Reasoning on Schemata of Formulæ

ar X iv : 1 20 4 . 29 90 v 1 [ cs . L O ] 1 2 A pr 2 01 2 Reasoning on Schemata of Formulæ ⋆

A logic is presented for reasoning on iterated sequences of formulæ over some given base language. The considered sequences, or schemata, are defined inductively, on some algebraic structure (for instance the natural numbers, the lists, the trees etc.). A proof procedure is proposed to relate the satisfiability problem for schemata to that of finite disjunctions of base formulæ. It is shown tha...

Reasoning on Schemata of Formulae

A logic is presented for reasoning on iterated sequences of formulæ over some given base language. The considered sequences, or schemata, are defined inductively, on some algebraic structure (for instance the natural numbers, the lists, the trees etc.). A proof procedure is proposed to relate the satisfiability problem for schemata to that of finite disjunctions of base formulæ. It is shown tha...

Schemata of Formulæ in the Theory of Arrays

A paramodulation-based calculus for refuting schemata of clause sets defined by rewrite rules

We devise a calculus based on the resolution and paramodulation rules and operating on schemata of formulæ. These schemata are de ned inductively, using convergent rewrite systems encoding primitive recursive de nitions. The main original feature of this calculus is that the rules operate on formulæ or terms occurring at arbitrary deep positions inside the considered schemata, thus a ecting the...

A New Similarity Measure for Guiding Generalizations Search

Few works are available in the literature to define similarity criteria between First-Order Logic (FOL) formulæ, where the presence of relations causes various portions of one description to be possibly mapped in different ways onto another description, which poses serious computational problems. Hence, the need for a set of general criteria that are able to support the comparison between formu...