By Gabriele Kern-Isberner

ISBN-10: 3540423672

ISBN-13: 9783540423676

Conditionals are omnipresent, in way of life in addition to in clinical environments; they characterize general wisdom got inductively or realized from books. They tie a versatile and hugely interrelated community of connections alongside which reasoning is feasible and that are utilized to various events. accordingly, conditionals are vital, but in addition fairly frustrating gadgets in wisdom representation.
This booklet offers a brand new method of conditionals which captures their dynamic, non-proportional nature really good through contemplating conditionals as brokers moving attainable worlds in an effort to determine relationships and ideology. This realizing of conditionals yields a wealthy thought which makes complicated interactions among conditionals obvious and operational. Moreover,it offers a unifying and more desirable framework for wisdom illustration, nonmonotonic reasoning, trust revision,and even for wisdom discovery.

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Extra resources for Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents

Sample text

Investigating iterated revision, Darwiche and Pearl [DP97a] explicitly took conditional beliefs into account, and they advanced four postulates in addition to the AGM axioms to model what may be called conditional preservation under revision by propositional beliefs: DP-postulates for conditional preservation: (C1) If C |= B then Ψ |= (D | C) iff Ψ B |= (D | C). (C2) If C |= B then Ψ |= (D | C) iff Ψ B |= (D | C). (C3) If Ψ |= (B | A) then Ψ (C4) If Ψ B |= (B | A). B |= (B | A) then Ψ |= (B | A).

E. the worlds satisfying Bel (Ψ precisely those worlds satisfying A that are minimal with respect to A) are Ψ. This theorem shows an important connection between the pre-ordering associated with an epistemic state Ψ and the process of revising Ψ by propositional beliefs. 11) ([BG93]), and such that Mod (Ψ ) = min Ψ (Ω). The smoothness condition is also called limit assumption, see [Gro88, Lew73]. Such epistemic states (Ψ, Ψ ) correspond to Boutilier’s revision models, as described in [BG93]. Because we assume the numbers of possible worlds to be finite, the smoothness condition is trivially fulfilled.

5: We represent conditionals by generators of a (freeabelian) group and define the conditional structure of a world. Using group theoretical structures makes it possible to calculate with conditionals, or with their effects on worlds, respectively. 6). We show that probability functions and ordinal conditional functions which are indifferent with respect to some set of conditionals follow quite a simple conditional-logical pattern. 5. Revisions by sets of conditionals and representations of sets of conditionals will be called c-revisions and c-representations, respectively.

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Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents by Gabriele Kern-Isberner


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