Department of Computer Science, Cornell University
on leave from:
Department of Computer Science, IME
University of Sao Paulo
We present the general notion of approximations of logics and discuss our recent results.
We present a unifying semantical and proof-theoretical framework for investigating depth-bounded approximations to Boolean Logic, namely approximations in which the number of nested applications of a single structural rule, representing the classical Principle of Bivalence, 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 framework we present here brings to light a general approach to logical inference that is quite different from the standard Gentzen-style approaches, while preserving some of their nice proof-theoretical properties.
Joint work with Marcello D'Agostino and Dov Gabbay