Models of language meaning
Category theory is a branch of mathematics describing relationships among objects, and able to represent the subtle meanings in natural language. Such representation will be necessary if realistic speech interface with computers is ever to become possible. The EU-funded MEANCATS (Category theory for meaning assembly and the semantics-pragmatics interface) project mathematically modelled how languages convey complex meaning. The model was inspired by earlier work in the analysis of programming languages. MEANCATS research focused on three linguistic phenomena. The list included: "conventional implicatures", which introduce information in an indirect way; and linguistic expressions able to be interpreted from several points of view. The third topic was expressions of uncertainty in language. Researchers created a generalised mathematical model of complex language meanings, built upon category theory. The model provided a general way of constructing meanings. It also offered a logical calculus describing how meanings emerge from isolated language units (words) to more complex expressions (phrases and sentences). MEANCATS' rigorous formulation allowed researchers to state assumptions about how particular types of meanings are used. The model revealed meanings that would have remained hidden in conventional ad hoc approaches. The level of analysis could be calibrated depending on need, or by adding or removing semantic representations. Researchers implemented the model and calculus as an automated theorem prover. Starting from a set of linguistic resources, the prover automatically generated the meaning representations of interest to the researchers. The prover also was far faster and less error-prone compared to manual methods of semantic analysis. The group also incorporated the model into grammatical frameworks including Lexical Functional Grammar and Categorical Grammar. Such frameworks provided the toolchain which enables progression from raw linguistic expression to representation of meaning. The MEANCATS project's model demonstrated practical application of category theory. The work is a step towards naturalistic human-computer communication.
Keywords
Category theory, MEANCATS, meaning, language, model, logical calculus
