In spite of the fact that Arabic offers a well-studied theoretical and historical linguistic knowledge, unfortunately, it has so far received very little computational research and in particular on the level of semantic analysis. The most computational research efforts have been focused on morphological and syntax analysis, whereas research on Arabic computational semantics has been neglected. The main goal of this paper is to characterize the fundamental issues involved in deep logic-based semantic representation of Arabic sentences. The focus of attention of this work is relying on the principle of compositionality for Arabic semantic analysis, utilizing λ-calculus and type theory analysis of some Arabic syntactical constituents for achieving a semantic construction model for a fragment of ARABIC. Since semantic representation has to be compositional in Natural Language Understanding Systems, this approach offers a central concept for developing more intelligent and robust Arabic NLP systems.