I'm not sure I quite understand the motivation of the question, but here's some thoughts that maybe will bring a little clarity.
Start from a grammatical observation: in English there are basically three kinds of sentences:
- Assertions. "The cat is on the mat."
- Questions. "Is the cat on the mat."
- Commands. "Put the cat on the mat."
Now, logic (at the intro level) is concerned with assertions. The tools of logic can tell you, for any given set of assertions, whether they could all be true at the same time, or whether some subset of the assumptions provides a proof for other assertions, etc.
Epistemology is concerned with claims about knowledge, and knowledge involves at least the following two things: belief and truth. Whether a person believes something or not is a psychological matter. Let's say that somebody, S, believes some sentence p just in case, if you were to ask S "Is p true?" she would say Yes.
Now, as I've defined it here, belief is clearly connected to assertion in some way. Something you believe is something you would sincerely assert if provided the appropriate occasion to do so. (You probably have lots of beliefs that you never actually assert, e.g. that Nice is a city in France.) On this construal, "opining that p," "being confident that p," "fearing, in your heart of hearts, that p" and so on will all be just particular ways of believing p. The difference between these different expressions is just the difference in the way that the believer feels emotionally about p, or how strong the person thinks her evidence for p is or something like that.
Of course it is possible for people to believe false things. So belief and truth come apart. It is also possible to believe something, that actually happens to turn out to be true, but your belief just happens to be correct by accident. Having knowledge is something stronger again than merely having a belief. Let's say that S knows that p just in case: (i) S believes that p, (ii) p is actually true, and (iii) there is some justification for S's believing p that shows it isn't just an accident that S believes that p.
It sounds like the author of your teaching company lecture is thinking something like this:
- ``facts'' are significant statements about the world that have to be established scientifically "There is lithium on mars"
- "definitions" are trivial truths that are knowable a priori. "Bachelors are unmarried men"
- "values" are subjective expressions of personal preferences. "Orange sorbet is the better than strawberry."
- "policies" are recommendations for how to act so as to get what one is aiming at. "If you want to see a good movie, read Roger Ebert's reviews first; he's never steered me wrong."
All of these sentences are assertions, grammatically speaking. But it sounds like the point of making such a classification is to say that only the first two kinds of assertions could ever be things that somebody knows to be true, because only the first two are objective, whereas the second two are subjective. This is the so-called "Fact/Value Dichotomy".
If you want to see a first rate philosopher talking about this dichotomy and why it is false, see Hilary Putnam's remarks here: http://www.youtube.com/watch?v=oLJfEVu3kbY