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Linglib.Phenomena.Modality.Studies.KlinedinstRothschild2012

@cite{klinedinst-rothschild-2012}: Disjunctive Syllogism Failure for Epistemic Modals #

@cite{klinedinst-rothschild-2012}

Klinedinst & Rothschild (2012) "Connectives without truth tables" (Natural Language Semantics 20(2):137-175) argue that the standard truth-table account of conjunction and disjunction fails for sentences with epistemic modals — citing among other things the failure of disjunctive syllogism.

The canonical example: from "Either the dog is inside or it must be outside" together with "It's not the case that the dog must be outside," classical logic concludes "The dog is inside." But for epistemic disjunction this conclusion is intuitively not warranted — the first premise was epistemically tautological (it carries no information), and so the second premise can be true without the dog actually being inside.

Holliday & Mandelkern (2024) §2.3 take the example up directly, noting that K&R cite Yalcin (2007) for the underlying observation. The orthologic account in HM 2024 then derives the failure of disjunctive syllogism from the non-Boolean structure of the regular-set ortholattice (formalized in Studies/HollidayMandelkern2024.lean::disjSyllogism_fails).

What's encoded #

The natural-language judgment that the inference is invalid — i.e., the conclusion does not follow from the premises despite the classical pattern suggesting otherwise. Cross-theory verification (against HM's orthologic, Veltman's update semantics, etc.) requires a formula-tree representation that's currently unavailable (deferred substrate work).

source
structure Phenomena.Modality.Studies.KlinedinstRothschild2012.DisjSyllIntuition :
Type

Disjunctive syllogism failure intuition: from p ∨ q and ¬q, classical logic concludes p. For epistemic-modal q, this inference is intuitively invalid. The natural-language premises and conclusion are recorded as String for documentation; cross-theory verification requires a formula-tree representation that's currently unavailable.

  • premise1 : String

    The first premise (the disjunction).

  • premise2 : String

    The second premise (the negated disjunct).

  • conclusion : String

    The classical conclusion.

  • valid : Bool

    Whether the inference is intuitively valid.

Instances For
    source
    def Phenomena.Modality.Studies.KlinedinstRothschild2012.instReprDisjSyllIntuition.repr :
    DisjSyllIntuition → Nat → Std.Format
    Equations
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    Instances For
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      @[implicit_reducible]
      instance Phenomena.Modality.Studies.KlinedinstRothschild2012.instReprDisjSyllIntuition :
      Repr DisjSyllIntuition
      Equations
      source
      def Phenomena.Modality.Studies.KlinedinstRothschild2012.disjSyllFailure :
      DisjSyllIntuition

      Klinedinst & Rothschild's canonical disjunctive-syllogism-failure example: "Either the dog is inside or it must be outside; it's not the case that the dog must be outside; therefore the dog is inside" is intuitively invalid for epistemic modals.

      K&R credit Yalcin (2007); the example reappears in @cite{holliday-mandelkern-2024} §2.3 as a centerpiece of the case for a non-classical logic.

      Equations
      • One or more equations did not get rendered due to their size.
      Instances For