The problem of the order of the conjuncts in the coordinating conjunction ‘and’: A logical-syntactic solution

From the mental models theory, it has been claimed that the conjunction commutativity law, that is, the logical law providing that the order of the conjuncts joined by the coordinating conjunction ‘and’ can be changed without modifying the truth-value of the sentence, is not always valid in real conversations in natural language. For this reason, based on that very theory, it has been proposed that the true sense of a sentence of that kind can only be suitably captured by a semantic theory, such as the one of the mental models, which resorts to iconic possibilities describing reality. However, in this paper, it is argued that the formal and basically syntactic frameworks can also correctly stand for the actual meaning corresponding to propositions with a coordinating conjunction such as ‘and’ to which the conjunction commutativity law does not seem, in principle, to apply. To do that, they do not have to significantly move away from classical logic, but only to add to the connectives in this last logic a modal operator akin to ‘Next’ in temporal logic, and this without the need to assume many more temporal logical elements.