Semantics and proof-theory of depth bounded Boolean logics

Marcello D'Agostino, Marcelo Finger, Dov Gabbay

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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 Stålmarck's method.

Original languageEnglish
Pages (from-to)43-68
Number of pages26
JournalTheoretical Computer Science
StatePublished - 8 Apr 2013


  • Automated deduction
  • Boolean logic
  • Natural deduction
  • Tractability


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