Informational semantics, non-deterministic matrices and feasible deduction

We present a unifying semantic and proof-theoretical framework for investigating depth-bounded approximations to Boolean Logic in which the number of nested applications of a single structural rule, representing the classical Principle of Bivalence (classical cut), is bounded above by a fixed natural number. These approximations provide a hierarchy of tractable logical systems that indefinitely converge to classical propositional logic. The operational rules are shared by all approximation systems and are justified by an "informational semantics" whereby the meaning of a logical operator is specified solely in terms of the information that is actually possessed by an agent.