Prepositions represent a grammatical category of frequent use in many European languages. The combination of their semantics with other lexical categories usually makes them difficult to be computationally tractable. As far as natural language processing is concerned, some studies have contributed to make progress on the usage of prepositions. However, there still exists a need to develop a model that allows tackling the problems which result from the disambiguation of prepositional semantics. The goal of this paper is to describe a lexico-conceptual model which can store the knowledge required to disambiguate predicate prepositions, as well as how this model can be exploited by a parser to extract the semantic representation of a text. The theoretical foundation of this approach, which is grounded on the premises of Role and Reference Grammar and FunGramKB, is illustrated with temporal adjuncts expressed by prepositional phrases in English.Prepositions represent a grammatical category of frequent use in many European languages. The combination of their semantics with other lexical categories usually makes them difficult to be computationally tractable. As far as natural language processing is concerned, some studies have contributed to make progress on the usage of prepositions. However, there still exists a need to develop a model that allows tackling the problems which result from the disambiguation of prepositional semantics. The goal of this paper is to describe a lexico-conceptual model which can store the knowledge required to disambiguate predicate prepositions, as well as how this model can be exploited by a parser to extract the semantic representation of a text. The theoretical foundation of this approach, which is grounded on the premises of Role and Reference Grammar and FunGramKB, is illustrated with temporal adjuncts expressed by prepositional phrases in English.