In some contexts, well-formed natural language cannot be expected as input to information or communication systems. In these contexts, the use of grammar-independent input (sequences of uninflected semantic units like e.g. language-independent icons) can be an answer to the users' needs. A semantic analysis can be performed, based on lexical semantic knowledge: it is equivalent to a dependency analysis with no syntactic or morphological clues. However, this requires that an intelligent system should be able to interpret this input with reasonable accuracy and in reasonable time. Here we propose a method allowing a purely semantic-based analysis of sequences of semantic units. It uses an algorithm inspired by the idea of ``chart parsing'' known in Natural Language Processing, which stores intermediate parsing results in order to bring the calculation time down. In comparison with using declarative logic programming - where the calculation time, left to a prolog engine, is hyperexponential -, this method brings the calculation time down to a polynomial time, where the order depends on the valency of the predicates.