Semantics and proof-theory of depth bounded Boolean logics

Authors:
Marcello Dagostino;Marcelo Finger;Dov Gabbay
Affiliations:
Department of Economics and Management, University of Ferrara, Italy;Department of Computer Science, University of Sao Paulo, Brazil;Bar Ilan University, Israel and Kings College London, United Kingdom and University of Luxembourg, Luxembourg
Venue:
Theoretical Computer Science
Year:
2013

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Abstract

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, and is common to several proof systems and algorithms, such as KE, KI and Stalmarck's method.