Drew McDermott. Nonmonotonic logic II. journal of the ACM, 22:33--57, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... it is contained in some extension The use of the credulous skeptical terminology in this context was first introduced by Touretzky et al. 15] but the distinction itself is older than this; it was already implicit in Reiter s paper on default logic, and was described explicitly by McDermott [10] as the distinction between brave and cautious reasoning. Makinson [8] refers to the first of the two credulous options described here as the choice option. could indeed be codified as a consequence relation, but it would be a peculiar one. According to this policy, the conclusion set associated ....

Drew McDermott. Non-monotonic logic II. Journal of the Association for Computing Machinery, 29:33--57, 1982.

....on nonmonotonic logics. Ginsberg has compiled some of the most prominent papers on nonmonotonic reasoning which appeared before 1987 in 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 ....

....operator cannot appear in the set of premises. 9 Autoepistemic logic is most directly related to McDermott and Doyle s [96] nonmonotonic logic as it was designed to avoid some problems of that logic. McDermott and Doyle style nonmonotonic logics were further developed first by McDermott [95] and then by Shvarts [135] Marek et al. 80] present a comprehensive study of the approach initiated by McDermott and Doyle. Schwarz [129] develops minimal model semantics for nonmonotonic modal logics. Konolige [60] proposes a hierarchical version of autoepistemic logic. Morris [102] introduces ....

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D. McDermott. Non-monotonic logic II. Journal of the ACM, 29:33--57, 1982.

....after going through a process of justification. In this process of justification the rebutting defeaters and undercutting defeaters play the role of blocking factors they are the relevant factors that can drive an agent to retract certain beliefs. In McDermott and Doyle s nonmonotonic logic [32, 33], Reiter s default logic [39] and Moore s autoepistemic logic [35] the consistency test can be seen as the verification of the nonexistence of relevant information interfering with certain inference. In all these logics there is a general pattern of inference that allows to assume A in the ....

McDermott, D. Non-Monotonic Logic II. Journal of Association for Computing Machinery 29 (1), pages 33-57. ACM (1980).

.... theorem for this programming language Regression plays a central computational role in the situation calculus; presumeably it also does so for the many other approaches to modelling dynamics in the artificial intelligence literature (e.g. the families of action languages [7] temporal logic [24], features and fluents [36] the event calculus and its relatives [38, 15, 1] For suitable analogues of our regressable sentences, can one prove soundness and completeness results for regression in these languages ....

D. McDermott. Non-monotonic logic II. J.ACM, 29:33--57, 1982.

....to the contrary. 5 4 The use of the credulous skeptical terminology to characterize these two broad reasoning strategies was first introduced in Touretzky et al. 30] but the distinction is older than this; it was noted already in Section 2. 2 of Reiter s [27] and was described in McDermott [23] as the distinction between brave and cautious reasoning. 5 The notion of presumption is discussed in detail by Edna Ullman Margalit [32] who argues that specific presumptions are justified by a mixture of probabilistic and value related considerations, and cites the presumption of innocence ....

Drew McDermott. Non-monotonic logic II. Journal of the Association for Computing Machinery, 29:33--57, 1982.

.... Ginsberg has compiled a number of the most prominent papers on nonmonotonic reasoning which appeared before 1987 in a single edition [35] From this work, default logic by Reiter [102] the family of circumscription type formalizations [78, 79] 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 ....

....about defaults is not quite straightforward, for example. Also expressions saying that something is believed or disbelieved prove to be useful, in particular, for queries and integrity constraints [105] but are not available in default logic. 2. 2 Nonmonotonic Modal Logics McDermott and Doyle [82, 81] proposed a scheme for dening a nonmonotonic modal logic for a given monotonic modal logic S. The language L L of a classical modal logic S is an extension of that of the propositional calculus and includes a new monadic operator L. So e.g. L(p ( Lq p) is a formula of L L 1 . For example, ....

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D. McDermott. Non-monotonic logic II. Journal of the ACM, 29:3357, 1982.

....the domain of the individuals in question. This work is centered around one of the nonmonotonic formalisms: autoepistemic logic suggested by Moore [ 1985 ] Autoepistemic logic was designed as a reconstruction of McDermott and Doyle s nonmonotonic logics [ McDermott and Doyle, 1980; McDermott, 1982 ] avoiding some of their diOEculties. We proceed now to a more detailed description of autoepistemic logic. Moore s autoepistemic logic models beliefs of an ideally rational agent, which is capable of perfect positive and negative introspection. Informally said, the agent introspects the logical ....

D. McDermott. Non-monotonic logic II. Journal of the ACM, 29:3357, 1982.

....default extensions under a suitable translation of normal logic programs into default theories. A key property is that separated autoepistemic logic is capable of handling consistently belief states where something is believed and disbelieved simultaneously. McDermott s non monotonic logics [15] including Marek and Truszczy#ski s strong autoepistemic logic [13] are shown to lack this property as well as a reasonable notion of stationary expansions. In Section 6, we return to semantical questions. We address Moore s critique [17] on McDermott and Doyle s Non monotonic modal logic I [16] ....

....stationary expansion h Delta 1 ; Delta 2 i where Delta 1 = fDq; r; Br; g and Delta 2 = Delta 1 [ fDp; p; Bp; g. The sentence p is unde ned while r is believed and q is disbelieved. The construction of De nition 17 is not successful for McDermott style nonmonotonic modal logics [15] which are based on monotonic modal logics S with the modality B subject to the necessitation rule. In these logics, expansions are solutions to Delta = CnS ( Sigma [ B Delta) De ning stationary expansions in the spirit of De nition 17 leads to conditions Delta 1 = CnS ( Sigma [ B Delta 2 ) ....

D. McDermott. Non-monotonic logic II. Journal of the ACM, 29:3357, 1982.

....transcends situation calculus, applying to other popular monotonic AI formalisms such as STRIPS like operators (Chapman, 1987; Fikes, 1971; Pednault, 1988) However, we interpret this observation instead as an indictment of these formalisms. Non monotonic logic (McCarthy, 1986; McDermott, 1980; McDermott, 1982; Reiter, 1980; Shoham, 1986a) offers an alternative but at a high computational cost. In addition, there are questions as to its adequacy (Hanks, 1986; McDermott, 1987) We propose a monotonic like formalism that is quite different than existing monotonic and non monotonic logics. While it is ....

McDermott, D. (1982) "Non-monotonic Logic II," Journal of the Association for Computing Machinery 29, 1, pp. 33-57.

....overhead of the multivalued approach is small in these cases. We then go on to consider the nonmonotonic case. We begin by presenting a fixed point description of nonmonotonic inference in Section 11.1. This description is related to existing fixed point work such as that appearing in [36, 38, 39, 41], but is more robust in the sense that fixed point extensions always exist in a multivalued setting. The fixed point solution will be unique if the bilattice is stratified, a point we investigate in Section 11.2. Once again, our notion is related to the more conventional one introduced into the ....

....be used directly to construct the closure of a truth assignment OE. We will address this point in subsequent sections; here, we only note the similarity between our result and the usual fixed point descriptions of nonmonotonic inference appearing in default logic [41] or modal descriptions of it [36, 38, 39]. The principal difference between our approach and earlier ones is that (20) in fact describes a substantially more general result, and that the appearance of as a well defined point of any bilattice guarantees that the fixed point equation (20) will have at least one solution (namely, the ....

D. McDermott. Non-monotonic logic II. Journal ACM, 29:33--57, 1982.

....reasoning. Several formalizations of non monotonic reasoning have been proposed, among which the best known are McCarthy s circumscription [McC80, McC86] Reiter s default theory [Rei80] Moore s autoepistemic logic [Moo85] reconstruction of non monotonic logics of McDermott and Doyle [MD80, McD82]) and Reiter s closed world assumption [Rei78] and its extensions, e.g. Minker s GCWA [Min82] All of these formalizations are obtained by augmenting a classical first order logic with some mechanism, which by allowing defeasible conclusions permits us to reason in the absence of complete ....

D. McDermott. Non-monotonic logic ii. Journal of the ACM, 29(1):33--57, 1982.

....on nonmonotonic logics. Ginsberg has compiled some of the most prominent papers on nonmonotonic reasoning which appeared before 1987 in 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 ....

....operator cannot appear in the set of premises. 9 Autoepistemic logic is most directly related to McDermott and Doyle s [96] nonmonotonic logic as it was designed to avoid some problems of that logic. McDermott and Doyle style nonmonotonic logics were further developed first by McDermott [95] and then by Shvarts [135] Marek et al. 80] present a comprehensive study of the approach initiated by McDermott and Doyle. Schwarz [129] develops minimal model semantics for nonmonotonic modal logics. Konolige [60] proposes a hierarchical version of autoepistemic logic. Morris [102] introduces ....

[Article contains additional citation context not shown here]

D. McDermott. Non-monotonic logic II. Journal of the ACM, 29:33--57, 1982.

....common to all the approaches, of the principles underlying this type of reasoning. Once identified, this deficiency is readily corrected with simple tools whose benefits, we believe, easily outweigh their cost. 3. 1 The Lottery Paradox The first problematic example is the Lottery Paradox [16, 31, 23, 27]. The lottery paradox arises in situations in which the conjunction of a set of assumptions, each reasonable individually, is inconsistent with what is known about the world. For example, in the paradigmatic case, it is usually safe to assume that any particular ticket in a lottery will not ....

Drew McDermott. Non-monotonic logic II. J.ACM, 29:33--57, 1982.

....use this belief to form and employ a default principle to the effect that any particular student will receive a B; rather, he examines each student s record to see what grade has been earned. In fact, if the teacher were to use such a default, it may well lead to a version of the Lottery Paradox [15, 20, 10, 35], since he may also have a strong belief that at least, say, 5 of the students will receive an A: then the default could lead him to guess that each individual student gets a B, which conflicts with the belief about some students receiving A s. Thus the decision to make inferences about ....

D. McDermott. Non-monotonic logic II. Journal of the ACM, 29:33--57, 1982.

.... Ginsberg has compiled a number of the most prominent papers on nonmonotonic reasoning which appeared before 1987 in a single edition [35] From this work, default logic by Reiter [102] the family of circumscription type formalizations [78, 79] McDermott and Doyle style nonmonotonic modal logics [82, 81], and Niemela and Schwind: Proof Systems for Nonmonotonic Logics 3 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 ....

....about defaults is not quite straightforward, for example. Also expressions saying that something is believed or disbelieved prove to be useful, in particular, for queries and integrity constraints [105] but are not available in default logic. 2. 2 Nonmonotonic Modal Logics McDermott and Doyle [82, 81] proposed a scheme for defining a nonmonotonic modal logic for a given monotonic modal logic S. The language L L of a classical modal logic S is an extension of that of the propositional calculus and includes a new monadic operator L. So e.g. L(p ( Lq p) is a formula of L L 1 . For example, ....

[Article contains additional citation context not shown here]

D. McDermott. Non-monotonic logic II. Journal of the ACM, 29:33--57, 1982.

....:p is not necessary. Hence, Mp is equivalent to :L :p. Ginsberg shows the relationship between autoepistemic logic and Kripke s approach to modal logic [Kri71] As observed by Shvarts [Shv90] AEL is one of the nonmonotonic logics that can be obtained from the approach of McDermott and Doyle [MD82]. Levesque [Lev90] generalizes Moore s notion of a stable expansion [Moo85a] to the full first order case. He provides a semantic account of stable expansions in terms of a second modal operator O, where O(w) is read as w is all that is believed. He characterizes stable expansions as: O(w) is ....

D. McDermott and J. Doyle. Non-monotonic logic II. Journal of the ACM, 29, pages 33--57, 1982.

.... models of a given input F : the sceptical (conservative) perspective accepts only facts which are true in all models, the credulous (liberal, brave) perspective accepts all facts which are true in some model, and the choice perspective simply yields (nondeterministically) one of the models (cf. McD82] It is well known that under most approaches (including circumscription and normal Default Logic) the union of two models is inconsistent, i.e. the credulous semantics yields inconsistent structures. This also holds for logic programming with inheritance (cf. Example 1) In case of logic ....

D. McDermott. Non-Monotonic Logic II. Journal of the ACM, 29:33--57, 1982.

....model of a Horn program or the well founded model of a general logic program, to compute default extensions. ffl The theory D( Delta) consisting of sentences which are true in all default extensions of a given default theory Delta, describes the so called cautious default semantics of Delta [McD82]. However, D( Delta) itself is not, in general, a default extension of Delta and thus, Partially supported by the Swedish National Board for Technical Development grant #90 1676. This work has been conducted while both authors were visiting the Computer Science Department at the University of ....

D. McDermott. Non-monotonic logic II. Journal of the ACM, 29(1):33--57, 1982.

....reasoning that corresponds to default logic. However, the non logical character of the extra conditions leads to dependence on the syntactic representation of the premises (Konolige 1988) One of the leading attempts to find a satisfying nonmonotonic modal logic is based on a scheme introduced by McDermott and Doyle (1980, 1982) for obtaining a nonmonotonic modal logic from a given monotonic modal logic. This approach has been further investigated, e.g, by Schwarz (1990, 1992) and Marek et al. 1991) Schwarz (1990) shows that also Moore s original autoepistemic logic can be seen as a McDermott and Doyle style ....

McDermott, D. 1982. Non-Monotonic Logic II. Journal of the ACM 29:33--57.

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Drew McDermott and Jon Doyle, "Non-Monotonic Logic II" (in progress)

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Drew McDermott. Nonmonotonic logic II. journal of the ACM, 22:33--57, 1982.

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