Simplification with renaming : a general proof technique for tableau and sequent-based provers /
Massacci, Fabio.
Cambridge [Cambridgeshire] : University of Cambridge, Computer  Laboratory,
[1997].
Abstract: "Tableau and sequent calculi are the basis for most popular interactive theorem provers for hardware and software verification.   Yet, when it comes to decision procedures or automatic proof search, tableaux are orders of magnitude slower than Davis-Putnam, SAT based procedures or other techniques based on resolution.  To meet this challenge, this paper proposes a theoretical innovation: the rule of simplification, which plays for tableaux the same role of subsumption for resolution and unit for Davis-Putnam.  This technique gives an unifying view of a number of tableaux-like calculi such as DPLL, KE, HARP, hyper- tableaux etc.  For instance, the stand-alone nature of the first-order Davis-Putnam-Longeman-Loveland procedure can be explained away as a case of Smullyan tableau with propositional simplification.  Beside its computational effectiveness, the simplicity and generality of simplification make possible its extension in a uniform way.  We define it for propositional and first order logic and a wide range of modal logics.  For a full-fledged first order simplification we combine it with another technique, renaming, which subsumes the use of free universal variables in sequent and tableau calculi.  New experimental results are given for random  SAT and the IFIP benchmarks for hardware verification."
"May 19, 1997."
Includes bibliographical references.
Abstract: "Tableau and sequent calculi are the basis for most popular interactive theorem provers for hardware and software verification.   Yet, when it comes to decision procedures or automatic proof search, tableaux are orders of magnitude slower than Davis-Putnam, SAT based procedures or other techniques based on resolution.  To meet this challenge, this paper proposes a theoretical innovation: the rule of simplification, which plays for tableaux the same role of subsumption for resolution and unit for Davis-Putnam.  This technique gives an unifying view of a number of tableaux-like calculi such as DPLL, KE, HARP, hyper- tableaux etc.  For instance, the stand-alone nature of the first-order Davis-Putnam-Longeman-Loveland procedure can be explained away as a case of Smullyan tableau with propositional simplification.  Beside its computational effectiveness, the simplicity and generality of simplification make possible its extension in a uniform way.  We define it for propositional and first order logic and a wide range of modal logics.  For a full-fledged first order simplification we combine it with another technique, renaming, which subsumes the use of free universal variables in sequent and tableau calculi.  New experimental results are given for random  SAT and the IFIP benchmarks for hardware verification."
Automatic theorem proving.
Problem solving