We have proposed a framework based upon the λ -calculus with higher-order intuitionistic types for the symbolic computation of the semantic analysis, integrating lexical data. This proposal is sufficient for many phenomena and accurately incorporates lexical semantics by the means of type theory, but some issues linger in the linguistic data. In the present paper, we revisit this proposal with a version of the λ -calculus based upon higher-order linear types, that aims to resolve those issues and present an integrated framework for meaning assembly.