For this exercise you can work with grammar4.lfg, which has integrated two OT-Marks to constrain PP-ambiguity. Alternatively, you can look at what has been added in grammar4.lfg and use it as a model while continuing work on your own grammar version.
Make sure the following sentences are rejected as ungrammatical (for the right reasons):
For possessive pronouns you can use the following f-structure (here the example is for my):
SPEC [POSS [PRED 'I', NUM sg, PERS 1, PRON-TYPE poss]]
NB: Whenever you have to build a new phenomenon into your grammar and you are not sure how to analyze it, a good strategy is to look at the big ParGram grammars available via the INESS XLE Webinterface for guidance.
The new grammar grammar4.lfg already contains two OT-Marks. They prefer local PP-attachment and choose an OBL analysis over an ADJUNCT analysis where there is a choice. This is fine for the most part, but causes problems elsewhere.
Go through your testsuite and try to regenerate each sentence. Note down what your results are. When there should be only one possibility but there are more, think about whether and how you can fix it. If you can fix it (easily), then do so.
One possibility is to constrain some of the possibilities by using OT-Marks. If want to do this, then you can make up relevant OT-Marks and rank them on the hierarchy called GENOPTIMALITYORDER (already included in grammar4.lfg).
XLE Documentation on Support for Optimality Theory for information on how to use OT-Marks.
XLE Documentation on the generator.
XLE Documentation on the FS-Chart Window and packed representations.
Frank, Anette, Tracy Holloway King, Jonas Kuhn, und John T. Maxwell III. 1998. Optimality Theory Style Constraint Ranking in Large-scale LFG Grammars. Proceedings of the LFG 98 Conference. CSLI Online Publications.