This paper proposes a fresh formulation of conceptually grounded meaning relations by way of construction of certain well-defined relations over the lexicon of a natural language. These relations are constrained by the logical structures of linguistic meanings across sentence and discourse contexts. One of the biggest advantages of such meaning relations is that they are not defined over, or do not ride on, the syntactic structure of a given language. Nor do they turn on compositional relations for the computation of meaning values. This helps in the formulation of meaning relations to be defined on the symbolic elements of a lexicon on the one hand, and to be extracted from the surface structure of linguistic constructions on the other. This has consequences not merely for the nature of lexical meaning but also for the construction of a kind of (shallow) semantic networks that can be used for semantic processing in natural language understanding or machine translation systems that are driven by a kind of shallow processing of linguistic meanings. Thus, this paper aims to show the usefulness of a kind of conceptually based characterization of linguistic meaning for its relevance to computational language processing. © 2018 CEUR-WS. All rights reserved.