Methodology is developed to attempt to construct simultaneously either a refutation or a model for a propositional formula in conjunctive normal form. The method exploits the concept of \autarky", which was introduced by Monien and Speckenmeyer. Informally, an autarky is a \self-suucient" model for some clauses, but which does not aaect the remaining clauses of the formula. Whereas their work w...

In this paper, we analyze 2CNF formulas from the perspectives of Read-Once resolution (ROR) refutation schemes. We focus on two types of ROR refutations, viz., variable-once refutation and clause-once refutation. In the former, each variable may be used at most once in the derivation of a refutation, while in the latter, each clause may be used at most once. We show that the problem of checking...

In this note we show that any k-CNF which can be refuted by a quasi-polynomial Res(polylog) refutation has a “narrow” refutation in Res (i.e., of poly-logarithmic width). Notice that while Res(polylog) is a complete proof system, this is not the case for Res if we ask for a narrow refutation. In particular is not even possible to express all CNFs with narrow clauses. But even for constant width...

Refutation texts are beneficial for removing misconceptions and supporting comprehension in science. Whether these beneficial effects hold true in the domain of statistics is, however, an open question. Moreover, the role of refutation texts for the accuracy in judging one’s own comprehension (metacomprehension accuracy) has received little attention. Therefore, we conducted an experiment in wh...

The refutation tree problem is to compute a refutation tree which is associated with the structure of a graph generated by a formal graph system (FGS).We present subclasses of FGSs, called simple FGSs, size-bounded simple FGSs and bounded simple FGSs. In order to show that the refutation tree problem for simple FGSs can be solved in polynomial time, we prove that the refutation tree problem for...