Scalar Implicature

Origin. Grice (1975), Horn, Levinson. Quantity maxim. Scalar alternatives. Exhaustification. Foundation of neo-Gricean pragmatics.

Models. Saying weaker implicates not-stronger. Scales of alternatives. Exhaustive interpretation. Grammaticalized or pragmatic. Reasoning about alternatives.

Formalism.

Gricean reasoning: Maxim of Quantity: be as informative as required. Speaker said "some." If "all" were true, would have said it. So: not all.

Scalar alternatives: ⟨some, most, all⟩. ⟨or, and⟩. ⟨possible, necessary⟩. ⟨warm, hot⟩. Ordered by strength.

Basic implicature: "Some students passed" +> not all passed. "John or Mary came" +> not both. Weaker asserted → stronger denied.

Exhaustification operator: EXH(S) = S ∧ ∧{¬S' : S' ∈ Alt(S), S' stronger}. Assert S, deny all stronger alternatives. Grammatical approach. Fox, Chierchia.

Embedded implicatures: "Every student read some book." Embedded: each read not all books? Debate: local vs global. Grammatical vs pragmatic.

Obligatory vs optional: Some implicatures obligatory (seem lexicalized). Others cancellable. "Some, in fact all, passed." Scalar variability.

Innocent exclusion: Don't exclude alternatives that entail asserting others. "John or Mary or both" — don't exclude "both." Formal constraint. Fox's approach.

Symbols.

Symbol	Unicode	Meaning
+>	—	implicates
Alt(S)	—	alternatives to S
EXH	—	exhaustification
⟨...⟩	—	Horn scale

Metatheory. Quantity reasoning. Alternatives. Exhaustification. Scales.

Applies to. Pragmatics. Scalar terms. Disjunction. Modals.

Limitations. Scale construction. Embedded cases. Global vs local. Free choice.