McDermott, D., and Doyle, J., 1978. Non-monotonic logic I, MIT AI Laboratory, Memo 486.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....assertions and our ability to use them to correctly draw further conclusions is seen as a manifestation of our intelligence. In consequence this question has received considerable attention in the AI community with many di#erent approaches and solutions being proposed (see, for example [4] 5] 6] [7], 8] 12] The key distinguishing feature of such assertions, as opposed to classical notions of logical consequence, is their possible non montonicity. For it is now certainly possible for and agent to believe whilst not believing If # and # then #. For example take # to be the cake ....

....via a purely logical analysis, a procession of ever more powerful consequence relations. At the same time they are able to use the justifications for these rules to criticise, through the failure of one or more of them, the main alternative approaches of circumscription [6] autoepistemic logics [7], 8] and default logic [5] Of the various consequence relations which they name, we believe, for the reasons they give, that their notion of rational consequence relation best sums up the properties that should possess given that it arises in this way. Precisely: Definition 1 A binary ....

D. McDermott and J. Doyle, Non-monotonic logic I, Artificial Intelligence 13 (1980) 41--72.

....Curiously, research in nonmonotonic reasoning (NMR) is often presented as aimed at characterizing just such changes in belief sets, yet it does no such thing. Nearly all investigations in NMR utilize static logics. What is characterized is a Reiter [ Reiter, 1980 ] and McDermott and Doyle [McDermott and Doyle, 1980] give such a characterization, for example. More recently in [Alchourron et al. 1985, Gardenfors, 1988 ] attention has swung to belief set change, but still not to the process of such change, i.e. this is still a relation between two static theories, T 1 and T 2 , where we may suppose T 1 to have ....

....active logics are inconsistent (and in fact derive much of their interest from their inconsistency) step models are not sufficiently general as defined. Many systems that exhibit nonmonotonic behavior have been described and studied in the literature, e.g. Clark, 1978, McCarthy, 1980, McDermott and Doyle, 1980, Reiter, 1980, Reiter, 1987 ] However, they are static systems, and don t model the on going reasoning of the agent. Thus, they don t provide a mechanism to recover when a default conclusion turned out to be wrong. where the default principle is: infer Q given P, if possible. Although these ....

D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence, 13(1,2):41--72, 1980.

....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 ....

....[23] inheritance reasoning [35] and abduction [52] 1.2 Autoepistemic Logic Autoepistemic logic is a modal logic with an operator L which is interpreted as is believed . It was originally introduced by Robert Moore [98, 100, 101] as a reconstruction of McDermott and Doyle s nonmonotonic logic [96] to avoid some peculiarities of this logic. Autoepistemic logic models the beliefs of an ideally rational agent who is capable of perfect introspection. The interesting question is to determine what is the set of beliefs of the agent given a set of sentences as the initial assumptions or premises ....

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D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence, 13:41--72, 1980.

....3) of all the formalisms considered in this paper. It is thus in the same league as a number of approaches to belief revision (see [55, 39, 73] and major formalisms of nonmonotonic reasoning, such as circumscription [67, 65] Reiter s default logic [82] McDermott and Doyle s nonmonotonic logic [69, 68], and Moore s autoepistemic logic [70] which are all complete (see Sections 7.2 and 7.3 for further discussion) All other approaches in Table 3 have (considerably) lower complexity. 4.3.1 General case At the low end of the complexity range, there are entailment, which has the same ....

....to belief revision are nonmonotonic logics. A number of nonmonotonic logics and formalisms have been proposed in the past decades for capturing common sense reasoning, including major formalisms such as circumscription [67, 65] default logic [82] Doyle and McDermott s nonmonotonic logics [69, 68], and Moore s autoepistemic logic [70] see [66] The computational complexity of nonmonotonic logics has been studied in many papers, e.g. 56, 87, 50, 74, 33, 21, 77] to mention a few comprehensive studies, and is quite well understood. As in the case of belief revision, the complexity of most ....

D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence, 13:41--72, 1980.

....out as a result of deduction in different contexts. The claim is that proofs built in this way are clearer and better resemble the kind of explanation that humans give when describing some phenomenon. This thesis is articulated discussing the example about non monotonic reasoning reported in [MD80]. 1 Introduction The main premise of this paper is that certain kinds of non monotonic reasoning can be solved within first order logic in a simple monotonic way by formulating problems in a suitable environment. One of the main issues against the use of first order logic for representing ....

....has proposed to express circumscription in first order logic. The non monotonicity comes out from letting the resolution theorem prover stop the computation not only with the empty clause but also with well formed formulas which are (disjunctions of) abnormality predicates. Doyle and McDermott [MD80] have proposed the use of a modal operator M (a more detailed discussion about M is in the next sections) This paper steps back and approaches the problem of formalizing non monotonicity and, more in general, problem solving using first order logic. Certain kinds of nonmonotonic reasoning can be ....

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D. McDermott and J. Doyle. Non-Monotonic Logic I. Artif. Intell., 13(1,2):41-- 72, 1980.

....shows that specificity cannot be treated independently from the context in which it is defined. ut Argumentation has been recognized lately as an important and natural approach to nonmonotonic reasoning [6, 9, 14, 30, 32, 33, 38, 45] It has been showed in [9] that many major nonmonotonic logics [22, 23, 25, 28, 34] represent in fact different forms of a simple system of argumentation reasoning. Based on the results in [9] a simple logic based argumentation system has been developed in [6] which captures well known nonmonotonic logics like autoepistemic logics, Reiter s default logics and logic programming ....

McDermott, D. and Doyle, J.: Nonmonotonic Logic I, AIJ'13, (1980) 41--72.

....logic attempts to formalise particular assumptions, and circumscription the basis for assuming that something is not true, a third approach was proposed that attempted to formalise nonmonotonic reasoning using the notion of what is known. Following the initial attempts by McDermott and Doyle [91, 90], Moore proposed his autoepistemic logic [94] which used ideas from modal logic to authorise conclusions that are either necessarily true, or not necessarily untrue. Moore claims that autoepistemic reasoning is the kind of reasoning intuitively employed in many situations, giving the example of ....

McDermott, D. V. and Doyle, J. (1980) Non-monotonic logic I. Articial Intelligence 13, 41-72.

....formalism. This is what makes negative introspection tractable. Once negative introspection is tractable, default reasoning based on negative introspection ( If I don t know x, then conclude y. becomes tractable. The non monotonic formalizations presented in [McCarthy, 1980, Reiter, 1980, McDermott and Doyle, 1980, Moore, 1983] are not tractable for they all require some sort of a consistency check (or its equivalent) to be done in order to make a default conclusion. Step logic, in contrast, provides a tractable non monotonic formalism. In [Ginsberg, 1991] it is pointed out that although the original ....

D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence, 13(1,2):41-- 72, 1980.

....way to a future general theory of nonmonotonic reasoning. The present study 1 pertains mainly to two approaches to nonmonotonic reasoning. One is a default logic, suggested by Raymond Reiter in [25] the other is a modal approach to nonmonotonic reasoning, initiated by McDermott and Doyle in [22]. Default logic is based on the notion of a default rule holding between ordinary classical propositions, and the intended nonmonotonic theories representing plausible views of the world are de ned via a certain xed point construction (see below) The approach of McDermott and Doyle was based ....

D. McDermott and J. Doyle (1980) Nonmonotonic logic I. Articial Intelligence 13:41-72.

....is nowadays well understood, as its monotonicity (adding new information will never invalidate old conclusions) contrasts to the non monotonic nature of commonsense reasoning. Thus, a number of logical formalisms, aimed at modeling commonsense reasoning, has been devised, among them modal logics [53, 55], default logic [63] and circumscription [52] cf. also [50, 46] Logic programming with negation [44] and or disjunction [45] shares with those formalisms the property of being non monotonic. Its formalism is simple and natural, and its semantics has rigorous mathematical foundations; ....

D. McDermott and J. Doyle. Non-Monotonic Logic I. Artificial Intelligence, 13:41--72, 1980.

.... system along the lines of [8] This provides us with many natural semantics, such as the grounded (well founded) the preferred and the stable semantics [8] These semantics are arguably the most popular and widely accepted semantics for non monotonic and common sense reasoning in the literature [15, 4, 19, 27]. Moreover, we address the problem of actually computing negation as failure. In this respect, we introduce the class of strati ed production systems, where negation as failure can be computed using a simple bottom up operator. As for the case of general strati ed argumentation systems, strati ed ....

....natural semantics of GPS can be de ned using the theory of argumentation. 3. 1 Argumentation systems Argumentation has been recognized lately as an important and natural approach to nonmonotonic reasoning [5, 14, 18, 21, 22, 23, 26, 28] It has been shown [8] that many major nonmonotonic logics [20, 19, 25] represent in fact 9 di erent forms of a simple system of argumentation reasoning. Based on the results in [8] a simple logic based argumentation system has been developed in [4] which captures well known nonmonotonic logics like autoepistemic logics, Reiter s default logics and logic ....

D. McDermott and J. Doyle. Non-Monotonic Logic I. Articial Intelligence, 13(1-2):41-72, 1980.

....3) of all the formalisms considered in this paper. It is thus in the same league as a number of approaches to belief revision (see [55, 39, 73] and major formalisms of nonmonotonic reasoning, such as circumscription [67, 65] Reiter s default logic [82] McDermott and Doyle s nonmonotonic logic [69, 68], and Moore s autoepistemic logic [70] which are all P 2 complete (see Sections 7.2 and 7.3 for further discussion) All other approaches in Table 3 have (considerably) lower complexity. 4.3.1 General case At the low end of the complexity range, there are entailment, which has the same ....

....to belief revision are nonmonotonic logics. A number of nonmonotonic logics and formalisms have been proposed in the past decades for capturing common sense reasoning, including major formalisms such as circumscription [67, 65] default logic [82] Doyle and McDermott s nonmonotonic logics [69, 68], and Moore s autoepistemic logic [70] see [66] The computational complexity of nonmonotonic logics has been studied in many papers, e.g. 56, 87, 50, 74, 33, 21, 77] to mention a few comprehensive studies, and is quite well understood. As in the case of belief revision, the complexity of most ....

D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence, 13:41--72, 1980.

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McDermott, D., and Doyle, J., 1978. Non-monotonic logic I, MIT AI Laboratory, Memo 486.

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McDermott, D., and Doyle, J., 1980. Non-monotonic logic---I, Artificial Intelligence 13, 41-72.

....Bern Langassstrasse 51, CH 3012 Bern, staerk iam.unibe.ch October 1990 Abstract In [6] Moore has introduced a logic to represent the beliefs of ideal rational agents, called autoepistemic logic. This logic was presented as an improvement of the non monotonic logic of McDermott and Doyle in [4]. We give a new method to characterize the fixpoints in both logics and thus obtain decision procedures for several problems in this context. Although the two logics are conceptually very di#erent our method is very uniform. 1 Introduction Non monotonic systems often use non constructive fixpoint ....

....with help of Corollary 4. Question (3) can be answered with the algorithm above. 8 6 The non monotonic logic of McDermott and Doyle In this section we shall show that the methods developed in the previous sections are applicable to the propositional non monotonic logic of McDermott and Doyle in [4]. Some of our results were already proved by Shvarts in [8] but the point of this section are not the theorems but the uniform transformation of notions like extension and labeling and the correspondence of extensions and admissible labelings. McDermott and Doyle use a language with a modal ....

D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence, 13:41--72, 1980.

....every S (as we observe later in Theorem 20.1) so finding an extension is trivial. The other five problems may all be computed by guessing sets E D and accepting iff the desired condition is true, all deterministic polynomial computations from the above theorems. 13 [Charniak, Riesbeck, and McDermott 1980] 18 (18.63) Conjecture. Find E 2 QExts(S) is NP complete. 18.64) Question. Is Find E 2 FGExts(S) NP complete (18.65) Theorem. Is E 2 Exts(S) Is E 2 QExts(S) and Is QExts(S) are in co NP. Proof. We see E = 2 Exts(S) is in NP by first checking E 2 Exts(S) deterministically as ....

....Coherence is not decidable. 24.18) Theorem (Church) Consistency is not decidable. For some special cases, such as finite sentential and monadic sets, arguability and inevitability appear decidable. But rather than continue this topic here, we refer to the discussions in [Reiter 1980] [McDermott and Doyle 1980], and [Davis 1980] 32 Attitudinal theories x25. In the previous theories of reasoned assumptions, there was no commitment to what state components signified, other than reasons. Elements of the domain were not in themselves any familiar psychological organization, but merely the components ....

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McDermott, D., and Doyle, J., 1980. Non-monotonic logic---I, Artificial Intelligence 13, 41-72.

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McDermott, D., and Doyle, J. 1980. Non-monotonic logic I. Artificial Intelligence 13:41--72.

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McDermott, D., Doyle, J.: Nonmonotonic logic 1. In: Artificial Intelligence, number 13 (1980) 41--72.

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McDermott,D. and Doyle,J., 1980, Non-monotonic logic I, Articial Intelligence, 13: 41-72.

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D. McDermott and J. Doyle, `Nonmonotonic logic I', Artificial Intelligence Journal, 13, 41--72, (1980).

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D. McDermott and J. Doyle, `Nonmonotonic logic I', Artificial Intelligence Journal, 13, 41--72, (1980).

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D. McDermott and C. Doyle, Non-monotonic Logic I, Artificial Intelligence, 13:41-72, 1980.

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D. McDermott and J. Doyle. Non-monotonic logic I. Artificial Intelligence Journal, 13:41--72, 1980.

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D. McDermott and J. Doyle. "Non monotonic logic I". Artificial Intelligence, 13(1,2):4172, 1980.

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McDermott, D. & J.Doyle (1980) 'Non-monotonic Logic, I'Artificial Intelligence 13: 41-72.

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