In typical cases, past tense morphology simply marks that the eventuality described by the predicate is located prior to the time of utterance, cf. (1).
(1) John had a car (last year / *next year).
But, this is not always the case. For example, in Sequence of Tense cases, as in (2), the contribution of past tense appears to be vacuous.
(2) John dreamed he had a car.
In counterfactual conditionals like (3), the past tense in the antecedent conveys that she does not own a car right now.
(3) If she had a car now, she could drive to school.
Sometimes, past tense is even compatible with reference to times in the future, cf. (4).
(4) We were meeting tomorrow, right?
In some languages, past tense morphology may be used in imperatives, even though imperatives, being performative generally require a present or future interpretation, cf. (5).
(5) Hat dat gedaan. (Dutch)
And finally, past tense morphology can sometimes convey particular speech acts, cf. (6).
(6) We had three beers, please. (Said to a waiter)
The apparently divergent semantic contribution of past tense morphology has received a large amount of study with respect to counterfactual conditionals and SoT. In contrast, the other three phenomena have not been investigated into much detail. What is even more remarkable is that these phenomena have almost always been analyzed independently from each other, not as a uniform property of past tense morphology.
This project aims at contributing an overarching perspective on past tense morphology that covers all usages, including those that seem to deviate from past tense reference, taking into account the cross-linguistic variation with respect to the meaning of past tense. Establishing the range of cross-linguistic variation is a necessary ingredient for any theory of form-meaning (mis)matches, since it forms strong diagnostics in determining what constraints this variation is subject to and why this should be so. By doing so, we will be able to determine whether the phenomena outlined above are cross-linguistically independent or are correlated. If they are typologically related, this would call for a more integrated theory of past tense morphology. Hence, typological research can be used as an empirical testing ground to evaluate different theories of the semantics of past morphology.