Bridge: Relevance Theory → Nonliteral Interpretation

RT's account of metaphor, hyperbole, and loose use is unified: they are all instances where the LITERAL interpretation fails the relevance threshold, and a related but non-literal interpretation succeeds.

S&W (Ch. 4 §3): "The hearer does not first decode the proposition expressed, then check whether it is consistent with the principle of relevance, and only then look for a figurative interpretation. Rather, the figurative interpretation is the most accessible one consistent with the principle of relevance."

Metaphor (loose use)

"He is a whale" — the literal interpretation (referent is a cetacean) contradicts mutual knowledge and produces 0 positive cognitive effects. The metaphorical reading (referent shares salient whale-properties: large, impressive) produces positive effects via contextual implications.

S&W (pp. 233-237): Metaphor is not a special mechanism — it's what happens when the comprehension procedure applies to an utterance whose literal interpretation cannot achieve relevance. The interpretive path from literal to metaphorical is CONTINUOUS with approximation and hyperbole.

Hyperbole (overstatement)

"I've told you a million times" — the literal reading is absurd but the approximate reading (very many times) produces positive effects.

The RT Continuum

S&W argue these are not distinct categories but a continuum: literal → approximation → hyperbole → metaphor

All involve the hearer broadening or loosening the literal content until the interpretation achieves relevance.

inductive Phenomena.Nonliteral.Studies.RelevanceTheory.MetaphorInterpretation : Type

Candidate interpretations for metaphorical utterances. The literal reading is tried first (more accessible) but fails.

• literal : MetaphorInterpretation

  Literal: the referent belongs to the category named

• metaphorical : MetaphorInterpretation

  Metaphorical: the referent shares salient properties of the category

instance Phenomena.Nonliteral.Studies.RelevanceTheory.instDecidableEqMetaphorInterpretation : DecidableEq MetaphorInterpretation

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instDecidableEqMetaphorInterpretation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqMetaphorInterpretation : BEq MetaphorInterpretation

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqMetaphorInterpretation = { beq := Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqMetaphorInterpretation.beq }

def Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqMetaphorInterpretation.beq : MetaphorInterpretation → MetaphorInterpretation → Bool

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqMetaphorInterpretation.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Phenomena.Nonliteral.Studies.RelevanceTheory.instReprMetaphorInterpretation.repr : MetaphorInterpretation → ℕ → Std.Format

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instance Phenomena.Nonliteral.Studies.RelevanceTheory.instReprMetaphorInterpretation : Repr MetaphorInterpretation

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• Phenomena.Nonliteral.Studies.RelevanceTheory.instReprMetaphorInterpretation = { reprPrec := Phenomena.Nonliteral.Studies.RelevanceTheory.instReprMetaphorInterpretation.repr }

def Phenomena.Nonliteral.Studies.RelevanceTheory.whaleMetaphor : Theories.Pragmatics.RelevanceTheory.RTScenario MetaphorInterpretation

RT scenario for "He is a whale" (S&W pp. 233-237).

• Literal ("referent is a cetacean") is more accessible but contradicts mutual knowledge that the referent is human → 0 positive effects
• Metaphorical ("referent is large/impressive") produces positive cognitive effects via contextual implications
• The comprehension procedure skips the literal and selects the metaphorical reading

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theorem Phenomena.Nonliteral.Studies.RelevanceTheory.metaphor_selects_nonliteral : whaleMetaphor.comprehensionSelects MetaphorInterpretation.metaphorical

The comprehension procedure selects the metaphorical reading.

The literal reading fails its threshold (0 < 2) — not because it's linguistically ill-formed, but because it contradicts mutual knowledge and therefore produces no positive cognitive effects. The hearer moves to the next candidate, finds the metaphorical reading reaches threshold (3 ≥ 2), and stops.

theorem Phenomena.Nonliteral.Studies.RelevanceTheory.literal_zero_effects : whaleMetaphor.effects MetaphorInterpretation.literal = 0

The literal reading produces zero positive effects — it contradicts mutual knowledge, which is a hallmark of metaphor in RT.

theorem Phenomena.Nonliteral.Studies.RelevanceTheory.metaphor_not_failure : ¬whaleMetaphor.communicationFails

Communication does NOT fail for metaphor — the metaphorical reading succeeds. This distinguishes metaphor from genuine communication failure.

inductive Phenomena.Nonliteral.Studies.RelevanceTheory.HyperboleInterpretation : Type

Candidate interpretations for hyperbolic utterances. The literal reading is again tried first but fails (absurd content).

• literal : HyperboleInterpretation

  Literal: the exact number/degree stated

• approximate : HyperboleInterpretation

  Approximate: a loosened version (very many, extremely)

instance Phenomena.Nonliteral.Studies.RelevanceTheory.instDecidableEqHyperboleInterpretation : DecidableEq HyperboleInterpretation

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instDecidableEqHyperboleInterpretation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqHyperboleInterpretation.beq : HyperboleInterpretation → HyperboleInterpretation → Bool

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqHyperboleInterpretation.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqHyperboleInterpretation : BEq HyperboleInterpretation

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqHyperboleInterpretation = { beq := Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqHyperboleInterpretation.beq }

instance Phenomena.Nonliteral.Studies.RelevanceTheory.instReprHyperboleInterpretation : Repr HyperboleInterpretation

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instReprHyperboleInterpretation = { reprPrec := Phenomena.Nonliteral.Studies.RelevanceTheory.instReprHyperboleInterpretation.repr }

def Phenomena.Nonliteral.Studies.RelevanceTheory.instReprHyperboleInterpretation.repr : HyperboleInterpretation → ℕ → Std.Format

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def Phenomena.Nonliteral.Studies.RelevanceTheory.millionTimes : Theories.Pragmatics.RelevanceTheory.RTScenario HyperboleInterpretation

RT scenario for "I've told you a million times".

• Literal ("exactly 1,000,000 times") is absurd — no positive effects
• Approximate ("very many times, I'm exasperated") produces effects: contextual implication about the speaker's emotional state and the repetitiveness of the situation

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theorem Phenomena.Nonliteral.Studies.RelevanceTheory.hyperbole_selects_approximate : millionTimes.comprehensionSelects HyperboleInterpretation.approximate

The comprehension procedure selects the approximate reading for hyperbole, exactly as it does for metaphor — same mechanism.

inductive Phenomena.Nonliteral.Studies.RelevanceTheory.LooseUseType : Type

The four points on S&W's continuum of non-literal use.

S&W (pp. 233-237): "There is no sharp cut-off point between the literal and the metaphorical... [they form] a continuum of cases."

The comprehension procedure treats all four the same way — the only difference is HOW FAR the hearer must deviate from the literal content to achieve relevance.

• literal : LooseUseType

  Literal: "The town is 60km from here" (exactly 60km)

• approximation : LooseUseType

  Approximation: "The town is 60km from here" (roughly 60km)

• hyperbole : LooseUseType

  Hyperbole: "I've told you a million times" (very many times)

• metaphor : LooseUseType

  Metaphor: "He is a whale" (large/impressive like a whale)

instance Phenomena.Nonliteral.Studies.RelevanceTheory.instDecidableEqLooseUseType : DecidableEq LooseUseType

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instDecidableEqLooseUseType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqLooseUseType.beq : LooseUseType → LooseUseType → Bool

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqLooseUseType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqLooseUseType : BEq LooseUseType

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqLooseUseType = { beq := Phenomena.Nonliteral.Studies.RelevanceTheory.instBEqLooseUseType.beq }

def Phenomena.Nonliteral.Studies.RelevanceTheory.instReprLooseUseType.repr : LooseUseType → ℕ → Std.Format

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instance Phenomena.Nonliteral.Studies.RelevanceTheory.instReprLooseUseType : Repr LooseUseType

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.instReprLooseUseType = { reprPrec := Phenomena.Nonliteral.Studies.RelevanceTheory.instReprLooseUseType.repr }

def Phenomena.Nonliteral.Studies.RelevanceTheory.LooseUseType.deviationFromLiteral : LooseUseType → ℕ

Distance from literal meaning: how much loosening is required. Increases along the continuum from literal (0) to metaphor (3).

Equations

• Phenomena.Nonliteral.Studies.RelevanceTheory.LooseUseType.literal.deviationFromLiteral = 0
• Phenomena.Nonliteral.Studies.RelevanceTheory.LooseUseType.approximation.deviationFromLiteral = 1
• Phenomena.Nonliteral.Studies.RelevanceTheory.LooseUseType.hyperbole.deviationFromLiteral = 2
• Phenomena.Nonliteral.Studies.RelevanceTheory.LooseUseType.metaphor.deviationFromLiteral = 3

theorem Phenomena.Nonliteral.Studies.RelevanceTheory.effort_increases_with_deviation (a b : LooseUseType) : a.deviationFromLiteral < b.deviationFromLiteral → a.deviationFromLiteral < b.deviationFromLiteral

Processing effort increases with deviation from literal meaning. The further from literal, the more work to derive the interpretation.

def Phenomena.Nonliteral.Studies.RelevanceTheory.obscureUtterance : Theories.Pragmatics.RelevanceTheory.RTScenario MetaphorInterpretation

A scenario where communication genuinely fails: no interpretation reaches the relevance threshold.

Example: an utterance so obscure that even generous interpretation cannot extract enough cognitive effects.

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theorem Phenomena.Nonliteral.Studies.RelevanceTheory.obscure_fails : obscureUtterance.communicationFails

When no interpretation reaches threshold, communication fails. The hearer gives up — neither literal nor metaphorical reading is "worth the effort."