While the purpose of a conventional proof calculus is to axiomatise the set of valid sentences of a given logic, a refutation system, or complementary calculus, is concerned with axiomatising the invalid sentences. Instead of exhaustively searching for counter models for some sentence, refutation systems establish invalidity by deduction and thus in a purely syntactic way. Such systems are rele...

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 proofs can be viewed as a special case of constraint propagation, which is a fundamental technique in solving constraint-satisfaction problems. The generalization lifts, in a uniform way, the concept of refutation from Boolean satisfiability problems to general constraint-satisfaction problems. On the one hand, this enables us to study and characterize basic concepts, such as refutat...

In this paper we present a refutation procedure to compute goals in a deductive database according to particular views of it. Views are deened by a set of constraints rules. The declarative semantics of the constrained database is deened and the given refutation procedure is proved correct and complete for positive range{restricted databases. The extension of the procedure to deal with negation...

Haken proved that every resolution refutation of the pigeon hole formula has at least exponential size. Groote and Zantema proved that a particular OBDD computation of the pigeon hole formula has an exponential size. Here we show that any arbitrary OBDD refutation of the pigeon hole formula has an exponential size, too: we prove that the size of one of the intermediate OBDDs is at least Ω(1.025).

In this note we argue that semantic cutting planes refutations are stronger than syntactic ones. In particular, we give a formula for which any refutation in syntactic cutting planes requires exponential length, while there is a polynomial length refutation in semantic cutting planes. This means that syntactic cutting planes does not p-simulate (nor simulate) semantic cutting planes. We also gi...

In this paper we present a refutation procedure to compute goals in a deductive database according to particular views of it. Views are deened by a set of constraints rules. The declarative semantics of the constrained database is deened and the given refutation procedure is proved correct and complete for positive range{restricted databases. The extension of the procedure to deal with negation...

This microgenetic study strived to understand instantaneous peer influences on the moment-bymoment and session-by-session development of relational thinking within and across dialogic smallgroup discussions using an approach called Collaborative Reasoning. An analysis encompassing 32,511 turns for speaking during 176 discussions indicated that peer support and refutation influenced the developm...

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the common signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the r...

Outline 1. A neutral approach to proof and refutation.