In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The approximation extends the signature and preserves unsatisfiability: if the simplified clause set is satisfiable in some model, so is the original clause set in the s...

The standard notions of tautology and subsumption can be naturally generalized, (so that refutation completeness is preserved with respect to the associated deletion), within the context of (a speciied set of) modiied deduction rules for binary clausal resolution-refutation which build-in the reeexiv-ity, symmetry, transitivity and predicate substitutivity axioms for equality. The generalized n...

Building on the work of Daniely et al. (STOC 2014, COLT 2016), we study the connection between computationally efficient PAC learning and refutation of constraint satisfaction problems. Specifically, we prove that for every concept class P, PAC-learning P is polynomially equivalent to “random-right-hand-side-refuting” (“RRHS-refuting”) a dual class P∗, where RRHS-refutation of a class Q refers ...

Refutation texts, rhetorical tools designed to reduce misconceptions, have garnered attention across four decades and many studies. Yet, the ability of a refutation text change learner’s mind on topic needs be qualified modulated. In this critical review, we bring sources constraints often overlooked by researchers. Methodological issues identified centered problems using single (or very few) w...

Counterexample-guided abstraction refinement is a well-established technique in verification. In this paper we instantiate the idea for firstorder logic theorem proving. Given a clause set N we propose its abstraction into a clause set N ′ belonging to a decidable first-order fragment. The abstraction preserves satisfiability: if N ′ is satisfiable, so is N . A refutation in N ′ can then either...