Conversational implicatures arise from Grice's maxim violations and depend on logical form. 'Some students passed' conversationally implicates 'not all passed' (scalar implicature). Formal semantics distinguishes logical form (semantic content, where 'some' is existentially quantified) from pragmatic enrichment (why a speaker chose 'some' over 'all'). This distinction unifies semantic and pragmatic phenomena under a rigorous framework.
You've already studied Grice's cooperative principle and the four conversational maxims (quantity, quality, relation, manner) that generate implicatures from apparent maxim violations. And you've worked with formal pragmatics — the project of modeling context, information state, and common ground in formal terms. This topic asks how those two frameworks interact: what is the relationship between the logical form of an utterance (what it strictly and literally means, in a truth-conditional sense) and the pragmatic inferences it generates?
The logical form of a sentence is its semantic content — the proposition it expresses, evaluable for truth or falsity against a model. "Some students passed" has the logical form ∃x[student(x) ∧ passed(x)]: there exists at least one thing that is a student and passed. Notice that this is consistent with *all* students passing — the existential quantifier sets a floor, not a ceiling. Yet when you hear "Some students passed," you typically infer that not all students passed. This is a scalar implicature, arising from the maxim of quantity: the speaker said "some" when she could have said "all"; since she knows which, and didn't say "all," she must not believe "all" is true.
The key theoretical point is that the scalar implicature is pragmatic enrichment, not part of the logical form. The truth-conditional content of "some" is just "at least one." The "not all" inference is generated by reasoning about why a cooperative speaker chose this expression from a Horn scale — an ordered set of alternatives ⟨some, most, all⟩ where stronger forms asymmetrically entail weaker ones. Using a weaker form implicates that stronger forms do not apply. This analysis extends beyond quantifiers: "or" implicates "not both" (from ⟨or, and⟩), "possible" implicates "not certain" (from ⟨possible, probable, certain⟩), "warm" implicates "not hot." Each case follows the same pattern: the speaker chose a weaker term when a stronger one was available, implicating that the stronger term does not hold.
The formal-pragmatic perspective makes clear why distinguishing logical form from pragmatic enrichment matters. Scalar implicatures are cancellable without contradiction: "Some students passed — in fact, all of them did" is perfectly coherent. Semantic entailments are not cancellable: "All students passed — in fact, some didn't" is a logical contradiction. This cancellability test is the diagnostic: if you can felicitously add "in fact, more strongly..." without contradiction, the inference is pragmatic, not semantic. Game-theoretic and Optimality-Theoretic approaches to pragmatics now formalize this reasoning as rational inference about speaker choices, giving Grice's informal maxims a precise computational interpretation and connecting implicature theory rigorously to the truth-conditional logical form tradition.