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Axiology (from Greek ἀξία, axia: "value, worth"; and -λογία, -logia: "study of") is the philosophical study of value.
It is a branch of philosophy that includes politics (Scientia civilis), ethics (Scientia moralis), aesthetics, etc.
What would be a good Latin translation of it? Preferably of the form Scientia + -lis. I know that I could latinize axiology to axiologia but I would rater not use a loan word.
I gather axiology is about the things people value rather than value in the economic sense, so pretium is inappropriate, and while valor is presumably nearer the mark, it is not attested Classically—though neither are the terms scientia civilis and scientia moralis, of course.
Still, I would go with a derivative of aestimo (whence also English esteem), which covers both monetary and other kinds of value. The obvious noun aestimatio is also usually concerned with monetary value in the corpus because it became a term of art in Roman law, but I feel it's still usable and intuitively understandable in that a branch of philosophy that is concerned with monetary value would itself much more likely go with pretium instead. There is no corresponding adjective in -alis the way there is for civis/civilis and mos/moralis; if there were, it would be *aestimationalis, which is transparent but not attested.
Scientia is demonstrably fine, so no reason to change that.
So, my suggestion: scientia aestimātiōnum, the science of valuations. Or, if you don't mind neologisms: scientia aestimātiōnālis.
I can't think of any exact match for English's -ology suffix, but, taking a hint from Joonas's studium sapientiae for philosophia (from this link) I'd guess studium valorum or studium pretiorum would work.
Studium, according to my dictionary (Traupman), means eagerness, enthusiasm, keenness, or study. It's not an exact match for -ology, but there is considerable overlap. In my experience, -ologists usually are quite keen on their field.
There are other options for studium, of course. There is disciplina, which perhaps better captures the organized methodology or study of a field. You mentioned scientia, which could also work, especially if by "science" you mean mainly a body of knowlege. If you mean the craft or skill of the field, you could go with calliditas pretiorum. If you are talking about the profession, you could use artificium pretiorum, the "craftmanship of values".
Like with studium none of these is an exact match for axiologia, but if you want to avoid Greek roots you'll have to compromise, or resort to circumlocutions.
If by values you are talking about morals and not economics, then you will probably want to replace pretiorum with morum, finium or valorum in the examples above. Both mores and finis have specialized meaning in philosophical Latin, and valor may as well.
