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Natural deduction for non-classical logics

Basin, David A. and Matthews, Seán and Viganò, Luca

August 1996, 44 pages.

Status: available - back from printing

We present a framework for machine implementation of families of non-classical logics with Kripke-style semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate combinations we capture both partial and complete fragments of large families of non-classical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of correctness and proof normalization. We have implemented our work in the Isabelle Logical Framework.

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  AUTHOR = {Basin, David A. and Matthews, Se{\'a}n and Vigan{\`o}, Luca},
  TITLE = {Natural deduction for non-classical logics},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-96-2-006},
  MONTH = {August},
  YEAR = {1996},
  ISSN = {0946-011X},