Reasoning in Natural Language in using Combinatory Logic and Topology An example with aspect and temporal relations

We are studying how Curry’s Combinatory Logic can be used for giving an adequate analysis of different gram matical problems such as diatheses, tenses and aspects, and lexical analyses by formal representations of meanings of verbal predicates and prepositions. The paper intends to show how Combinatory Logic can solve on the one hand, the formal representations of tenses and aspects in natural languages with the help of the topology of intervals and, on the other hand, the problem of the synthesis of a lexical predicate from a formal description of its meaning by means of a semantic cognitive scheme (SCS). We want to explain, in following an example, how can be explained the “natural” inference between two utterances like John took the Mary’s pen. > Now, John has got the pen.