Extension Rule for Non-Clausal Propositional Calculus

Authors:
Kazimir Majorinc
Affiliations:
Faculty of Natural Sciences and Mathematics, University of Zagreb, Zagreb, Croatia. kmajor@public.srce.hr
Venue:
Fundamenta Informaticae
Year:
1997

Citing 3
Cited 0

A satisfiability tester for non-clausal propositional calculus

Information and Computation
Machine synthesis of mathematical theorems

Journal of Logic Programming
One more occurrence of variables makes satisfiability jump from trivial to NP-complete

SIAM Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

Van Gelder has described a few reasons for satisfiability testing without transformation of formulas into CNF and has developed an algorithm for this problem. We have introduced two possible improvements. First, we have used directed acyclic graphs for the representation of formula, instead of representation in the form of a tree or a string of characters. Second, we have allowed a limited introduction of new variables, again without transformation to CNF. In terms of a proof system, Van Gelder’s algorithm does not p-simulate system described here. Some generalizations of notions of propositional formula, satisfiability, etc. are introduced.