Halevi is an interesting character, both a poet and a philosopher; he's most famous for his poetry, but he is also known for his philosophical work, Kitab al-Khazari. You can get a sense of Halevi's approach from the Jewish Encyclopedia's summary:
The work is divided into five essays ("ma'amarim"), and takes the form of a dialogue between the pagan king of the Chazars and a Jew who had been invited to instruct him in the tenets of the Jewish religion. After a short account of the incidents preceding the conversion of the king, and of the conversations of the latter with a philosopher, a Christian, and a Moslem concerning their respective beliefs, the Jew appears on the stage, and by his first statement startles the king; for, instead of giving him proofs of the existence of God, he asserts and explains the miracles performed by Him in favor of the Israelites. The king expresses his astonishment at this exordium, which seems to him incoherent; but the Jew replies that the existence of God, the creation of the world, etc., being taught by religion, do not need any speculative demonstrations. Further, he propounds the principle upon which his religious system is founded; namely, that revealed religion is far superior to natural religion. For the aim of ethical training, which is the object of religion, is not to create in man good intentions, but to cause him to perform good deeds. This aim can not be attained by philosophy, which is undecided as to the nature of good, but can be secured by religious training, which teaches what is good. As science is the sum of all the particles of truth found by successive generations, so religious training is based upon a set of traditions; in other words, history is an important factor in the development of human culture and science.
Halevi is in many ways the al-Ghazali of Judaism; in other words, he gives a philosophical critique of what he sees as excessive pretensions among the philosophers. And, like al-Ghazali, he raises some interesting issues with arguments worth taking seriously.