ABSTRACT. Propositional logic is the main ingredient used to build up SAT solvers which have gradually become powerful tools to solve a variety of important and complicated problems such as planning, scheduling, and verifications. However further uses of these solvers are subject to the resulting complexity of transforming counting constraints into conjunctive normal form (CNF). This transformation leads, generally, to a substantial increase in the number of variables and clauses, due to the limitation of the expressive power of propositional logic. To overcome this drawback, this work extends the alphabet of propositional logic by including the natural numbers as a means of counting and adjusts the underlying language accordingly. The resulting representational formalism, called pseudo-propositional logic, can be viewed as a generalization of propositional logic where counting constraints are naturally formulated, and the generalized inference rules can be as easily applied and implemented as arithmetic.