Implicatures in Continuation-Based Dynamic Semantics by Reasoning in the Context

Abstract

The translation of natural language expressions into logical representations provides a formal semantics for linguistic study and contributes to natural language processing applications. Amongst current formalisms for this task, de Groote [2006]'s continuation-based dynamic semantics - as systematized and extended by Lebedeva [2012] - distinguishes itself by returning to the principles of the first extensive formal semantics for natural language (Montague [1970a,b, 1973]): using only standard tools from mathematical logic in a fully compositional way, it captures phenomena such as cross-sentential pronominal anaphora, quantifier scope and presupposition projection. Discourse context is incorporated as a parameter, meaning its structure may be changed while preserving much of the operation of the framework. Exploiting this feature, I define a more elaborate context structure to allow for basic commonsense reasoning, and show how this can be used to capture implicature-related content with typical instances from three classes of meaning: Grice [1975]'s conversational implicatures; Grice [1975]'s conventional implicatures, with a focus on but; and the 'CI' of Potts [2005b], specifically supplementary content. I do this in the spirit of using only common tools from mathematical logic by adapting Poole's framework for default and abductive reasoning (Poole [1988, 1989, 1990]), a way of using classical logic for commonsense reasoning by viewing reasoning as theory formation. I situate this work within Potts [2015] call for shifting focus from "splitting and lumping" into meaning classes to "rich theories of properties" by suggesting formal definitions of properties of these meaning classes, in a formalism that is now capable of a range of presuppositions, conversational implicatures, conventional im- plicatures, and CIs.