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 development is the conceptual center of the e-book, the place the authors mix the tips 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, conception revision, and epistemic considerations.

It is appropriate for researchers within the quarter of computing device technology and mathematical logic.

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I (X) ⊆ Z, μI (Z) ⊆ Y . 1 The Main Result of Chapter 10 Consider {Ui : i ∈ I}, the set of functions f from I to {Ui : i ∈ I} with f (i) ∈ Ui , and a subset of this product. e. e. we can combine f and f to a new function in , as long as they agree on Y . g. if X | Y | Z holds, and Z ⊆ Z, then X | Y | Z holds, too, for any suitable I and . The problem is to find a full characterization for this ternary relation. Our main result here is that there is no characterization of the relation, of any fixed finite size.

2) Classical consequence determines specificity. g. the set penguins will have the valid default “not fly”. 1. (3) The sets to which defaults are attached determine the basic hierarchy. g. penguins are more exceptional than birds, etc. 4. (4) Elements of a set, which are not in any subset to which new defaults are attached, may satisfy all defaults valid for this set, or not. In the first case, they “sit” at the place of the set in the basic hierarchy. In the second case, they are very exceptional, as we have no standard reason why they should be exceptional.

1) (GH1): σ τ ∧ σ τ ∧ (σ ≺ τ ∨ σ ≺ τ ) ⇒ σσ ≺ τ τ . (2) (GH2): σσ ≺ τ τ ⇒ σ ≺ τ ∨ σ ≺ τ . g. τ ≺ σ might be the case, but σ ≺ τ wins in the end, so σ σ ≺ τ τ . τ τ ⇔σ τ and σ τ . ) (Thus, σ σ ≺ τ τ iff σ σ (4) (R1) σ ≺ σ iff ∀i(σi = σi or σi ≺ σi ) and ∃i(σi ≺ σi ). g. g. resulting in restricted, but not full, interpolation. 26, to be repeated briefly in Sect. 7 below. We take now a closer look at interpolation for nonmonotonic logic. 1 Overview 33 The Three Variants of Nonmonotonic Interpolation Consider preferential logic, and a rule like φ |∼ ψ.

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