P. Gardenfors and D. Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence, 65(2):197--245, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of resolution or disjunction contraction as demonstrated in the proof of Proposition 4.2. 2 4.4 Characterization of the QC consequence relation We now consider properties of the consequence relation. These properties have been much discussed in the context of non monotonic logics [Gab85, GM93] 17 and of relevance logics [AB75, Ten84] At the end of this section, we discuss the relevance to QC logic of these properties and associated results. Proposition 4.10 The property of reflexivity, defined as follows, succeeds for the QC consequence relation, where Delta 2 (L) ff 2 L. Delta ....

P Gardenfors and D Makinson. Non-monotonic inference based on expectations. Artificial Intelligence, 65:197--246, 1993.

.... by which an agent may, possibly, withdraw previously derived conclusions upon enlarging her set of hypotheses ( Mak 94] and belief revision, i.e. the process by which an agent changes her beliefs upon discovering some new information ( AGM 85, Gar 88] are well known (see, for example, GM 94, GR 95, MG 90, Rot 96] As a consequence, it is possible to translate particular problems in one area into problems in the other. One particular problem in nonmonotonic reasoning is the question of default entailment, i.e. when should we regard one item of so called default knowledge ....

....general case when the input is inconsistent with the prior belief set, the agent is forced to give up some of her prior beliefs. One way of determining precisely which sentences the agent should give up in this situation is to assign to the agent an E relation on L (see, for example, Gar 88, GM 94, Nay 94, Rot 92a, Rot 96] The intuitive meaning behind E relations is that # # should hold i# the agent finds it at least as easy to give up # as she does #, i.e. her belief in # is at least as entrenched as her belief in #. In cases of conflict the agent should then give up those ....

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P. Gardenfors and D. Makinson, Nonmonotonic inferences based on expectations, Artificial Intelligence 65 (2) (1994) 197--245.

....following the intuition and formalization of the original AGM postulates. To our knowledge this is the first complete set of postulates for the revision of explicit nonmonotonic knowledge (of course we are aware of the close relationship between belief revision and nonmonotonic reasoning [8], as well as work showing that belief revision can be achieved using default reasoning [4] Then we defined concrete revision and contraction operators, and showed that they fulfill the postulates, as well as adaptations of the Levi and Harper Identities. Our future work in the area will ....

P. Gardenfors and D. Makinson. Nonmonotonic Inference Based on Expectations. Artificial Intelligence 65 (1994): 197-245.

....belief revision is usually taken to be the result of the joint e#orts of Alchourron, Makinson and Gardenfors. The theory they eventually arrived at is know as the AGM approach to belief revision (or, simply, AGM) This approach is fully described in [7] later work in the same line includes [13] [8]. The central notion in AGM is that of belief set. A belief set is a set of sentences (of some propositional language) such that it may be rationally held by an individual, that is ( 7] ch.2.2) a consistent set closed under logical consequence (i.e. a theory) Definition 1. A set K of ....

Gardenfors, P., Makinson, D., Nonmonotonic inference based on expectations. Artificial Intelligence, 65, pp. 197-245, (1994)

....revision is usually taken to be the result of the joint efforts of Alchourron, Makinson and Gardenfors. The theory they eventually arrived at is know as the AGM approach to belief revision (or, simply, AGM theory) This approach is fully described in [7] later work in the same line includes [13] [8]. The central notion in AGM is that of belief set. A belief set is a set of sentences (of some propositional language) such that it may be rationally held by an individual, that is ( 7] ch.2.2) a consistent set closed under logical consequence. Definition 1. A set K of sentences is a ....

Gardenfors, P., Makinson, D., Nonmonotonic inference based on expectations. Artificial Intelligence, 65, pp. 197-245, (1994)

....(I6) If S j= Q 2 for some S 2 U( P; Q 1 ) then no Bel( P; Q 1 ; Q 2 ; Q n ) Bel( P; Q 1 ; Q 1 [ Q 2 ; Q 3 ; Q n ) Table 2: Interpretation of Postulates (C1) C6) and (I1) I6) 4. 2 Update Programs as Nonmonotonic Consequence Relations Following Gardenfors and Makinson [46, 26], belief revision can be related to nonmonotonic reasoning by interpreting it as an abstract consequence relation on sentences, where the epistemic state is fixed. In the same way, we can interpret update programs as abstract consequence relation on programs as follows. For a fixed epistemic state ....

P. Gardenfors and D. Makinson. Nonmonotonic Inferences Based on Expectations. Artificial Intelligence, 65(2):197--245, 1994.

....(I6) If S j= Q 2 for some S 2 U( P; Q 1 ) then no Bel( P; Q 1 ; Q 2 ; Q n ) Bel( P; Q 1 ; Q 1 [ Q 2 ; Q 3 ; Q n ) Table 2: Interpretation of Postulates (C1) C6) and (I1) I6) 4. 2 Update Programs as Nonmonotonic Consequence Relations Following Gardenfors and Makinson [43, 26], belief revision can be related to nonmonotonic reasoning by interpreting it as an abstract consequence relation on sentences, where the epistemic state is fixed. In the same way, we can interpret update programs as abstract consequence relation on programs as follows. For a fixed epistemic state ....

P. Gardenfors and D. Makinson. Nonmonotonic Inferences Based on Expectations. Artificial Intelligence, 65(2):197--245, 1994.

....CCD in terms of disjunction, with much simpler definitions of independence than the above probabilistic ones. This framework is the one of possibility theory, which has strong connections with belief change [Dubois and Prade, 1991; Dubois and Prade, 1992] and ordering based nonmonotonic reasoning [G ardenfors and Makinson, 1994; Benferhat et al. 1997] 1 Gardenfors also introduces a fifth axiom stating that relevance is syntax independent when cast in the setting of a formal language. Such an axiom is superfluous in our representational setting. A ROADMAP OF QUALITATIVE INDEPENDENCE 5 3 POSSIBILITY THEORY In this ....

....possibility can be cast into modal logic and is equivalent to that underlying Lewis [1986] logic of conditionals. The dual necessity orderings lie at the core of the AGM theory of belief revision (under the name epistemic entrenchment [G ardenfors, 1988] or expectation orderings [G ardenfors and Makinson, 1994] as well as of theories of nonmonotonic reasoning that exploit a partial or complete ordering of interpretations of a language (such as that of Shoham [1988] Kraus et al. 1990] Goldszmidt and Pearl [1992] Lehmann and Magidor [1992] and Boutilier [1994] Tight links between possibility ....

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P. Gardenfors and D. Makinson. Non-monotonic inference based on expectations. Artificial Intelligence, 65, 197--245, 1994.

....Z such that (1) A j B = A j d B : fb 2 B : 9a b 2 A8a 0 2 A8b 0 2 B(d(a b ; b) d(a 0 ; b 0 ) g: 1.3. 2 Revision based on pseudo distances The representation results of [AGM95] the semantics of Grove [Gro88] and the very close connection with the rational relations of [LM92] showed in [GM94], all leave essentially 8 unanswered the question of the nature of the dependence of the revision T T 0 on its left argument, T . Since we, like most researchers in Artificial Intelligence, are mostly interested in iterated revisions, proper understanding, and semantics, for this dependence is ....

P. Gardenfors and D.Makinson, "Nonmonotonic Inference based on Expectations ", Artificial Intelligence, Vol. 65, No. 1, pp. 197-245, 1994.

.... is that of finding the greatest set of generating defaults D 0 such that W [ Cons(D 0 ) is consistent (see also [Mac91] This is essentially the parsimony principle of Reiter [Rei87] for computing diagnoses, successively extended by Poole [PGA87, Poo88, Poo89b] and by Gardenfors and Makinson [GM94a] to handle normal defaults. Reiter computes hitting sets, for which an algebraic method is provided, to find out diagnoses, while Schwind and Risch [SR91] do not solve the problem of how to compute extensions. The problem is that, in the general case, it is not sufficient to make the tableau open ....

P. Gardenfors and D. Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence Journal, 65:197--246, 1994.

....repair the set of defaults so as to produce the desired conclusion. 1 INTRODUCTION It seems that there is now a general agreement about the foundations of exception tolerant reasoning which have been proposed by Lehmann and his colleagues (Kraus et al. 1990; Lehmann and Magidor, 1992) and by G rdenfors and Makinson (1994) who provide basic systems of postulates for nonmonotonic consequence relations. From these proposals two systems are particularly emerging: on the one hand the System P (P for preferential) which offers a basic core for commonsense reasoning but provides a very cautious inference machinery. On ....

Gärdenfors P., Makinson D. (1994) Nonmonotonic inference based on expectations. Artif. Intelligence, 65, 197-245.

.... the relation between abduction and non monotonic reasoning and their combination, we refer to that part of the literature on non monotonic reasoning that has investigated on the finitistic inference operation j (mainly Gabbay [10] Kraus, Magidor Lehmann [19] and Gardenfors and Makinson [12]) The basic (and common to all approaches) idea of non monotonic reasoning is to infer, from a given knowledge Theta of the world, more than it is deductively implied from Theta. The studies about the non monotonic inference relation j have been directed to regulate this strongest inference ....

P. Gardenfors and D. Makinson. Non monotonic inference based on expectations. Artificial Intelligence Journal 65:197--246, 1994.

....bases, and different sets of postulates for belief base revision have been proposed. An overview on these approaches may be found in [7] Some of the solutions use an additionnal selection mechanism, similar to the G rdenfors Makinson selection functions used in the revision of closed theories [6]. The most objective of these functions is obtained when one selects and intersects all the subsets of the theory K that can be retained, but it turns out that the resulting revision operation (full meet revision) is of little use in closed theories (Alchourron Makinson triviality theorem, 1] ....

P. Gärdenfors, D. Makinson "Nonmonotonic inference based on expectations", Artificial Intelligence 65, 197-245, 1994.

.... Introduction In the last ten years, many works in nonmonotonic reasoning have focused on the determination of natural properties for a nonmonotonic consequence relation that are likely to achieve a satisfactory treatment of plausible reasoning in the presence of incomplete information [24] 32] [26]. Further, Pearl [41] has suggested that Adams logic of infinitesimal probabilities [1] is a good basis for nonmonotonic reasoning, and indeed the core properties of a nonmonotonic consequence relation are present in this logic. These properties constitute the basis of the inference system P (P ....

....w of y is preferred among the models of f, and (f) max( f y) f y) The consequence relationship . p satisfies most of the remarkable properties recalled in Section 2: LLE, RW, AND, OR,CM, Cut and RM, as well as a weakened version of reflexivity and a strong form of consistency preservation [26]: Restricted reflexivity (RR) if a then a . p a; Consistency Preservation (CP) a . p ) CP and RR are typical of the possibilistic approach. CP, RR, Cut and AND imply what could be called Nihil ex absurdo [4] p a) For suppose .p a, a ; then by RR, a .p a and since a a .p a, ....

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P. Gärdenfors, D. Makinson, Nonmonotonic inference based on expectations. Artif. Intellig., 65, 1994, 197-245.

....ranking as moving it down j ranks one rank at a time. Finally, based on the well known connections between belief revision, possibilistic reasoning and nonmonotonic reasoning, maxi adjustments can be applied to possibilistic knowledge bases [Dubois et al., 1994] and nonmonotonic knowledge bases [Gardenfors and Makinson 1994, Lehmann 1992] 4 Subsumption Removal The idea of using reasons to determine what information to retract during the contraction of a sentence ff works well for all beliefs except for some ranked at degree(B; ff) For example, if fi ff, fi and ff are equally ranked, then neither fi ff nor ....

Gardenfors, P. and Makinson, D. [1994], Nonmonotonic Inference Based on Expectations, Artificial Intelligence 65: 197 -- 245.

....an ordering among models to determine those that are minimal, is reminiscent of the orderings used in belief revision to determine transitively relational partial meet revision functions. More detailed investigations into the connections between the two kinds of models have begun recently (see [6]) The guiding idea is that when we try to find out whether C follows nonmontonically from B, the background information that we use for the inference does not only contain what we firmly believe, but also information about what we expect in the given situation. If we denote the set of sentences ....

.... relation iff there is an expectation ordering such that the following condition holds: C#) B # C iff C Cn( B D: B D ) This definition can now be used together with the translations of the revision postulates into the nonmonotonic formalism to give a representation theorem (proved in [6]) Theorem 11: Let be an expectation ordering over L. Then the inference relation # that it determines by (C#) satisfies all the translations of postulates (K 1) K 8) Theorem 12: Let # be any inference relation on L that satisfies all the translations of postulates (K 1) K 8) Then # ....

Grdenfors, P. and D. Makinson. (1992): "Nonmonotonic inferences based on expectations", manuscript, Cognitive Science, Lund University.

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P. Gardenfors and D. Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence, 65, 197-245, 1994.

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P. Gardenfors and D. Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence, 65(2):197--245, 1994.

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P. Gardenfors and D. Makinson. Nonmonotonic inference based on expectations. In Proceedings of the third International Conference on Principles of Knowledge Representation and Reasoning. Morgan Kaufmann, 1991.

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P. Gardenfors and D. Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence Journal, 65:197--246, 1994.

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P. Grdenfors and D. Makinson, Nonmonotonic inference based on expectations, Artificial Intelligence 65(1994), 197-245.

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P. Gardenfors and D. Makinson. Nonmonotonic inference based on expectations. Artificial Intelligence, 65(2):197--245, 1994.

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Gardenfors and Makinson. Nonmonotonic inference based on expectation. 1991.

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Gardenfors and Makinson. Nonmonotonic inference based on expectation. 1991.

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Gärdenfors P., Makinson D., Non-monotonic inference based on expectation. Artificial Intelligence, 1993, to appear.

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