Thomason, R. and Horty, J. (1989). Logics for inheritance theory. In Proceedings of the 2nd International Workshop on Nonmonotonic Reasoning, pages 220--237.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....1987b) had claimed, perhaps not very persuasively, that this misunderstands the nature and purpose of default logic. Chapter 3. Current approaches to nonmonotonic reasoning 71 in support of Tweety s inability to fly than does bird in support of its flying ability. Thomason and Horty, in (Thomason and Horty, 1989), provide four valued autoepistemic logic. Path based relations are mapped onto expressions in their version and model theoretic accounts are provided of various properties of inheritance. Thomason and Horty are not convinced that translating inheritance networks into standard nonmonotonic logic ....

Thomason, R. and Horty, J. (1989). Logics for inheritance theory. In Proceedings of the 2nd International Workshop on Nonmonotonic Reasoning, pages 220--237.

....only require membership in one extension [ Reiter, 1980, Moore, 1985, Poole, 1988 ] These latter systems seem to get the one step default property for the wrong reason, namely by being able to predict a proposition and also predict its negation. iii) is given up in inheritance systems [ Thomason and Horty, 1988 ] These allow (i) ii) and (iv) however they lack the expressiveness of the richer logic based formalisms. iv) is not given up by any system I know, although it is argued [ Israel, 1980, Perlis, 1987, Kyburg, 1988 ] that commonsense reasoning does indeed require reasoning under ....

....the lottery paradox. We predict any particular lottery ticket is not going to win. When we conjoin many such predictions problems arise. One of the reasons the lottery paradox example is so persuasive is because of our intuitions about wanting to prefer more specific knowledge [ Touretzky, 1986, Thomason and Horty, 1988, Poole, 1985, Geffner, 1988 ] One intuition behind specificity is exactly the one step default property (we prefer the one step default that emu s don t fly over the longer argument that emus are birds and birds fly) If this is so, any method that compares extensions or models (without regard ....

R. H. Thomason and J. F. Horty, "Logics for Inheritance Theory", in Proceedings of the 2nd International Workshop on Non-Monotonic Reasoning, Springer-Verlag, Lecture Notes in Artificial Intelligence, No. 346, pp. 220-237.

....over inheritance of :p (resp. p) through the class r . See Figure 4(b) That is, for any pair of arcs hq; pi and hr; pi, such that there is a directed path from q to r, it is the case that hr; pi OE p hq; pi: 2. For acyclic inheritance networks, the specificity relationship is dynamic [38] , and can be obtained by generalizing Condition 1b. That is, it must satisfy the following conditions: a) A fact always overrides a default conclusion. Hence, if E(i; r) then for all children q : hq; ri OE r hi; ri (b) The notion of local specificity we can espouse is as follows: If, on the ....

....specificity relation used to disambiguate inheritance conflicts wrt a common property by an individual via a set of nodes, depends only on the set of nodes, and not on the individual inheritance paths . But one can argue that this is counter intuitive, as illustrated below. Consider Figure 5(a) [38] . A p is a q and a q is an r, and hence, p is more specific than r. One can then view the arcs from a and b to r as being redundant. So, both a and b, inherit :s from p. On the other hand, in Figure 5(b) 38] a is not a q. So the arc from a to r can be interpreted as contributing an ....

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R. Thomason and J. Horty, Logics for inheritance theory, In Non-Monotonic Reasoning , M. Reinfrank, J. de Kleer, M. Ginsberg, and E. Sandewall (eds.), Springer-Verlag, 1989.

....cyclic inheritance networks. However, such a generalization complicates the semantics somewhat, taking the definitions in the direction of [19, 21] 2.3 Priority Constants The priority constant in p : represents the type and the relative strength of evidence in support of p. Following [3, 4, 12, 37, 38, 10], priority constants are considered along two different dimensions: in one, evidence is ordered on the basis of truth content ; in the other, it is ordered on the basis of knowledge or information content . The information dimension is defined as follows. First, the set of priority constants P ....

R. Thomason and J. Horty, Logics for inheritance theory, in: M. Reinfrank, J. de Kleer, M. Ginsberg, and E. Sandewall (eds.), Non-Monotonic Reasoning, Springer-Verlag (1989).

....We denote by Cons( Phi) the union of the following two node sets: fu(a) if there is a positive path from object node a to u in Phig f:u(a) if there is a negative path from object node a to u in Phig. Example 4. Consider the defeasible inheritance network Gamma of Figure 2, as given in [30]. This inheritance theory has three credulous extensions: Phi 1 = f1; 2; 13; 15; 16; 157; 1579g Phi 2 = f1; 2; 13; 15; 16; 168g Phi 3 = f1; 2; 24; 15; 16; 168g Given an inheritance network Gamma , a path (u; oe; x) is said to be simple if there is no path (u; oe 0 ; x) such that the set ....

R.H. Thomason and J.F. Horty. Logics for inheritance theory. In 2nd International Workshop for Non-Monotonic Reasoning, pages 220--237, 1988.

....Consider the following example: Example 1.1 Suppose we have as defaults birds fly , emus don t fly , and as facts emus are birds and Tweety is an emu . There is a very strong preference for concluding Tweety doesn t fly based on specificity [ Touretzky, 1986, Poole, 1985, Loui, 1987, Thomason and Horty, 1988 ] We prefer to use the more specific knowledge about emus over the more general knowledge about birds. The instances of the facts that are relevant to the conclusion are emu(tweety) emu(tweety) bird(tweety) 1) Using the same defaults, if we change the facts by swapping the role of emu ....

....about Tweety, instances of general information (such as square(tweety) rectangle(tweety) and derived information (such as bird(tweety) Levesque makes no attempt to automatically use specificity. This work should also be contrasted to the work in inheritance systems [ Touretzky, 1986, Thomason and Horty, 1988, Stein, 1989 ] We are trying to add a notion of specificity to a general logic system, and want the non defeasible statement emus are birds to be exactly the logical statement 8X emu(X) bird(X) This work is most closely related to the sceptical inheritance of [ Stein, 1989 ] both allow ....

R. H. Thomason and J. F. Horty, "Logics for Inheritance Theory", Proc. Second International Workshop on NonMonotonic Reasoning.

.... applicable defaults, the one applicable to emus is more specific and thus should be preferred over the more general default about birds (it is a more specific default as it is about a more specific class) This notion of preference for more specific knowledge has been advocated by many authors [46, 35, 26, 24, 11, 45, 31]. If we don t want to conclude Tweety does not fly in example 2.5, it seems as though the default emus don t fly can never be used. Whenever it is able to be used, the birds fly default is also applicable, and competes with this default. Thus, unless we want a default to be useless, we should ....

....the user add priorities 3 [26, 3] The user would make the emu s don t fly default have higher priority than the birds fly default; when they compete, as in this example, the higher priority default would prevail. 3. Incorporate specificity into the default reasoning system automatically, [46, 35, 24, 11, 45, 29, 1]. This is discussed further in section 3. 2.2.2 Inheritance of cancellation Based on the information in example 2.5, we also want to conclude that Polly, who looks like an emu, is an emu. This is similar to the previous specificity case, in that the direct default if it looks like an emu, it is ....

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R. H. Thomason and J. F. Horty, "Logics for Inheritance Theory", in Proceedings of the 2nd International Workshop on Non-Monotonic Reasoning, Springer-Verlag, Lecture Notes in Artificial Intelligence, No. 346, pp. 220-237, 1988.

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Thomason, R.H. and Horty, J.F., (1988). Logics for Inheritance Theory, in: Proceedings of the 2nd Workshop on Nonmnontonic Reasoning, Grassau, FRG, pp. 220-237, Springer Verlag.

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