This paper addresses the problem of the acquisition of the syntax of propositional logic. An approach based on general purpose cognitive capacities such as invention, adoption, parsing, generation and induction is proposed. Self-organisation principles are used to show how a shared set of preferred lexical entries and grammatical constructions, i.e., a language, can emerge in a population of autonomous agents which do not have any initial linguistic knowledge. Experiments in which a population of autonomous agents constructs a grammar that allows communicating the formulas of a propositional logic language are presented. These experiments extend previous work by considering a larger population and a much larger search space of grammar rules. In particular the agents are allowed to order the expressions associated with the constituents of a logical formula in arbitrary order. Previous work assumed that the expressions associated with the connectives should be placed in the first position of the sentence.

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