Halliday & Matthiessen (1999: 422-3):
It would seem that formal semantics is quite far from the concerns of cognitive science; but formal semantics is often carried out within the broad program that cognitive scientists adopt. Writing from a cognitive standpoint, Johnson-Laird (1983) assesses model-theoretic semantics as follows:The power of model-theoretic semantics resides in its explicit and rigorous approach to the composition of meanings. ... Some idealisations definitely complicate the 'ecumenical' use of model-theoretic semantics as a guide to psychological semantics. One such idealisation is the mapping of language to model without any reference to the human mind, and this omission gives rise to certain intractable difficulties with the semantics of sentences about beliefs and other such prepositional attitudes. These difficulties are readily resolved within the framework of mental models, (p. 180)... model-theoretic semantics should specify what is computed in understanding a sentence, and psychological semantics should specify how it is computed, (p. 167)Johnson-Laird's own psychological approach is one based on mental models.