Download e-book for kindle: A New Perspective on Nonmonotonic Logics by Dov M. Gabbay, Karl Schlechta

By Dov M. Gabbay, Karl Schlechta

ISBN-10: 3319468154

ISBN-13: 9783319468150

ISBN-10: 3319468170

ISBN-13: 9783319468174

In this e-book the authors current new effects on interpolation for nonmonotonic logics, summary (function) independence, the Talmudic Kal Vachomer rule, and an equational resolution of contrary-to-duty tasks. The bankruptcy on formal building is the conceptual middle of the ebook, the place the authors mix the tips of various kinds of nonmonotonic logics and their research of 'natural' thoughts right into a formal common sense, a unique preferential development that mixes formal readability with the intuitive merits of Reiter defaults, defeasible inheritance, idea revision, and epistemic considerations.

It is appropriate for researchers within the quarter of laptop technological know-how and mathematical logic.

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Thus, there might well be φ-models where ψ fails, but these are not among the φ-models closest to m. The distance will, of course, express the difference between the situation m and the models considered. Thus, in the first scenario, situations where it rains and there is no extreme wind condition are closer to the original one than those where a hurricane blows. In the original approach, distances from each possible actual situation are completely independent. It can, however, be shown that we can achieve the same results with one uniform distance over the whole structure, see Schlechta and Makinson (1994).

3) We turn to the third variant, φ |∼ α |∼ ψ. This is probably the most interesting one, as (a) it is more general, as it loosens the connection with classical logic, (b) it seems more natural as a rule, and (c) it is also connected to more natural laws about size. Again, we do not have a complete characterization, only sufficient conditions about size. 26 that (μ ∗ 1) or (μ ∗ 4) entail interpolation of the type φ |∼ α |∼ ψ. 1. So we see that, roughly, semantical interpolation for nonmonotonic logics works when abstract size is defined in a modular way—and we find independence again.

Note, that (<-Abs) implies that always τ = τ , τ ≺ τ , τ ≺ τ , or τ ⊥τ holds. 4 Let again, I = J ∪ J with J ∩ J = ∅. For each i ∈ I Xi = ∅, let I := {Xi : i ∈ I}, J, J analogously, and let ⊆ J, ⊆ J . Let σ, τ ∈ J, σ , τ ∈ J , and let relations ≺ be defined on I, J, J. (We will not distinguish them as ≺I , etc. ) As usual, will denote ≺ or =. Analogously, σi will be an element of Xi , and we suppose relations ≺ are defined on all Xi , and on arbitrary J for (R1) below. (1) (GH1): σ τ ∧ σ τ ∧ (σ ≺ τ ∨ σ ≺ τ ) ⇒ σσ ≺ τ τ .

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

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