Philippe Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning, pages 357--367, Cambridge, MA, April 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....conditional connectives are allowed only in the consequent of conditional formulas. This restriction arises naturally out of the deontic, and in general defeasible logic, literature. Almost all logics for defeasible conditionality use only the flat (i.e. non nested) part of CL, see e.g. [Alc93,Bel90,Bel91,Del87,Del88,Han69,KLM90,Lam91,Leh89]) and some admit iteration of the conditional connective only in the consequent of conditional formulas (this is the case with [CT92] s four valued conditional logic for knowledge update and [GMS96] s treatment of hypothetical logic programming) As we shall see, this restriction has its pros ....

Philippe Lamarre. S4 as the conditional logic of nonmonotonicity. In J. Allen, R. Fikes, and E. Sandwall (eds.), Principles of Knowledge Representation and Reasoning (KR`91), pages 357--367, Morgan Kaufman Publishers, San Mateo (Ca), 1991.

....for future work. 7 Related Work In this section, we consider some work on complexity issues for related subjects. 7. 1 Conditional Modal Logics A stream of semantics for conditional knowledge bases, which we have not considered in this paper, is inherited from conditional modal logics, cf. [26, 27, 14, 15, 59, 36]. Roughly speaking, in these approaches a conditional statement is true at a world w in a set of possible worlds W , if is true in a set f(w; of selected worlds in which is true. The worlds f(w; may be the least exceptional, most normal, etc worlds from the view of w. To capture these ....

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proc. 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR-91), Cambridge, MA, pp. 357--367. Morgan Kaufmann, 1991.

....7 Related Work In this section, we consider some work on complexity issues for related subjects. INFSYS RR 1843 00 06 7. 1 Conditional Modal Logics A stream of semantics for conditional knowledge bases, which we have not considered in this paper, is inherited from conditional modal logics, cf. [26, 27, 14, 15, 59, 36]. Roughly speaking, in these approaches a conditional statement is true at a world w in a set of possible worlds W , if is true in a set f(w; of selected worlds in which is true. The worlds f(w; may be the least exceptional, most normal, etc worlds from the view of w. To capture these ....

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proc. 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR-91), Cambridge, MA, pp. 357--367. Morgan Kaufmann, 1991.

....In this paper, we have established a sharp picture of the complexity of major approaches to default reasoning from conditional knowledge bases. A stream of semantics for conditional knowledge bases that we have not considered in this paper is inherited from conditional modal logics, cf. [15, 16, 8, 42, 21]. Roughly speaking, evaluates in a Lewis style system at a world w to true, if in a set of selected worlds in which is true (the most plausible, least exceptional ones etc) also is true. Such logics allow nested use of , which is not the case in conditional knowledge bases. For example, ....

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning (KR-91), pages 357--367, 1991.

....where we write as usual 3ff = def :2:ff. I(ffjfi) def 2 (fi 3(fi 2(fi ff) O(ffjfi) def ( ff fi) ff fi) I(ffjfi) We have M;w j= I(ffjfi) if the preferred fi worlds of R(w) are ff worlds, and ff eventually becomes true in all infinite descending chains of fi worlds [35,4]. Finally, we have M;w j= O(ff j fi) if we have w 2 6 w 1 for all w 1 ; w 2 2 R(w) such that M;w 1 j= ff fi and M;w 2 j= ff fi, and M;w j= I(ffjfi) The logic PDL is the definition of these three layers in a modal preference logic. Definition 1. PDL) The bimodal language L is formed from a ....

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR'91), pages 357--367. Morgan Kaufmann, 1991.

....is obligatory is defined in terms of deontic betterness. I(ffjfi) def 2 (fi 3(fi 2(fi ff) O(ffjfi) def (ff fi :ff fi) I(ffjfi) We have M;w j= I(ff j fi) if the preferred fi worlds are ff worlds, and ff eventually becomes true in all infinite descending chains of fi worlds [21, 3]. Finally, we have M;w j= O(ffjfi) if we have w 2 6 w 1 for all w 1 ; w 2 2 W such that M;w 1 j= ff fi and M;w 2 j= ff fi, and M;w j= I(ffjfi) The logic PDL is defined by defining these three layers in a modal preference logic. Definition 1 (PDL) The bimodal language L is formed from a ....

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the KR'91, pages 357--367, 1991.

....proposition fi may be inferred from ff iff fi is true in every world that is minimally abnormal or atypical among those satisfying ff. This has been formalized in several different ways ( 10] 1] 2] 3] 4] and its relations to standard modal logic and conditional logics investigated ( 2] [21]) A general framework unifying defeasible consequence, belief revision and conditional logics has been proposed in [19] For a discussion on the several faces of the minimality paradigm see [23] 1 To refer to a default true : ffi=ffi it is enough to specify only the formula ffi. We adopt this ....

Philippe Lamarre. S4 as the conditional logic of nonmonotonicity. In James Allen, Richard Fikes, and Erik Sandewall, editors, KR 91: Principles of Knowledge Representation and Reasoning - Proceedings of the Second International Conference, pages 357--367. Morgan Kaufmann Publishers, 1991.

....space reasons in this section we only sketch how the exception logic can be extended to a default logic, i.e. how no conflict axioms and conflict resolution mechanisms can be added. Sceptical (i.e. level 2) defaults are defined in the modal preference logic (the sceptical phase 2 default is from [Lam91,Bou94]) The sceptical phase 2 default fi 8 ff is true in a model if ff is true in all most preferred fi worlds (and eventually become true in every infinite descending chain of fi worlds) and the sceptical phase 1 default fi s ff is a combination of the credulous phase 1 default and the sceptical ....

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the KR'91, pages 357--367, Cambridge, 1991.

....vice versa. Therefore, our results cannot be derived, even through a suitable translation, by the above works, although intuition and motivation should be credited to both. Relations of orderings of sentences with other systems performing some sort of nonmonotonic reasoning are abundant ( 7] 8] [28], 29] 47] 53] 13] such as Pearl s system Z ( 43] conditional logic ( 49] 31] and possibilistic logic ( 12] It is worth mentioning that orderings appear frequently in the literature of nonmonotonic logic. Orderings of models lead to the preferential model framework ....

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of KR91, pages 357--367, Cambridge, MA, 1991.

.... such that ff is true in all the worlds following w 1 in the chain (including w 1 itself since RK is reflexive) This construction has already been used, for example to prove some connections between modal logics, conditional logics and non monotonic preference inference relations in [Lam91]. Similar considerations on RB support the definition of B . 4 Belief, certainty, and knowledge: an axiomatic system Consider the following axiomatic system: Definition 3 Axiomatic system The system contains the axioms of the propositional calculus plus: ffl knowledge K(ff fi) Kff Kfi) ....

....Lehmann, and Magidor in [KLM90] for preferential inference relations. This is not that surprising, however, since the notion of preference has been used to give an intuitive underlying explanation of belief. The links between these inference relations and S4 are now well known (see, for example, [Lam91]) The axioms linking knowledge and belief are perhaps the most interesting. Among them, the first two are also simple adaptation of rules used by Kraus, Lehman, and Magidor to characterize preference inference relations. The third one is probably the most intuitive; we know of almost no approach ....

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proc. Second Conference on Knowledge Representation and Reasoning, Boston, MA, 1991.

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Philippe Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the Second International Conference on the Principles of Knowledge Representation and Reasoning, pages 357--367, Cambridge, MA, April 1991.

No context found.

P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR'91), pages 357-367. Morgan Kaufmann, 1991.

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P. Lamarre. S4 as the conditional logic of nonmonotonicity. In Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning (KR'91), pages 357--367, Cambridge, 1991.

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