Between Logic and Common Sense: The Formal Semantics of Words

One of the most important properties of human languages is their ability to convey intricate meanings. The vastness and effectiveness of those meanings for everyday communication and reasoning transcends all known non-human languages, including other animal languages and artificial languages. For studying communication and reasoning in language, an indispensable empirical concept is entailment: the relation between premises and valid conclusions expressed as natural language sentences. Entailment relations may appear between sentences due to the presence of words and expressions like other, either...or, not or exactly five, whose meanings have been studied in logical frameworks since antiquity. However, entailments may also appear due to semantic properties of “non-logical” words like parrot, hug, far or knowledge. Such content words constitute the bulk of the lexicon in all natural languages. Without considering them, it is simply impossible to understand entailment phenomena and human reasoning in general. However, while content words have played an important role in cognitive psychology and artificial intelligence, their meanings have turned out to be richer and fuzzier than what current logical techniques in semantics can handle. As a result, the study of entailment has lagged behind important advances of other areas in the study of language. This program will develop a comprehensive model of entailment in language. A new framework of Content Sensitive Formal Semantics will treat the interactions between common sense meanings of content words (e.g. parrot) and logical operators in language (e.g. not). The resulting model of entailment is expected to constitute a breakthrough in our understanding of linguistic reasoning and its practical applications.