@cite{kao-levy-goodman-2016} — A Computational Model of Linguistic Humor in Puns

@cite{kao-levy-goodman-2016}

Kao, J.T., Levy, R., & Goodman, N.D. (2016). A Computational Model of Linguistic Humor in Puns. Cognitive Science, 40, 1270–1285.

Findings

1. Ambiguity (entropy of meaning distribution) distinguishes puns from non-puns
2. Distinctiveness (KL divergence of supporting words) predicts funniness within puns
3. Both meanings must be plausible AND supported by different parts of the sentence

Data

The study used 435 sentences:

• 65 identical-homophone puns (e.g., hare/hair)
• 80 near-homophone puns (e.g., tooth/truth)
• 290 non-pun control sentences

Funniness rated on 1–7 scale, z-scored across participants.

See Phenomena.Polysemy.Studies.ErkHerbelot2024 for the SDS↔Kao bridge.

structure Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.PhoneticPun : Type

A phonetic pun with two meanings

• sentence : String

  The pun sentence

• ambiguousWord : String

  The ambiguous word (as written)

• homophone : String

  The homophone/near-homophone

• isIdentical : Bool

  Whether it's an identical or near homophone

• funniness : ℚ

  Mean funniness rating (z-scored)

• ambiguity : ℚ

  Ambiguity score (entropy of P(m|w))

• distinctiveness : ℚ

  Distinctiveness score (symmetrized KL divergence)

instance Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.instReprPhoneticPun : Repr PhoneticPun

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.instReprPhoneticPun = { reprPrec := Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.instReprPhoneticPun.repr }

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.instReprPhoneticPun.repr : PhoneticPun → ℕ → Std.Format

Equations

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

structure Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.NonPunSentence : Type

A non-pun control sentence

• sentence : String

  The sentence

• ambiguousWord : String

  The phonetically ambiguous word

• homophone : String

  The homophone

• funniness : ℚ

  Mean funniness rating (z-scored)

• ambiguity : ℚ

  Ambiguity score

• distinctiveness : ℚ

  Distinctiveness score

instance Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.instReprNonPunSentence : Repr NonPunSentence

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.instReprNonPunSentence = { reprPrec := Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.instReprNonPunSentence.repr }

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.instReprNonPunSentence.repr : NonPunSentence → ℕ → Std.Format

Equations

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

Key Examples

These examples from the paper illustrate the ambiguity/distinctiveness measures.

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.magicianHare : PhoneticPun

"The magician got so mad he pulled his hare out"

• hare supported by: magician
• hair supported by: mad, pulled High ambiguity (both meanings plausible) + High distinctiveness (different support)

Equations

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

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.hareField : NonPunSentence

Control: "The hare ran rapidly across the field" Only hare meaning is supported; hair is implausible. Low ambiguity, moderate distinctiveness.

Equations

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

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.dentistTooth : PhoneticPun

"A dentist has to tell a patient the whole tooth"

• tooth supported by: dentist, patient
• truth supported by: tell, whole High ambiguity + High distinctiveness

Equations

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

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.dentistExamines : NonPunSentence

Control: "A dentist examines one tooth at a time" Only tooth meaning plausible.

Equations

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

Key Statistical Results

From Table 2 and Results section:

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.punVsNonpun_ambiguity_tstat : ℚ

Puns have significantly higher ambiguity than non-puns (t = 7.89, p < .0001)

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.punVsNonpun_ambiguity_tstat = 789 / 100

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.punVsNonpun_distinctiveness_tstat : ℚ

Puns have significantly higher distinctiveness than non-puns (t = 6.11, p < .0001)

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.punVsNonpun_distinctiveness_tstat = 611 / 100

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.distinctiveness_funniness_correlation : ℚ

Within puns, distinctiveness correlates with funniness (r = .28, p < .001)

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.distinctiveness_funniness_correlation = 28 / 100

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.ambiguity_funniness_correlation : ℚ

Within puns, ambiguity does NOT correlate with funniness (r = .03, p = .697)

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.ambiguity_funniness_correlation = 3 / 100

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.model_r_squared : ℚ

Model R² for predicting funniness from ambiguity + distinctiveness

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.model_r_squared = 25 / 100

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.regression_intercept : ℚ

Regression intercept

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.regression_intercept = -2139 / 1000

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.regression_ambiguity_coef : ℚ

Ambiguity coefficient (significant predictor)

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.regression_ambiguity_coef = 1915 / 1000

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.regression_distinctiveness_coef : ℚ

Distinctiveness coefficient (significant predictor)

Equations

• Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.regression_distinctiveness_coef = 264 / 1000

Theoretical Framework

Ambiguity (Entropy)

Amb(M) = -Σ_k P(m_k|w) log P(m_k|w)

High ambiguity means both meanings are near-equally likely given the words. This is necessary but not sufficient for humor.

Distinctiveness (Symmetrized KL Divergence)

Dist(F_a, F_b) = D_KL(F_a||F_b) + D_KL(F_b||F_a)
              = Σ_i [ln(F_a(i)/F_b(i)) · F_a(i) + ln(F_b(i)/F_a(i)) · F_b(i)]

Where F_a = P(f|m_a, w) is the distribution over which words are semantically relevant given meaning m_a.

High distinctiveness means different words support different meanings. This predicts fine-grained funniness within puns.

Connection to Incongruity-Resolution Theory

The paper argues:

• Ambiguity ≈ presence of incongruous meanings (incongruity detection)
• Distinctiveness ≈ each meaning has coherent support (incongruity resolution)

Both are needed for humor: incongruity alone is puzzling, not funny.

More Examples from Supplementary Materials

The full dataset is available at: http://web.stanford.edu/~justinek/punpaper/results.html

def Phenomena.Nonliteral.Humor.Studies.KaoEtAl2016.examplePuns : List PhoneticPun

Example puns with their ratings (representative sample)

Equations

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

Summary: @cite{kao-levy-goodman-2016}

Main Contributions

1. First computational model predicting fine-grained funniness in puns
2. Formal measures (ambiguity, distinctiveness) derived from language processing model
3. Empirical validation with 435 sentences and human ratings

Insight

Puns are funny when:

1. Both meanings are plausible (high ambiguity)
2. Different words support different meanings (high distinctiveness)

Neither alone is sufficient:

• High ambiguity + low distinctiveness → confusing, not funny
• Low ambiguity + high distinctiveness → one meaning clearly wins, not funny

Relevance to SDS

The distinctiveness measure captures the same intuition as SDS conflict detection: different sources of evidence point to different interpretations.

In Kao's model: different words → different meanings In SDS: selectional vs scenario → different concepts