In order to properly interpret and process or operators in deductive databases including indefinite clauses, we propose to use Lasez′s Strong Model Semantics(LSMS) which is reasonably simple yet powerful enough to support both exclusive and inclusive interpretations. Conventional semantics either fail to support both interpretations or simply too complex. Therefore, in this paper we study advantages and difficulties of representing indefinite information, and as for the solution to difficulties, we show how LSMS can be used to support both inclusive or and exclusive or interpretations. We also investigate and analyze it′s properties and show how it semantically differs from others. We believe that LSMS is the only "reasonably simple" semantics that supports both inclusive and exclusive interpretations.