Trivalent Logics and Natural Language Meaning – TriLogMean

A standard tenet of classical formal semantics, as originally developed by logicians, is that declarative sentences are always either true or false, i.e. have bivalent truth-conditions. When studying natural languages, however, there are good reasons to go beyond this bivalence assumption and to adopt the tools of so-called trivalent logics, in which a sentence can receive a non-standard truth-value (`neither true nor false’). For instance, sentences containing vague expressions (e.g. ‘Mary is tall’) can be thought of as being neither true nor false in so-called borderline cases (e.g., if Mary is slightly above the average size), in which case they are assigned the ‘undefined’ truth-value. And presuppositional sentences (e.g. ‘Peter stopped smoking’, which presupposes that Peter used to smoke) can be thought of as being neither true nor false in contexts where their presuppositions are not satisfied (presupposition failure). While trivalent systems have been applied to various linguistic phenomena (such as presuppositions, vagueness, conditional sentences, see the introduction by Cobreros, Egré, Ripley, van Rooij to the forthcoming special issue of the Journal of Non-Classical Applied Logics), a unified model that can deal simultaneously with these various phenomena is still missing. We aim to develop a theory based on a trivalent semantic system that will be able to model these various phenomena together, including in cases where they interact (e.g., sentences containing both presuppositional expressions and vague expressions). Furthermore, we will extend the use of trivalent logics to empirical domains where they have not been used extensively, such as the semantics of plural expressions and interrogative sentences.

Our goal is to construct such a model by systematically investigating various ways of applying trivalent systems to natural language meaning. This project thus has both a formal side, concerned with a detailed investigation of the predictions of various trivalent semantic systems, and an empirical side, centered on the empirical domains that can provide motivation for the use of trivalent semantics. This empirical side will be in part investigated by means of controlled experimental methods. This project will focus on the following empirical domains: the projection problem for vagueness and presuppositions, with a specific emphasis on the role of linear order and projection in quantified environments and the treatment of referential indeterminacy in the case of plural expressions, with extensions to the semantics of embedded interrogatives and conditionals.

If successful, this project will result in a unified framework which will provide a formally explicit and predictive theory of a broad range of linguistic phenomena, which reflect core components of the human language faculty. It will bring together at least three distinct research areas, namely philosophical logic, formal semantics, and pragmatics.