Download A New Perspective on Nonmonotonic Logics by Dov M. Gabbay, Karl Schlechta PDF

By Dov M. Gabbay, Karl Schlechta

In this publication the authors current new effects on interpolation for nonmonotonic logics, summary (function) independence, the Talmudic Kal Vachomer rule, and an equational answer of contrary-to-duty tasks. The bankruptcy on formal building is the conceptual center of the publication, the place the authors mix the information of different types of nonmonotonic logics and their research of 'natural' options right into a formal common sense, a different preferential building that mixes formal readability with the intuitive benefits of Reiter defaults, defeasible inheritance, thought revision, and epistemic considerations.

It is appropriate for researchers within the sector of computing device technological know-how and mathematical logic.

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1 The Main Result of Chapter 11 The main result of this Chapter is a special preferential structure, constructed using ideas from inheritance, Reiter defaults, theory revision, and epistemic considerations. The construction itself is simple, and is based on our conceptual analysis, and the reader is invited to read Sect. 2, as well as the beginning sections of Chap. 11, to see where the ideas came from. The single most important idea is probably that influence changes are rare, provided our concepts are “reasonable”.

1. 1 Overview 43 Suppose φ and φ are defaults attached to A, then a normal element of A − A should satisfy φ and φ . g. if it were a member of A ⊆ A, where the default in question may not hold. g. A − A in our example. The elements of ω(X) will have an order among themselves: the more defaults they satisfy, the better they are. 3. As indicated, elements of ω(X) are more abnormal than those of μ(X), so they should sit higher in the hierarchy. 4. All details are found in Sect. 1. 4 What We Achieved (1) A clear and well-examined semantics with nice logical properties in the form of a special preferential structure.

Analogously, for X, Y ⊆ I, X ∩ Y = ∅, x ∈ U X, y ∈ U Y , let P(x, y) := P({u ∈ U : u X = x and u Y = y}). We sometimes set P(xy) := P(x, y), when there is no ambiguity. (4) Finally, for X, Y , Z ⊆ I pairwise disjoint, x ∈ U X, y ∈ U Y , z ∈ U Z, let , P(x | y, z) := P(x,y,z) , etc. P(x) = P(x, z)/P(z)or P(x, z) = P(x) ∗ P(z) if Y = ∅ If Y = ∅, we shall also write X || Z P for X | Y | Z P . When the context is clear, we may omit the “P”. We also write ¬ X || Z P , when X || Z P is not the case. Here, and for other types of independence, we will sometimes write X, X | Y | Z , etc.

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