structure Phenomena.Conditionals.ConditionalPerfectionDatum : Type

Conditional Perfection

The phenomenon where "If A then C" is interpreted as "A iff C".

Example: "If you mow the lawn, I'll give you $5" → Often interpreted as: "If you DON'T mow the lawn, I WON'T give you $5"

This is an "invited inference" - not entailed, but strongly suggested.

• sentence : String

  The conditional sentence

• perfectedReading : String

  The perfected (biconditional) reading

• perfectionObserved : Bool

  Whether perfection is typically inferred

• conditions : String

  Any special conditions for the inference

def Phenomena.Conditionals.instReprConditionalPerfectionDatum.repr : ConditionalPerfectionDatum → ℕ → Std.Format

Equations

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

instance Phenomena.Conditionals.instReprConditionalPerfectionDatum : Repr ConditionalPerfectionDatum

Equations

• Phenomena.Conditionals.instReprConditionalPerfectionDatum = { reprPrec := Phenomena.Conditionals.instReprConditionalPerfectionDatum.repr }

def Phenomena.Conditionals.lawnMowingExample : ConditionalPerfectionDatum

Classic example from Geis & Zwicky

Equations

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

def Phenomena.Conditionals.mathExample : ConditionalPerfectionDatum

Example where perfection is NOT inferred

Equations

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

def Phenomena.Conditionals.disjunctiveAntecedent : ConditionalPerfectionDatum

Example where perfection is blocked

Equations

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

structure Phenomena.Conditionals.MissingLinkDatum : Type

Missing-Link Infelicity

The phenomenon where conditionals with unrelated antecedent and consequent sound odd or unacceptable.

Example: "If my coffee is cold, the Eiffel Tower is in Paris" → True (material conditional) but pragmatically odd

This is explained by the assertability-based semantics: the conditional is infelicitous because P(C|A) ≈ P(C), indicating no connection.

• sentence : String

  The conditional sentence

• materiallyTrue : Bool

  Whether the material conditional is true

• felicitous : Bool

  Whether the sentence sounds felicitous

• explanation : String

  Explanation for the (in)felicity

instance Phenomena.Conditionals.instReprMissingLinkDatum : Repr MissingLinkDatum

Equations

• Phenomena.Conditionals.instReprMissingLinkDatum = { reprPrec := Phenomena.Conditionals.instReprMissingLinkDatum.repr }

def Phenomena.Conditionals.instReprMissingLinkDatum.repr : MissingLinkDatum → ℕ → Std.Format

Equations

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

def Phenomena.Conditionals.coffeeEiffelExample : MissingLinkDatum

Classic missing-link example

Equations

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

def Phenomena.Conditionals.coinPresidentExample : MissingLinkDatum

Another missing-link example

Equations

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

def Phenomena.Conditionals.rainUmbrellaExample : MissingLinkDatum

Felicitous conditional for comparison

Equations

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

structure Phenomena.Conditionals.DouvenPuzzleDatum : Type

Douven's Puzzle (@cite{douven-2008}, discussed in @cite{grusdt-lassiter-franke-2022})

A puzzle about when conditionals are assertable.

Scenario: You have an almost-fair coin (51% heads). Is it appropriate to assert "If you flip the coin, it will land heads"?

Intuition: NO - despite P(H|flip) = 0.51 > 0.5, the conditional seems too weak.

This suggests assertability requires P(C|A) >> P(C), not just P(C|A) > 0.5. The threshold θ ≈ 0.9 in Grusdt et al. captures this.

• conditionalProb : ℚ

  P(C|A) in the scenario

• unconditionalProb : ℚ

  P(C) (unconditional probability of consequent)

• intuitivelyAssertable : Bool

  Intuitive judgment: is the conditional assertable?

• sentence : String

  The conditional sentence

def Phenomena.Conditionals.instReprDouvenPuzzleDatum.repr : DouvenPuzzleDatum → ℕ → Std.Format

Equations

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

instance Phenomena.Conditionals.instReprDouvenPuzzleDatum : Repr DouvenPuzzleDatum

Equations

• Phenomena.Conditionals.instReprDouvenPuzzleDatum = { reprPrec := Phenomena.Conditionals.instReprDouvenPuzzleDatum.repr }

def Phenomena.Conditionals.douvenCoinFlip : DouvenPuzzleDatum

The original Douven scenario

Equations

• Phenomena.Conditionals.douvenCoinFlip = { conditionalProb := 51 / 100, unconditionalProb := 51 / 100, intuitivelyAssertable := false, sentence := "If you flip the coin, it will land heads" }

def Phenomena.Conditionals.highProbCase : DouvenPuzzleDatum

A case where assertion IS appropriate

Equations

• Phenomena.Conditionals.highProbCase = { conditionalProb := 95 / 100, unconditionalProb := 1 / 2, intuitivelyAssertable := true, sentence := "If you water the plant, it will grow" }

def Phenomena.Conditionals.baseRateCase : DouvenPuzzleDatum

Edge case: P(C|A) high but P(C) also high

Equations

• Phenomena.Conditionals.baseRateCase = { conditionalProb := 95 / 100, unconditionalProb := 90 / 100, intuitivelyAssertable := false, sentence := "If you use sunscreen, you won't get sunburned" }

structure Phenomena.Conditionals.IndicativeSubjunctivePair : Type

Indicative/Subjunctive Split

English (and many languages) distinguish:

• Indicative: "If it rains, the game is cancelled"
• Subjunctive: "If it were to rain, the game would be cancelled"

These have different interpretations:

• Indicative: epistemic uncertainty, open whether A is true
• Subjunctive: counterfactual, A is assumed false

Example: "If Oswald didn't kill Kennedy, someone else did" (indicative) - TRUE "If Oswald hadn't killed Kennedy, someone else would have" (subjunctive) - FALSE/UNCERTAIN

• indicative : String

  The indicative version

• subjunctive : String

  The subjunctive/counterfactual version

• indicativeJudgment : String

  Judgment on indicative

• subjunctiveJudgment : String

  Judgment on subjunctive

instance Phenomena.Conditionals.instReprIndicativeSubjunctivePair : Repr IndicativeSubjunctivePair

Equations

• Phenomena.Conditionals.instReprIndicativeSubjunctivePair = { reprPrec := Phenomena.Conditionals.instReprIndicativeSubjunctivePair.repr }

def Phenomena.Conditionals.instReprIndicativeSubjunctivePair.repr : IndicativeSubjunctivePair → ℕ → Std.Format

Equations

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

def Phenomena.Conditionals.oswaldExample : IndicativeSubjunctivePair

Adams' Oswald example

Equations

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

def Phenomena.Conditionals.weatherExample : IndicativeSubjunctivePair

Standard minimal pair

Equations

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

structure Phenomena.Conditionals.ConditionalQuestionDatum : Type

Conditionals in questions exhibit interesting behavior.

"If it rains, will the game be cancelled?" vs "Will the game be cancelled if it rains?"

These are typically equivalent, but word order can affect focus/presupposition.

• question : String

  The conditional question

• expectedAnswer : String

  The expected answer form

• notes : String

  Notes on interpretation

instance Phenomena.Conditionals.instReprConditionalQuestionDatum : Repr ConditionalQuestionDatum

Equations

• Phenomena.Conditionals.instReprConditionalQuestionDatum = { reprPrec := Phenomena.Conditionals.instReprConditionalQuestionDatum.repr }

def Phenomena.Conditionals.instReprConditionalQuestionDatum.repr : ConditionalQuestionDatum → ℕ → Std.Format

Equations

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

def Phenomena.Conditionals.conditionalQuestionExample : ConditionalQuestionDatum

Equations

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

structure Phenomena.Conditionals.BiscuitConditionalDatum : Type

Biscuit Conditionals

Non-causal conditionals where the consequent's truth doesn't depend on the antecedent.

Example: "If you're hungry, there are biscuits on the table" → The biscuits are there regardless of whether you're hungry

The antecedent specifies WHEN the information is relevant, not a cause.

• sentence : String

  The biscuit conditional

• paraphrase : String

  Paraphrase showing the structure

• consequentDepends : Bool

  Whether consequent depends on antecedent

instance Phenomena.Conditionals.instReprBiscuitConditionalDatum : Repr BiscuitConditionalDatum

Equations

• Phenomena.Conditionals.instReprBiscuitConditionalDatum = { reprPrec := Phenomena.Conditionals.instReprBiscuitConditionalDatum.repr }

def Phenomena.Conditionals.instReprBiscuitConditionalDatum.repr : BiscuitConditionalDatum → ℕ → Std.Format

Equations

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

def Phenomena.Conditionals.classicBiscuit : BiscuitConditionalDatum

Equations

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

def Phenomena.Conditionals.anotherBiscuit : BiscuitConditionalDatum

Equations

• Phenomena.Conditionals.anotherBiscuit = { sentence := "If you need me, I'll be in my office", paraphrase := "I'll be in my office (relevant if you need me)", consequentDepends := false }

structure Phenomena.Conditionals.ConditionalGeneralizations : Type

Key empirical generalizations about conditionals

• perfectionObserved : Bool

  Conditional perfection is observed

• missingLinkInfelicitous : Bool

  Missing-link conditionals are infelicitous

• highThresholdRequired : Bool

  High threshold required for assertability (not just > 0.5)

• indicativeSubjunctiveDiffer : Bool

  Indicative ≠ subjunctive in truth conditions

• biscuitConditionalsExist : Bool

  Biscuit conditionals exist (non-causal)

def Phenomena.Conditionals.observedGeneralizations : ConditionalGeneralizations

Equations

• Phenomena.Conditionals.observedGeneralizations = { }