theologise vs excogitate

theologise and excogitate both are verbs.

Word	Noun	Adjective	Verb	Adverb
theologise	No	No	Yes	No
excogitate	No	No	Yes	No

As verbs, excogitate is a hypernym of theologise; that is, excogitate is a word with a broader meaning than theologise:

theologise: make theoretical speculations about theology or discuss theological subjects
excogitate: reflect deeply on a subject

Other hypernyms of theologise include chew over, contemplate, meditate, mull, mull over, muse, ponder, reflect, ruminate, speculate, think over.

theologise (verb)	excogitate (verb)
make theoretical speculations about theology or discuss theological subjects	reflect deeply on a subject
treat from a theological viewpoint or render theological in character	come up with (an idea, plan, explanation, theory, or principle) after a mental effort