Monotone sequent calculus and resolution
Commentationes Mathematicae Universitatis Carolinae (2001)
- Volume: 42, Issue: 3, page 575-582
- ISSN: 0010-2628
Access Full Article
top
Abstract
topHow to cite
topBílková, Marta. "Monotone sequent calculus and resolution." Commentationes Mathematicae Universitatis Carolinae 42.3 (2001): 575-582. <http://eudml.org/doc/248791>.
@article{Bílková2001,
abstract = {We study relations between propositional Monotone Sequent Calculus (MLK --- also known as Geometric Logic) and Resolution with respect to the complexity of proofs, namely to the concept of the polynomial simulation of proofs. We consider Resolution on sets of monochromatic clauses. We prove that there exists a polynomial simulation of proofs in MLK by intuitionistic proofs. We show a polynomial simulation between proofs from axioms in MLK and corresponding proofs of contradiction (refutations) in MLK. Then we show a relation between a resolution refutation of a set of monochromatic clauses (CNF formula) and a proof of the sequent (representing corresponding DNF formula) in MLK. Because monotone logic is a part of intuitionistic logic, results are relevant for intuitionistic logic too.},
author = {Bílková, Marta},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {intuitionistic propositional logic; monotone logic; sequent calculus; resolution; complexity of proofs; complexity of proofs; monotone logic; intuitionistic propositional logic; sequent calculus; resolution},
language = {eng},
number = {3},
pages = {575-582},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Monotone sequent calculus and resolution},
url = {http://eudml.org/doc/248791},
volume = {42},
year = {2001},
}
TY - JOUR
AU - Bílková, Marta
TI - Monotone sequent calculus and resolution
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2001
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 42
IS - 3
SP - 575
EP - 582
AB - We study relations between propositional Monotone Sequent Calculus (MLK --- also known as Geometric Logic) and Resolution with respect to the complexity of proofs, namely to the concept of the polynomial simulation of proofs. We consider Resolution on sets of monochromatic clauses. We prove that there exists a polynomial simulation of proofs in MLK by intuitionistic proofs. We show a polynomial simulation between proofs from axioms in MLK and corresponding proofs of contradiction (refutations) in MLK. Then we show a relation between a resolution refutation of a set of monochromatic clauses (CNF formula) and a proof of the sequent (representing corresponding DNF formula) in MLK. Because monotone logic is a part of intuitionistic logic, results are relevant for intuitionistic logic too.
LA - eng
KW - intuitionistic propositional logic; monotone logic; sequent calculus; resolution; complexity of proofs; complexity of proofs; monotone logic; intuitionistic propositional logic; sequent calculus; resolution
UR - http://eudml.org/doc/248791
ER -
References
top- Atserias A., Galesi N., Gavalda R., Monotone Proofs of the Pigeon Hole Principle, preprint, Barcelona University, 1999. Zbl0989.03065MR1795891
- Atserias A., Galesi N., Pudlák P., Monotone Simulations of Nonmonotone Propositional Proofs, ECCC Report TR00-087, 2000.
- Cook S.A., Reckhow R.A., The relative efficiency of propositional proof systems, J. Symbolic Logic 44 (1979), 36-50. (1979) Zbl0408.03044MR0523487
- Pudlák, P., On the complexity of the propositional calculus, in Sets and Proofs, Invited papers from Logic Colloquium 1997, S.B. Cooper and J.K. Truss eds., Cambridge University Press, 1999, pp. 197-218. MR1720576
- Takeuti G., Proof Theory, North-Holland, second edition, 1987. Zbl0681.03039MR0882549
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.