contains only normal defaults. The fragment of DL corresponding to normal default theories under Reiter s extensions is called normal DL (NDL) Seminormal ....

D.W. Etherington. Reasoning with Incomplete Information. Pitman, London, 1988.

....abnormal birds formula circumscription does not sanction the inference that penguins can y. There is also pointwise circumscription [82] in which the circumscription, instead of being carried out everywhere simultaneously, is performed by minimising one point at a time, and domain circumscription [47] which provides a formalisation of the so called domain closure assumption; the assumption that the only individuals that a system must deal with are those explicitly named. While default logic attempts to formalise particular assumptions, and circumscription the basis for assuming that something ....

Etherington, D. Reasoning with incomplete information, Pitman, London, 1988.

....done by giving a translation of default theories into TEL theories. Minimal consequence can then be used to give the sceptical consequences of a default theory. 4 Domain Circumscription (D CIRC) One of the earliest approaches to nonmonotonic reasoning is circumscription ( Mc77] Mc80] Da80] [Et88]) a preferential logic based on first order predicate logic. Domain circumscription is one of several forms of circumscription. Semantically, in domain circumscription the intuition is that in an intended model of a formula there should not be more elements than necessary. This intuition is ....

....a minimal model of a first order sentence , if (i) M and (ii) for all structures N, if N and N M then N = M. c) For sentences , we say is a d circumscriptive consequence of , denoted . min d c , if is true in all minimal models of . We refer the reader to [Mc77] Mc80] [Et88] for standard results and motivation for domain circumscription. 5 Downward Persistence for MEL We are interested in the class of formulae which are preserved under going to more preferred models and their link with the rule of monotonicity. We will first give a characterization of this class ....

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D.W. Etherington, Reasoning with Incomplete Information, Morgan Kaufmann Publishers, Inc., Los Altos, California, 1988

....we briefly review the large body of related work on circumscription, autoepistemic logic, and database theory. At the end of this section, we summarize the key differences between this body of work and ours. The bulk of previous work has investigated the logic of closed world reasoning (e.g. [45, 23, 78, 63, 52]) and the semantics of theory updates (e.g. 33, 41, 12] Results include logical axiomatizations of the closed world assumption (CWA) exploring the relationship between the CWA and circumscription, distinguishing between knowledge base revision and knowledge base update, and more. Although ....

D. Etherington. Reasoning with Incomplete Information. Morgan Kaufmann Publishers, Inc., Los Altos, CA, 1988. 168

....f , in general, could take the actual form of KB into account. This happens in the following example of a modelpreserving translation. Example 3 We reduce a fragment of skeptical default logic (Kautz Selman, 1991) to circumscription with varying letters, using the transformation introduced by Etherington (1987). Let #D, W # be a prerequisite free normal (PFN) default theory, i.e. all defaults are of the form :# # , where # is a generic formula. Let Z be the set of letters occurring in #D, W #. Define PD as the set of letters a # :# # # D . The function f can be defined in the ....

....Proof. Since inference in skeptical default logic is in # p 2 , it is also in ### p 2 . ### p 2 hardness comes from a simple reduction from circumscription. Indeed, the circumscription of a formula T is equivalent to the conjunction of the extensions of the default theory #T, D#, where (Etherington, 1987): D = # # : x i x i # As a result, CIRC(T ) Q if and only if Q is implied by #T, D# under skeptical semantics. Since #T, D# only depends on T (and not on Q) this is a # nu comp reduction. Since inference for circumscription is # ## p 2 complete (see Theorem 11) it ....

Etherington, D. V. (1987). Reasoning with incomplete information. Morgan Kaufmann, Los Altos, Los Altos, CA.

....McDermott and Doyle style nonmonotonic modal logics [82, 81] Niemel# and Schwind: Proof Systems for Nonmonotonic Logics 3 and autoepistemic logic [84] stand out as most popular logical formalizations of nonmonotonic reasoning. For example, the article of Reiter [103] and the books of Etherington [25], Besnard [7] and Brewka [13] provide introductions to nonmonotonic reasoning. In this article we rst review brieAEy the basic notions of default logic, nonmonotonic modal logics, and circumscription, present key complexity results and discuss relationships of between the approaches. Then we ....

....E L. Dene E 0 = W (4) and for all i = 0; 1; E i 1 = Cn(E i ) apply D;E (E i ) 5) Then E is an extension of (D; W ) if and only if E = 1 [ i=0 E i : 6) Default logic is one of the most prominent formalizations of nonmonotonic reasoning. The books of Besnard [7] Etherington [25], and Marek and Truszczy#ski [76] are good sources on default logic. There is a body of results indicating that default logic can capture a large number of dioeerent forms of nonmonotonic reasoning. Default logic is especially closely related to reasoning in logic programs and deductive databases ....

[Article contains additional citation context not shown here]

D.W. Etherington. Reasoning with Incomplete Information. Pitman, London, 1988.

No context found.

Etherington, D.W. : A Semantics for Default Logic, Proc. IJCAI-87, pp. 495-498; see also in: D.W. Etherington, Reasoning with Incomplete Information, Morgan Kaufmann, 1988

No context found.

Etherington, D. 1988. Reasoning with incomplete information. Research notes in Arti cial Intelligence. Morgan Kaufmann.

No context found.

David Etherington. Reasoning with incomplete Information. PhD thesis, University of British Columbia, 1986.

No context found.

David Etherington. Reasoning with incomplete Information. PhD thesis, University of British Columbia, 1986.

No context found.

D. Etherington. Reasoning with incomplete Information. PhD thesis, University of British Columbia, 1986.

No context found.

D. Etherington. Reasoning with incomplete information. Morgan Kaufman, 1988.

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D. Etherington. Reasoning with incomplete information. Morgan Kaufman, San Mateo, CA, 1988.

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D. Etherington. Reasoning with incomplete information. Morgan Kaufman, San Mateo, CA, 1988.

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Etherington, D. 1988. Reasoning with Incomplete Information, Research Notes in Arti cial Intelligence, Los Altos, CA: Morgan Kaufmann.

No context found.

David Etherington. Reasoning with Incomplete Information. Pitman Publishing, London, 1988.

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D Etherington. Reasoning with Incomplete Information. Pitman, 1988.

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D. Etherington, Reasoning with Incomplete Information (Morgan Kaufmann, Los Altos, CA, 1988).

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