Classical proof forestry

Classical proof forestry

Classical proof forests are a proof formalism for first-order classical logic based on Herbrand’s Theorem and backtracking games in the style of Coquand. First described by Miller in a cut-free setting as an economical representation of firstorder and higher-order classical proof, defining features of the forests are a strict focus on witnessing terms for quantifiers and the absence of inessent...

A Uniform Proof Procedurefor Classical and Non - Classical LogicsJens

We present an eecient proof procedure for classical and non-classical logics. The proof search is based on the matrix-characterization of validity where the emphasis on paths and connections avoids redundancies occurring in sequent or tableaux calculi. Our uniform technique of path-checking is applicable to arbitrary formulae and a generalization of Bibel's connection method for classical logic...

A Uniform Proof Procedure for Classical and Non-Classical Logics

G. Görz & S. Hölldobler, eds. KI-96: Advances in Artificial Intelligence, LNAI 1137, pp. 307–319, c ©Springer Verlag, 1996. Abstract. We present a proof procedure for classical and non-classical logics. The proof search is based on the matrix-characterization of validity where an emphasis on paths and connections avoids redundancies occurring in sequent or tableaux calculi. Our uniform path-che...

Classical BI: Its Semantics and Proof Theory

We present Classical BI (CBI), a new addition to the family of bunched logics which originates in O’Hearn and Pym’s logic of bunched implications BI. CBI differs from existing bunched logics in that its multiplicative connectives behave classically rather than intuitionistically (including in particular a multiplicative version of classical negation). At the semantic level, CBI-formulas have th...

Non-classical Aspects in Proof Complexity