A non-monotonic logic is a logic whose consequence relation is not monotonic. A logical inference is monotonic whenever a formula α is a consequence of a set of formulas ∑ , then α is also a consequence of any set of formulas ∑� containing ∑. On the other hand there are reasoning systems which are non-monotonic in the sense that we often derive conclusions on the basis of incomplete information that we may retract when we are given more complete information. The most familiar non-monotonic formalisms are default logic, autoepistemic logic and preference logics. We briefly discuss them, investigate their relations and then provide some algebraic notions and principles behind these logics.