In order to modelize the reasoning of intelligent agents represented by a poset T, H. Rasiowa introduced logic systems called “Approximation Logics”. In these systems a set of constants constitutes a fundamental tool. In this paper, we consider logic systems called L'T without this kind of constants but limited to the case where T is a finite poset. We study the tableau method for this system and we prove its completeness for a class of formulas with respect to an algebraic (...) semantics. (shrink)