The Logic of Conventional Implicatures

Christopher Potts
Department of Linguistics, UC Santa Cruz


The history of conventional implicatures is rocky, their current status uncertain. I return to Grice's (1975) original definition with an eye open for novel support. I argue that, even without textbook examples such as therefore and but, conventional implicatures would still be widely attested in natural language. Grice's definition characterizes a class of speaker-oriented commitments that trace back to individual lexical items and invariably yield semantic multidimensionality. These properties unify the (syntactically diverse) factual domain, which divides fairly easily into two broad classes: (i) supplements, including appositive relatives, nominal appositives, (As)-parentheticals, speaker- and topic-oriented adverbs, and utterance modifiers (chapter 3); and (ii) expressives, including adjectives like damn, the descriptive content of epithets, some kinds of subjunctive voice, and honorification in Japanese (chapter 4). I define a higher-order lambda calculus that provides the tools we need for formalizing Grice's definition and in turn for modelling the meanings of the expressions in (i)-(ii). The logic, which extends and sharpens the insights of Karttunen and Peters 1979, imbues the label conventional implicature with theoretical content. Though considerable attention is paid to the model-theoretic aspects of the investigation, particularly as they relate to the formal modelling of discourses, much of the dissertation concerns the nature of natural language semantic composition, which we can study independently of a specific class of structures. In the setting of the logic I define, conventional-implicature content is often distinguished solely in the meaning language. Thus, the facts under discussion seem to provide reason to view a representational language for meanings as an essential part of semantic theory. I close by asking what happens when we make slight revisions to Grice's definition. Removing speaker-orientation results in another rich class of semantically multidimensional constructions, including many that were originally classified as conventional-implicature contributors. I show that the meaning language defined here yields a theory of them as well.