D. Makinson and P. Gardenfors, Relations between the logic of theory change and nonmonotonic logic, in: A. Fuhrmann, M. Morreau (eds.), The Logic of Theory Change, LNAI 465, (Springer Verlag, 1990) 185--205.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... 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 (hereafter just ....

D. Makinson and P. Gardenfors, Relations between the logic of theory change and nonmonotonic logic, in: A. Fuhrmann, M. Morreau (eds.), The Logic of Theory Change, LNAI 465, (Springer Verlag, 1990) 185--205.

....when a new piece of information arrives. The aim of this section is to give an answer to this question even when the new piece of information is a program. The change operators introduced in this section are inspired by the duality existing between revision and rational inference relations [10, 13]. So the first operator can be seen as the relativization of the rational closure [19] to the forward chaining logic. The second operator is an extension of the first one and it is aimed to satisfy a little bit more of transitivity [3, 4] Definition 3 (Exceptional sets of literals and rules) ....

P. Gardenfors and D. Makinson. Relations between the logic of theory change and nonmonotonic logic. In The Logic of Theory Change, Workshop, Konstanz, FRG, Octuber 1989, pages 185--205. Springer-Verlag, 1989. Lecture Notes in Artificial Intelligence 465.

....of 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 ....

Makinson, D., Gardenfors, P., Relations between the logic of Theory change and Nonmonotonic Logic. In Fuhrmann, A., Morreau, M. (eds): The Logic of Theory Change, Springer-Verlag, Berlin, (1991)

....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 ....

Makinson, D., Gardenfors, P., Relations between the logic of Theory change and Nonmonotonic Logic. In Fuhrmann, A., Morreau, M. (eds): The Logic of Theory Change, SpringerVerlag, Berlin, (1991)

....1992] Cardenfors and Marinson 1994] Zhang 1996] The key idea is translating B K A into AB and vice versa. As claimed in [Ghrdenfors and Makinson 1994] this translation makes sense only on the finite level. The idea of infinite revision functions seems to make good intuitive sense. see [Makinson and Grdenfors 1991 ]P.190) There have been several proposals for multiple belief changes ( Fuhrmann 1988] Rott 1992] Hansson 1992] Fuhrmann and Hansson 94] Zhang 1995] Zhang 1996] This paper is by no means to present an alternative one. Instead of that, we attempt to combine these approaches and develop ....

D. Makinson and P. Grdenfors, Relations between the logic of theory change and nonmonotonic logic, in: A. Fuhrmann and M. Morteau eds. The Logic of Theory Change, (LNCS 465, SpringerVerlag, 1991) 185-205.

....the NWOP of K induced by . Then ]or all sentence A in L, A ig A Proof: I is sucie by lemma 5.1 ad lemma 9.1 o show ha 11 is an extension of a) K El K e K S F) However, it follows straightforward kom the constructions of extension of a NWOP DT and K F. Makinson and Ghrdenfors in [17] showed that the postulates for belief revision can be translated into postulates for nonmonotonic logic. However, as they pointed out, the idea of infinite revision function would make better intuitive sense. In fact, if we follows their ways of translating F[ A as A K F, then it is easy to ....

D. Makinson, P. Grdenfors, Relations between the Logic of theory change and nonmonotonic logic, in: A. Fuhrmann and M. Morteau eds. The Logic of Theory Change, (Lecture Notes in computer Sience 465, Springer-Verlag, Berlin, Germany, 1991) 185-205.

....theory which satisfies all the rules under con sideration and discuss limitations of methods based on consequence relations for the study of nonmonotonic reasoning. I Introduction In recent years much work has been done on the relationship between nonmonotonic reasoning and belief revision [Makinson and G irdenfors 1991] [Brewka 1991] Nebel 1992] Cravo and Martins 1993] Li 1993] G irdenfors and Makinson 1994] Boutflier 1994] G irdenfors and Rott 1995] Zhang 1996] A very close correspondence be tween them has been found based on the following formal translation: A I KC iff CK A The main idea is to ....

....be tween them has been found based on the following formal translation: A I KC iff CK A The main idea is to identify revision of a belief set K by a proposition A with nonmonotonic inference from A under the guidance of the background knowledge K. With this connection, it has been shown in [Makinson and G irdenfors 1991] [Girdenfors and Rott 1995] that each postulate for the belief revision function can be translated into a plausible conditions on the nonmono tonic inference relation I ; conversely, almost all the plausible conditions on the nonmonotonic inference re lation in the literature can also be ....

David Makinson, Pe- ter Grdenfors, Relations between the logic of theory change and nonmonotonic logic, in: A. Fuhrmann and M. Morteau eds. The Logic of Theory Change, (LNCS 465, Springer-Verlag, Berlin, Germany, 1991) 185-205.

.... in Chapters 3 and 4) Such a study has not been undertaken previously whereas investigations of the relationship between TMSs and abduction have (e.g. 112] Moreover, links have been investigated between belief revision and other areas of artificial intelligence (e.g. nonmonotonic reasoning [34, 72]) It was mentioned earlier that we are interested in accounts of rational belief change. G ardenfors and Rott [35] adopt the following rationality criteria or integrity constraints : The results in this section may be found in the AGM literature; in particular, they are collected together in ....

....minimally entrenched. The first three postulates (SEE1) SEE3) turn out to be quite significant and any ordering satisfying them is referred to as an expectations ordering [34] Such orderings provide a strong link between the AGM account of belief revision and nonmonotonic inference [34, 72]. G ardenfors and Makinson supply the following properties satisfied by expectations orderings, some of which will be useful in proving results later in this dissertation. Lemma 2.2.17 ( 33] i) ff fi or fi ff (Connectivity) In fact, they cannot be given up at all given our second ....

[Article contains additional citation context not shown here]

David Makinson and Peter G ardenfors. Relations between the logic of theory change and nonmonotonic logic. In A. Fuhrmann and M. Morreau, editors, The Logic Of Theory Change, pages 185--205. Lecture Notes in Artificial Intelligence 465, Springer Verlag, 1990.

....(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 ....

D. Makinson and P. Gardenfors. Relations Between the Logic of Theory Change and Nonmonotonic Logic. In A. Fuhrmann and M. Morreau, editors, The Logic of Theory Change, pages 185--205. Springer, 1990.

.... revision has studied an obvious alternative: the revision of epistemic states expressed as nonmonotonic theories [4, 9, 16, 2, 6] This is somewhat surprising since close relationships between properties of nonmonotonic inference relations and postulates for belief revision have been established [10]. Indeed, one of the reasons why nonmonotonic logics were invented is their ability to handle conflicts and inconsistencies, one of the major issues in belief revision. If this is the case, shouldn t it be possible to use the power of nonmonotonic inference to simplify revision In fact, in this ....

Makinson, D., Gardenfors, P., Relations Between the Logic of Theory Change and Nonmonotonic Logic, in: A. Fuhrmann and M. Morreau (eds.), The Logic of Theory Change, Springer LNAI 465, Berlin, 1991

.... to well known principles of nonmonotonic reasoning, in the sense that a belief revision function for a theory T satisfles the belief revision postulate ifi the nonmonotonic consequence relation Inf associated with and T satisfles the reasoning principle in question (cf. Rott 1998, Sec.3) (Makinson and Gardenfors 1991). There is a similar connection between belief revision functions and conditionals, which I consider in some detail in the next subsection. 10.2 Conditionals and Belief Revision: The Ramsey Test Instead of asking when a conditional p q is true, we might ask a difierent question: when should ....

Makinson, D. and P. Gardenfors (1991). Relations between the logic of theory change and nonmonotonic logic. In The Logic of Theory Change, Berlin, pp. 185-205. Springer.

....information in face of recalcitrant evidence is intimately connected with patterns of nonmonotonic inference. In fact, nonmonotonic inference and the theory of belief change (that typically employs minimal loss of information) have been viewed as different perspectives on the same underlying logic [MG90, GM94]: the nonmonotonic (plausible) inference j ( is a plausible conclusion from ) can be taken to mean that accepting as a new piece of information results in our adopting as a belief [GM94] Accordingly, the principle of minimal change has played a crucial role in approaches to ....

.... inference relations and belief revision operators (a statement of the form 2 K is seen as non monotonic inference from to given K as a set of background expectations (explicit translations of the AGM axioms into corresponding properties for non monotonic inference are provided in [MG90]) we expect a corresponding belief revision operator to our inference relation , one that accounts for the varying responses of the agent to new information depending on its consistency with older information. The revision operator so devised works as both an abduction operator and AGM revision ....

David Makinson and Peter Gardenfors. Relations between the logic of theory change and nonmonotonic logic. In A. Fuhrmann and M. Morreau, editors, The Logic Of Theory Change, pages 185--205. Lecture Notes in Artificial Intelligence 465, Springer Verlag, 1990.

.... of Poole and Brewka, and developed a system for default reasoning, called ranked default theory(RDT) As a very important result, Nebel established a relation between RDT and revised belief revision (called prioritized base revision) which strengthened Makinson and G ardenfors s result ([6]) about the connections between nonmonotonic reasoning and belief revision. The goal of this paper is to further extend Nebel s results so as to obtain more direct and general connections between default reasoning and belief revision. we will present a general framework for default reasoning , ....

....revision operation, introduced by Zhang et al. 7] 8] This result provides a solution to the problem whether there is a correspondence between belief revision and default logic for the in nite case. As a by product, we also give an answer of the question, raised by Makinson and G ardenfors ([6]) of whether there is a counterpart contraction in nonmonotonic logic. 1.1 Preliminaries Throughout this paper, we consider rst order language L with the standard logical connectives : and . A sentence in L is a well formed formula without free variables. We denote individual ....

[Article contains additional citation context not shown here]

David Makinson, Peter Gardenfors, Relations between the Logic of theory change and nonmonotonic logic, in: A. Fuhrmann and M. Morreau eds., The Logic of Theory Change, (LNCS 465, Springer-Verlag, 1991), 185-205.

....revision functions) turns out to admit a genuinely foundationalist interpretation. 5.2 Belief revision and nonmonotonic inference We establish in this section a connection between preferential revision functions and nonmonotonic inference relations. As was argued by G ardenfors and Makinson in [19], belief revision and nonmonotonic inference are actually two sides of the same coin . Thus, any revision function on a xed belief set K generates the following nonmonotonic inference relation: A j B i B 2 K A Moving in the other direction, given a nonmonotonic inference relation j , ....

.... set K generates the following nonmonotonic inference relation: A j B i B 2 K A Moving in the other direction, given a nonmonotonic inference relation j , there is a natural way of de ning its belief set , K j as the set of propositions that are nonmonotonically inferred in j (see [19]; the authors attributed the idea to Hans Rott) K j = fA j j Ag In addition, notice that if M is a model of a nonmonotonic inference relation j , then :A j expresses the fact that A holds in all states of M. Consequently, such propositions can be seen as describing the internal logic of ....

[Article contains additional citation context not shown here]

D. Makinson and P. Gardenfors, Relations between the logic of theory change and nonmonotonic logic, The Logic of Theory Change (A. Fuhrmann and M. Morreau, eds.), Springer Verlag, 1991, Lecture Notes in AI, 465, pp. 185-205.

....notion of an epistemic state that explicitly embodies essential features of current representations given for belief change. Epistemic states turn out to be quite similar to models for nonmonotonic inference relations suggested in [11] Moreover, guided by the idea of G ardenfors and Makinson (see [8, 15]) that belief change and nonmonotonic inference are actually two sides of the same coin , we show in the paper that belief contraction, viewed as an operation on epistemic states, corresponds to a new kind of a nonmonotonic inference relation with rules of the form If A is not believed, then ....

D. Makinson and P. Gardenfors, Relations between the logic of theory change and nonmonotonic logic, The Logic of Theory Change (A. Fuhrmann and M. Morreau, eds.), Springer Verlag, 1991, Lecture Notes in AI, 465, pp. 185-205.

....(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 ....

D. Makinson and P. Gardenfors. Relations Between the Logic of Theory Change and Nonmonotonic Logic. In A. Fuhrmann and M. Morreau, editors, The Logic of Theory Change, pages 185--205. Springer, 1990.

....of AGM (safe hierarchies, partial meet functions, systems of spheres and epistemic entrenchments) and in the next section we will prove that they are indeed equivalent. Freund and Lehmann chose instead to consider the connection existing between theory change and non monotonic reasoning [ G ardenfors and Makinson, 1991 ] and study the e ect of the new postulate on the (non monotonic) inference relation. The main result in their paper is the proof that revisions satisfying K 1 to K 9 stand in oneto one correspondence with rational, consistency preserving non monotonic inference relations. 3.6 Equivalences In ....

P. Gardenfors and D. Makinson. Relations between the logic of theory change and nonmonotonic logic. In The logic of theory change (Konstanz, 1989), pages 185-205. Springer, Berlin, 1991.

....criterion for dependence (CCD) and Gardenfors s conjunction criterion for independence (CCI) With the Levi Identity (Gardenfors 1988) it is possible to obtain similar results for belief revision. One can as well obtain similar results for nonmonotonic reasoning, using the correspondence of (Makinson and Gardenfors 1990) between the former and revision. We are convinced that dependence is a fruitful notion in the study of belief change and nonmonotonic reasoning, and that a lot of things remain to be done in this area. In particular we think that it will be a useful tool in the practical implementation of ....

D. Makinson, P. Gardenfors (1990), Relations between the logic of theory change and nonmonotonic logic. In: The Logic of Theory Change, eds. A. Fuhrmann, M. Morreau, Springer Verlag, LNCS 465, pp 185-205.

.... different researchers have put forward different proposals, with different applications in mind, including database dynamics [1] reason maintenance systems [6, 7] reasoning about actions [14, 39] belief change in a static world [9] belief change in a dynamic world [23] and nonmonotonic logics [5, 24], to mention only a few. An approach to rational belief change that has influenced much of this discussion is the AGM model [2] In the AGM model, a belief state (epistemic state) is represented as a belief set (i.e. as a set of sentences K closed under the consequence operation of a suitable ....

Makinson, D. and P. Gardenfors, "Relations between the Logic of Theory Change and Nonmonotonic Logic", in A. Fuhrmann and M. Mourreau, eds., The Logic of Theory Change, Lecture Notes in Artificial Intelligence 465, Springer Verlag, 1991.

.... correspondence between nonmonotonic inference and belief revision: j A i A 2 K where K is the set of nonmonotonic tautologies, that is, K = fB : j Bg: It is easy to see that this is a generalization of the relationship between nonmonotonic reasoning and (single) belief revision given by [Makinson and G ardenfors 1991] [G ardenfors and Rott 1995] where K was interpreted as the background knowledge of nonmonotonic reasoning. More precisely, we have Theorem 1 (Zhang et al. 1997b) Let K be a consistent closed set in language L and a general revision function over K. Let j 2 L L is a relation which satis ....

D. Makinson and P. Gardenfors, Relations between the logic of theory change and nonmonotonic logic, in: A. Fuhrmann and M. Morreau eds. The Logic of Theory Change, (LNCS 465, Springer-Verlag, Berlin, Germany, 1991) 185-205.

.... approaches of Poole and Brewka, and developed a system for default reasoning, called ranked default theory(RDT) As a very important result, Nebel established a relation between RDT and revised belief revision (called prioritized base revision) which strengthened Makinson and Gardenfors s result ([8]) about the connections between nonmonotonic reasoning and belief revision. The goal of this paper is to further extend Nebel s results so as to obtain more direct and general connections between default reasoning and belief revision. we will present a general framework for default reasoning , ....

....in the generalized framework. 3 Nebel (1992) also give a similar result. He give a relationship between RDT with constraints and prioritized removal operation. See [10] page 77 78 for the detail) 10 5 Related Work and Conclusion As mentioned above, there are several literatures ( 2] 4] 5] [8] [9] 13] discussing about the relationships between nonmonotonic reasoning and belief revision. In [8] Makinson and Gardenfors investigated the relations between belief revision and nonmonotonic logic. They tried to translate the membership in belief revision,y 2 K x, into the inference ....

[Article contains additional citation context not shown here]

David Makinson, Peter Gardenfors, Relations between the Logic of theory change and nonmonotonic logic, in: A. Fuhrmann and M. Morreau eds., The Logic of Theory Change, (LNCS 465, Springer-Verlag, 1991) 185-205.

....[ 1990 ] for example, called belief revision and nonmonotonic logics two sides of the same coin. In fact, a number of desirable properties of nonmonotonic logics [ Kraus et al. 1990; Lehman and Magidor, 1992 ] have direct counter parts as postulates in belief revision and vice versa [ Makinson and Gardenfors, 1991 ] This also translates to concrete instances of revision schemes and nonmonotonic logics. For example, cautious reasoning in Brewka s level default theories [ 1989; 1991 ] is identical to revising a belief base under the prioritized base scheme by [ Nebel, 1991 ] Also inference from ....

David Makinson and Peter Gardenfors. Relations between the logic of theory change and nonmonotonic logic. In A. Fuhrmann and M. Morreau, editors, The Logic of Theory Change, volume 465 of Lecture Notes in Artificial Intelligence. Springer-Verlag, Berlin, Heidelberg, New York, 1991.

....logic, it can be shown that the formal structures of the two theory areas, as they have developed, are surprisingly similar. The aim of this section is to show that it is possible to translate concepts, models, and results from one area to the other. This translation was first given in [9]. In the same way as for the theory of belief revision one can discuss postulates for nonmonotonic reasoning. It was Gabbay [3] who initiated this kind of investigation by focussing on the formal properties of a nonmonotonic inference relation # so that A # B hold between two propositions A and ....

....sense that if A 7 B, then A C 7 B, for any C. By definition, nonmonotonic inferences do not satisfy this condition, but Gabbay proposes that such an inference relation # should at least satisfy cautious monotony which is the condition that if A # B and A # C, then A C # B. Grdenfors and Makinson [9] suggest a method of translating postulates for belief revision into postulates for nonmonotonic logic, and vice versa. The key idea for the translation from belief revision to nonmonotonic logic is that a statement of the form B K A is seen as a nonmonotonic inference from A to B given the set K ....

Makinson, D. and P. Grdenfors (1991): "Relations between the logic of theory change and nonmonotonic logic", The Logic of Theory Change, ed. by A. Fuhrmann and M. Morreau (Berlin: Springer-Verlag), 185--205.

No context found.

D. Makinson and P. Gardenfors, Relations between the logic of theory change and nonmonotonic logic, in: A. Fuhrmann and M. Morreau eds. The Logic of Theory Change, (LNCS 465, Springer-Verlag, 1991) 185-205.

No context found.

David Makinson and Peter Gardenfors. Relations between the logic of theory change and nonmonotonic reasoning. In The Logic of Theory Change, pages 185--205, Berlin, 1991. Springer Verlag.

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