The Acquisition of Linguistic Competence for Communicating Propositional Logic Sentences

We describe some experiments which show how a language expressive enough to allow the communication of meanings of the same complexity as propositional logic formulas can emerge in a population of autonomous agents which have no prior linguistic knowledge. We take an approach based on general purpose cognitive capacities, such as invention, adoption and induction, and on self-organisation principles applied to a particular type of linguistic interaction known as a language game. 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 in the sentence. Previous work assumed that the expressions associated with the connectives should be always placed in the first position of the sentence. Another difference is that communication is considered successful in a language game if the meaning interpreted by the hearer is logically equivalent to the meaning the speaker had in mind. In previous experiments the meanings of speaker and hearer were required to be syntactically equal. This allows us to observe how a less strict grammar in terms of word order emerges through the self-organisation process, which minimizes the learning effort of the agents by imposing only those order relations among the components of a sentence that are necessary for language understanding.