The next 10 years (actually, this is more than 10 years...)

The purpose of grammar is, more or less, to enable us to convey to our hearers the 'who-did-what-to-whom' of an event that we was them to know about.  It's this knowledge which enables us to figure out, in English at least, that the mouse is doing something slightly unusual in 'the mouse is chasing the cat out of the house'.

My earlier research focused on ambiguity - which often (but not always) comes about when a point in the sentence is reached at which alternative assignments of the 'who', 'what' and 'whom' are possible. But one does not need to study ambiguity to find out how the human sentence processing mechanism goes about using grammatical knowledge to work out these assignments ('thematic role assignments').  In the mid 1990s I started to look at completely unambiguous sentences embedded in contexts.  In one series of experiments (Altmann, 1999), subjects read short stories such as 'A car veered out of control down a road.  In its path were some dustbins and some pigeons.  It injured a tourist that stepped out from the kerb'.  People had no particular problem with that.  But now consider this version: 'A car veered out of control down a road.  In its path were some dustbins and some boxes. It injured a tourist that stepped out from the kerb'.  In this case, as people read the word 'injured', they thought that the sentence no longer made sense.  And if they thought it did make sense, they still took longer to read it than in the first version of the sentence.  The critical difference here is that the context in the 2nd doesn't provide anything that can be injured, whereas the 1st does (the pigeons).  So it looks as if people anticipate that whatever the verb will 'apply to' (i.e. its object) will be something previously mentioned in the context.

More recently, and together with Yuki Kamide, I've used a different paradigm to explore the timing with which the sentence processor assigns thematic roles.  Using a head-mounted eye-tracker, we can monitor people's eye movements around a visual scene as they listen to a description of that scene (or a description of something that may happen with the objects in that scene).  For example, the picture might show a boy, a toy car, a balloon, and a cake (you can view an example here).  People then either heard 'the boy will move the cake' (several things in the scene are moveable) or 'the boy will eat the cake' (only the cake is edible).  We found that, during the verb 'eat', people already shifted their eyes towards the cake (Altmann & Kamide, 1999).  More recently still, we found that if people heard 'the man will taste the beer' or 'the little girl will taste the sweets', people looked during the verb 'taste' at whatever object was most plausibly tasted by whoever was doing the tasting (the beer in the case of the man and the sweets in the case of the girl) - Kamide et al., 2003.

These findings (and others, including studies in Japanese where the verb comes at the end of the sentence), show that the human sentence processor very rapidly integrates grammatical knowledge and real world knowledge to anticipate what will be referred to next.  In this sense, an important element of sentence processing is predictive.

Even more recently, I and my colleagues have found out two more things about 'language-mediated eye movements'. First, the scene that the language refers to need not be concurrent with the unfolding language - if you take the scene away, leaving a blank screen, before the sentence starts, the eyes move to where the objects had been (Altmann, 2004). Second, if people hear a short story in which an object in the scene 'moves' to another part of the scene (in the story - the scene remains constant throughout), there is an increased tendency for their eyes tend to move, during subsequent mention of that object, to this new location even though the scene remains unchanged with the object at its original location. More recently, we repeated this last study, but took the scene away before playing people the recording of the story about the object moving from one part of the scene to another. The results were even more spectacular (but predictable: the eyes moved back to where the object would have been had it actually moved). This last work is described in Altmann & Kamide (2009).

You can read a more technical summary of this and other work (written for a grant proposal!) here. For a review of much of this work (but without the work described in the 2009 paper) you can read Altmann & Kamide (2007).

References

Altmann, G.T.M.   (1999). Thematic role assignment in context.   Journal of Memory and Language, 41, 124-145.
Altmann, G.T.M., and Kamide, Y .   (1999) Incremental interpretation at verbs: Restricting the domain of subsequent reference. Cognition , 73(3), 247-264.
Kamide, Y., Altmann, G.T.M., & Haywood, S. (2003). The time-course of prediction in incremental sentence processing: Evidence from anticipatory eye-movements. Journal of Memory and Language. 49, 133-159.