Gabbay, D. M. 1985. Theoretical foundations for nonmonotonic reasoning in expert systems. In Apt, K. R., ed., Logics and Models of Concurrent Systems. Springer.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....no application 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. ....

....(see for example [Tar56] However, to support some forms of non classical reasoning, some compromise on these properties needs to be made. For non monotonic reasoning a form of reasoning with information that is in some sense inconsistent [BH98] involves compromising on monotonicity [Gab85] However, this compromise results in other properties also being compromised. There are many choices over which combinations of properties can be supported for non monotonic reasoning [Mak94] The properties of reflexivity and monotonicity hold for the QC consequence relation. However, the ....

D Gabbay. Theoretical foundations of non-monotonic reasoning in expert systems. In K Apt, editor, Logics and Models of Concurrent Systems. Springer, 1985.

.... classical logic (an example for such a connection is the property right weakening: if CL oe OE and j then j OE) Later, was taken as any monotonic logic ( Freund and Lehmann, 1993] and in any language ( Arieli and Avron, 2000b] for other related works see also [Makinson, 1989; Gabbay, 1991; Freund et al. 1991; Lehmann and Magidor, 1992; Schlechta, 1996; Lehmann, 1998] In this paper we shall use the following notion: Definition 3.2 Let be an scr. A binary relation j between sets of formulas and sets of formulas is called plausible if it satisfies the following conditions: ....

D. M. Gabbay. Theoretical foundation for non-monotonic reasoning part ii: Structured nonmonotonic theories. In Brian Mayoh, editor, Proc. of SCAI'91. IOS Press, 1991.

....and Lev, 2000] Every finite Nmatrix is finitary. 3 Nonmonotonic Consequence Relations 3.1 Plausible consequence relations Monotonic consequence relations are not suitable for many applications in AI, and hence many systems that exhibit nonmonotonic behavior have been developed and studied. [Gabbay, 1985] began a theoretical investigation of conditions that nonmonotonic consequence relations should satisfy. It was suggested that such relations j should satisfy at least three basic conditions: Definition 3.1 A cautious consequence relation is a binary relation j between sets of formulas and ....

D. M. Gabbay. Theoretical foundation for non-monotonic reasoning in expert systems. In Krzysztof R. Apt, editor, Proc. of the NATO Advanced Study Inst. on Logic and Models of Concurrent Systems, pages 439--457. Springer-Verlag, 1985.

....that limits the previously considered distribution A to A ) that is consistent with the previous default selection (i.e. sel(A) 2 A ) should not lead us to revise this default selection. While quite convincing from a default reasoning perspective (in fact, it is a version of Gabbay s [2] restricted monotonicity principle) it is not entirely clear that this principle is an expression of the van Fraassen slogan. Indeed, at least from a geometric point of view, there does seem to exist little similarity between the two problems given by A and , and thus the requirement that they ....

D. Gabbay. Theoretical foundations for nonmonotonic reasoning in expert systems. In K. Apt, editor, Logics and Models of Cuncurrent Systems. Springer-Verlag, Berlin, 1985.

....# and # then #. For example take # to be the cake contains butter , # to be the cake tastes good and # to be the cake contains para#n . For our part however we find the approach of Lehmann, Magidor and Kraus (see [9] 3] and also the closely related work of Gabbay, Gardenfors, Makinson, [1], 11] 10] particularly attractive and the results we shall present here follow directly on from Lehmann et al. s [3] Not unnaturaly therefore we shall be assuming that the reader has some familiarity with that paper. The approach of Lehmann et al. is to treat conditional assertions such as If ....

....the monotonicity rule we had in addition that if # then normally #, then # would, under normal circumstances, be synonomous with # so, again under normal circumstances, # should follow from # # just if # followed from # alone. This formalises as the rule of cautious monotonicity (following [1]) In [9] 3] Kraus, Lehmann and Magidor discuss a number of possible rules and families of rules, based on considerations of the way the relation if . then normally. is used in natural language, to describe, via a purely logical analysis, a procession of ever more powerful ....

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D. M. Gabbay, Theoretical foundations for non-monotonic reasoning in expert systems, in: K. R. Apt, ed, Proceedings NATO Advanced Institute on Logics and Models of Concurrent Systems, La Colle-sur-loup, France (Springer, Berlin, 1985) 439-457.

....:fi m 62 E, fl 2 T . Let 2 H be a hypothesis with ff fi 2 T and fi 62 E. According to Definition 1, there is a possibly empty set of literals ae T such that j Gamma ff fi. Since ff fi 2 Xi, j Gamma ff. Hence, ff 2 T . Hence, E = Gamma R (E) 2 Gamma(E) 2 5 Closure properties Gabbay [7] has initiated the study of the closure properties of the non monotonic derivability relation (j) 7, 10, 11] Here, the non monotonic derivability relation is defined as: W j D if and only if B is the belief set of (D; W ) and 2 B. Gabbay [7] argues that there are three axioms that must be ....

....1, there is a possibly empty set of literals ae T such that j Gamma ff fi. Since ff fi 2 Xi, j Gamma ff. Hence, ff 2 T . Hence, E = Gamma R (E) 2 Gamma(E) 2 5 Closure properties Gabbay [7] has initiated the study of the closure properties of the non monotonic derivability relation (j) [7, 10, 11]. Here, the non monotonic derivability relation is defined as: W j D if and only if B is the belief set of (D; W ) and 2 B. Gabbay [7] argues that there are three axioms that must be satisfied by all nonmonotonic logics. Reflexivity if 2 W , then W j D ; Cautious Monotonicity if W j D ....

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D. M. Gabbay. Theoretical foundations of non-monotonic reasoning in expert systems, In: K. R. Apt (ed), Logic and models of concurrent systems, Springer Verlag, pages 439-457, 1985.

....Monotonicity, and express that, in certain situations, Monotonicity is required. Cautious Monotonicity 8A; B L A B C(A) C(A) C(B) Cautious Monotonicity is a restricted form of Monotonicity: any monotonic operation is cautiously monotonic. This property was rst introduced by D. Gabbay [16], in its nitary form and by D. Makinson [24, 25] in its in nitary form. It requires that one does not retract previous conclusions when one learns that a previous conclusion is indeed true. It seems to have been accepted as reasonable by all researchers in the eld. A discussion of its appeal ....

Dov M. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In Krzysztof R. Apt, editor, Proc. of the NATO Advanced Study Institute on Logics and Models of Concurrent Systems, 38 pages 439-457, La Colle-sur-Loup, France, October 1985. SpringerVerlag.

....monotonic case. At this point, we do not know whether there is a reasonable notion of pseudocompactness for which any nitary operation has a unique pseudo compact extension. It is only recently that the general study of nonmonotonic logics has begun and both frameworks have been used. So far, [8], 12] 13] 15] and [16] opted for the nitary framework, whereas [17] and [18] opted for the in nitary framework. The present work will build a bridge between the two frameworks. A di erent comparison of those two approaches may be found in [1] More precisely, since the nitary framework ....

Dov M. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In Krzysztof R. Apt, editor, Proc. of the NATO Advanced Study Institute on Logics and Models of Concurrent Systems, pages 439{ 457, La Colle-sur-Loup, France, October 1985. Springer-Verlag.

....both the weak one (based on the t pre order) and argumentation (j= 1 is included in j= t and in j= arg ) and this is still the case when some preference information is taken into account (j= 1 is included in j= 3. 3 Logical Properties Following seminal works in non monotonic logic [12, 17, 13, 15], a set of normative properties that a non monotonic inference relation should satisfy has been given in [13] This set of properties is called system P (for Preferential) Without this assumption, many of the inference relations trivialize, either because they coincide with the total relation ....

D. M. Gabbay. Theoretical foundations for nonmonotonic reasoning in experts systems. In K. Apt, editor, Logic and Models of Concurrent Systems. Springer Verlag, 1985.

....formulations, will turn out to be a fruitful step towards further computational developments in treating wide classes of nonmonotonic inferences. It is commonly acknowledged that the idea to study nonmonotonic logics in terms of their consequence relations can be traced back to Gabbay [18]. Since nonmonotonic reasoning was brought up in the computer science field in the seventies, a great number of formalisms have been developed. In the light of this plethora of different systems, the merit of Gabbay was to focus on the minimal theoretical properties which should characterize all ....

....CU. The system is then improved by developing a proof search method based on KE . Finally, we provide some remarks on further extensions and related works. 2 Nonmonotonic Consequence Relations and Conditional Logic The study of nonmonotonic consequence relations has been undertaken by Gabbay [18] who proposed three minimal conditions a (binary) consequence relation on a language L should satisfy to represent a nonmonotonic logic, i.e. #B;D #A #A;D #B More recently, Kraus, Lehmann and Magidor [29] have investigated the proof theoretic and semantic properties of a ....

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Dov M. Gabbay. Theoretical foundations for nonmonotonic reasoning in expert systems. In K.R. Apt, editor, Proc of the NATO Advanced Study Institute on Logics and Concurrent Systems, pages 439--457, Berlin, 1985. Springer-Verlag. 33

....reasoning. They are able to go beyond the deductively valid conclusions, but they are also able to determine whether there exists relevant information interfering with the generation of certain conclusions. In approaches to default reasoning based on conditional or intentional interpretations [15, 16, 8, 28, 22, 6] the notion of relevance appears when the incorporation of some relevant condition to the antecedent of a conditional results in a more exceptional (or less normal) situation, in which case the previously maintained conclusion must be retracted, or a conclusion that was omitted before must be ....

Gabbay, D. Theoretical Foundations for Non-monotonic Reasoning. Expert Systems, Logics and Models of Concurrent Systems, pages 439-459. Springer Verlag (1985).

....system designed to be used both as a refutation and a direct method of proof. Finally, we provide some remarks on computational issues and related works. 2 Nonmonotonic Consequence Relations and Conditional Logic The study of nonmonotonic consequence relations has been undertaken by Gabbay [10] who proposed three minimal conditions a (binary) consequence relation on a language L should satisfy to represent a nonmonotonic logic. More recently, Kraus, Lehmann and Magidor [16] have investigated the proof theoretic and semantic properties of a number of increasingly stronger families of ....

....tableau diagrams for the modal logic S4.3 to Delgrande s [7] conditional logic N. This extension is made possible by the correspondence between S4.3 and N. However, as Boutilier [4] has shown, N fails to validate the rule of Cautious Monotonicity, and thus it lies outside the scope of Gabbay s [10] minimal conditions for nonmonotonic consequence relations. Lamarre [17] takes a more direct approach by relying on Lewis [19] system of spheres models. However, his method does not cover CU. Moreover, as proof systems for CL, the systems just mentioned can be said to suffer of all well known ....

Dov. M. Gabbay. Theoretical Foundations for Nonmonotonic Reasoning in Expert Systems. In K. R. Apt, ed., Proc of the NATO Advanced Study Institute on Logics and Concurrent Systems, 439--457, 1985, Berlin, Springer-Verlag, 1985.

....frame were introduced and used as a semantical basis for these levels. Moreover, the semantical connections between the levels were identified. The notion of a belief state operator was inspired by the work on abstract (nonmonotonic) consequence relations (such as the studies of Gabbay, GAB 85] Shoham, SHO 87] and Kraus, Lehmann, and Magidor [KLM 90] and inference operations (see for example [MAK 89] and [MAK 94] The latter paper (but also [VOO 93] already suggests to look at intended belief sets abstractly. The level 2 description, using reasoning traces, is new, to our ....

Gabbay, D.M., "Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems", in: K.R. Apt (ed.), Logics and Models of Concurrent Systems, NATO ASI Series F13, Springer-Verlag, 1985, pp. 439-457.

....Thus, intuitively, the failure of some basic principles of nonmonotonic reasoning in the context of updates stems from the same nature of update semantics based on rule rejection, and not on the particular transformation chosen. 4.2. 1 General Patterns of Nonmonotonic Inference Relations Gabbay [25] was the first to propose the idea that the output of nonmonotonic systems should be considered as an abstract consequence relation, in order to get a clearer understanding of the diverse nonmonotonic reasoning formalisms. Ensuing research identified several important principles, based on both ....

D.M. Gabbay. Theoretical Foundations for Non-Monotonic Reasoning in Expert Systems. In K.R. Apt, editor, Logics and Models of Concurrent Systems, pages 439--457. Springer, 1985.

....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 B, if B follows nonmonotonically given A as a premise. The classical inference relation 7 is monotonic in the sense that if A 7 ....

Gabbay, D. (1985): "Theoretical foundations for nonmonotonic reasoning in expert systems", in Logic and Models of Concurrent Systems, K. Apt ed. (Berlin: Springer-Verlag).

....sense reasoning. Since ordinary reasoners may revise their views in light of new information, the conclusion an agent draws at a given time need not always increase monotonically with that agent s initially held assumptions. So some weakening of S2 seems to be the most natural route to go (see [11], 13] and [21] 1 We use fin to denote the finite subset relation. 2 We follow the standard convention to use Gamma; Delta to denote Gamma [ Delta and Gamma; A for Gamma [ fAg. 1 Another related development is the area of substructural logics ( 9] 26] and [31] Implicit in the ....

D. M. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In A. R. Krzysztof, editor, Logic And Models Of Concurrent Systems, pages 439--458. SpringerVerlag, 1984.

....by different definitions for the logical manipulation of formulae ff and for the algebraic manipulation of the labels i. Furthermore, many existing logics fit into the LDS framework, including temporal logics [10] modal and many valued logics [8] resource logics [15] and nonmonotonic logics [13, 11, 16]. 4.1 LDS for Default Logic We begin by showing how default logic can be handled by LDS. We assume the usual set of logical formulae, which we denote F , and we label each item in F with the symbol 0. We assume that default rules have the form, i : fl ; where ff; fi; fl 2 F , and i 2 2 N ....

D. Gabbay. Theoretical foundations for non-monotonic reasoning, part 2: Structured non-monotonic theories. In Proceedings of Scandinavian Conference on Artificial Intelligence, pages 19--40. IOS Press, 1991.

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Gabbay, D. M. 1985. Theoretical foundations for nonmonotonic reasoning in expert systems. In Apt, K. R., ed., Logics and Models of Concurrent Systems. Springer.

No context found.

D. M. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In Logics and Models of Concurrent Systems, K. R. Apt, ed. pp. 439--457. Springer-Verlag, Berlin, 1985.

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Dov M. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In KrzysztofR.Apt,editor,Proc. of the NATO Advanced Study Institute on Logics and Models of Concurrent Systems, pages 439--457, La Colle-sur-Loup, France, October 1985. Springer-Verlag.

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D.M. Gabbay. `Theoretical foundations for non-monotonic reasoning in expert systems', in K. Apt (ed), Logics and Models of Concurrent Systems, pp. 439--457. Springer--Verlag. Berlin, 1985.

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D.M. Gabbay, Theoretical foundations for non-monotonic reasoning in expert systems, Logics and Modes of Concurrent Systems, SpringerVerlag, Berlin, 1984, pp. 439-459.

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Gabbay, D.: \Theoretical foundations for non-monotonic reasoning in expert systems". In K. R. Apt (ed.), Logics and Models of Concurrent Systems, Berlin: Springer-Verlag, 1985.

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Dov M. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In Krzysztof R. Apt, editor, Proc. of the NATO Advanced Study Institute on Logics and Models of Concurrent Systems, pages 439--457, La Colle-sur-Loup, France, October 1985. Springer-Verlag.

No context found.

D. Gabbay. Theoretical foundations for non-monotonic reasoning in expert systems. In Krzysztof R. Apt, editor, Proc. of the NATO Advanced Study Institute on Logics and Models of Concurrent Systems, pages 439-457, La Collesur -Loup, France, October 1985. Springer-Verlag.

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