A Unified Framework for Natural Language Semantics and Pragmatics by Meta-Lambda Calculus and Linguistic Monads

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The aim of this project is to provide a uniform framework for the representations of natural language semantics and pragmatics, by means of Meta-Lambda Calculus (MLC) and (linguistic) monads. We have established a formal foundation of MLC and the notion of linguistic monads, especially its categorical semantics, the soundness theorems in the base- and the meta-level substitutions, and the soundness theorems for alpha/beta/eta-conversions in both the base- and the meta-levels.We have also provided some linguistic applications of MLC and their empirical evaluation. We proposed a unified system for describing phenomena that lie in the interface of semantic and pragmatic by means of linguistic monads such as "non-deterministic monad", "global variable monad (=state monad)", "continuation monad", and "conventional implicature monad".