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    Preferred models provide a general mechanism for inducing... — Carmelics
    Home/Modality & Possibility
    HistoryEditSee Inverse

    Preferred models provide a general mechanism for inducing a nonmonotonic consequence relation.

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.A function can be defined that maps each formula set Γ to a proper subset MΓ of the models of Γ.
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    • 2.Γ implies C only if C is satisfied by every model in MΓ rather than every model of Γ.
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    • 3.Because MΓ∪{A} is not assumed to be a subset of MΓ, the implication from Γ to C need not extend to supersets of Γ.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.The selection of 'preferred' models smuggles in normative criteria that cannot themselves be justified within the purely model-theoretic framework.
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    • 2.Hansson and Makinson demonstrated that different preference orderings over models yield incompatible consequence relations for identical premise sets.
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    • 3.A mechanism that produces arbitrary outputs depending on antecedently chosen preferences lacks the modal grounding required to track genuine possibility.
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    Reason against 2 of 2
    ?
    • 1.Kraus, Lehmann, and Magidor showed that preferred model semantics validates only System P, which is too weak to capture defeasible conditionals in natural reasoning.
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    • 2.Nonmonotonic consequence relations grounded in preferred models cannot distinguish epistemic from metaphysical sources of revisability, collapsing a distinction Kripke's work makes mandatory.
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    Modality & PossibilityTruth & Knowledge

    Related

    A function can be defined that maps each formula set Γ to a proper subset MΓ of ...A mechanism that produces arbitrary outputs depending on antecedently chosen pre...Because MΓ∪{A} is not assumed to be a subset of MΓ, the implication from Γ to C ...Hansson and Makinson demonstrated that different preference orderings over model...
    +4 moreShow less
    Kraus, Lehmann, and Magidor showed that preferred model semantics validates only...Nonmonotonic consequence relations grounded in preferred models cannot distingui...The selection of 'preferred' models smuggles in normative criteria that cannot t...Γ implies C only if C is satisfied by every model in MΓ rather than every model ...

    Similar

    Preferential entailment holds that A is a nonmonotonic consequence of ...85%Deductive-nomological models cannot accommodate one-off explanations.74%Deductive-nomological explanation requires that similar mechanisms giv...73%The quasi-causal model of metaphysical explanation is not the only ava...72%

    Source

    AI-extracted1/3 agreementValid
    SEP: logic-ai
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    The consequence relations of classical logics are monotonic. That is, if a set Γ of formulas implies a consequence C then a larger set Γ ∪ A will also imply C. A logic is nonmonotonic if its consequence relation lacks this property. Preferred models provide a general way to induce a nonmonotonic consequence relation. Invoke a function that for each Γ produces a subset MΓ of the models of Γ; in general, we will expect MΓ to be a proper subset of these models. We then say that Γ implies C if C i
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit