Showing papers on "Conjunctive normal form published in 1980"
08 Jul 1980
TL;DR: A modified resolution procedure is described which has been designed to prove theorems about general linear inequalities, using "variable elimination", and a modified form of inequality chaining, in order to reduce the size of the search space and to speed up proofs.
Abstract: A modified resolution procedure is described which has been designed to prove theorems about general linear inequalities. This prover uses "variable elimination", and a modified form of inequality chaining (in which chaining is allowed only on so called "shielding terms"), and a decision procedure for proving ground inequality theorems. These techniques and others help to avoid the explicit use of certain axioms, such as the transitivity and interpolation axioms for inequalities, in order to reduce the size of the search space and to speed up proofs. Several examples are given along with results from a computer implementation. In particular this program has proved some difficult theorems such as: The sum of two continuous functions is continuous.
85 citations
TL;DR: It is shown that leaving out one of the restrictions ( a ) to ( c ) yields classes of formulae whose decision problem can assume any prescribed recursively enumerable complexity in terms of many-one degrees of unsolvability.
4 citations
TL;DR: Two small classes of first order formulae without function symbols but with identity, in prenex conjunctive normal form with all disjunctions binary, are shown to have a recursively unsolvable decision problem, whereas for another such class an algorithm is developed which solves the decision problem of that class.
Abstract: Two small classes of first order formulae without function symbols but with identity, in prenex conjunctive normal form with all disjunctions binary, are shown to have a recursively unsolvable decision problem, whereas for another such class an algorithm is developed which solves the decision problem of that class. This solves the prefix problem for such classes of formulae except for the Godel-Kalmar-Schutte case.
3 citations