One of the many abilities that distinguish a mathematician from an automated deduction system is to be able to ooer appropriate expressions based on intuition and experience that are substituted for existentially quantiied variables so as to simplify the problem at hand substantially. We propose to simulate this ability with a technique called genetic programming for use in automated deduction....

This report documents the program and the outcomes of Dagstuhl Seminar 15381 “Information from Deduction: Models and Proofs”. The aim of the seminar was to bring together researchers working in deduction and applications that rely on models and proofs produced by deduction tools. Proofs and models serve two main purposes: (1) as an upcoming paradigm towards the next generation of automated dedu...

We present a new Curry-Howard correspondence for classical first-order natural deduction. We add to the lambda calculus an operator which represents, from the viewpoint of programming, a mechanism for raising and catching multiple exceptions, and from the viewpoint of logic, the excluded middle over arbitrary prenex formulas. The machinery will allow to extend the idea of learning – originally ...

Isabelle [3, 4] is a generic theorem prover. It suppports interactive proof in several formal systems, including first-order logic (intuitionistic and classical), higher-order logic, Martin-Löf type theory, and Zermelo-Fraenkel set theory. New logics can be introduced by specifying their syntax and rules of inference. Both natural deduction and sequent calculi are allowed. Isabelle’s approach i...

Cut elimination is a central result of the proof theory. This paper proposes a new approach for proving the theorem for Gentzen’s intuitionistic sequent calculus LJ, that relies on completeness of the cutfree calculus with respect to Kripke Models. The proof defines a general framework to extend the cut elimination result to other intuitionistic deduction systems, in particular to deduction mod...

Rewriting logic can be used to prototype systems for automated deduction. In this paper, we illustrate how this approach allows experiments with deduction strategies in a flexible and conceptually satisfying way. This is achieved by exploiting the reflective property of rewriting logic. By specifying a theorem prover in this way one quickly obtains a readable, reliable and reasonably efficient ...

Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics and have found numerous applications in computing. We prove more than hundred theorems of relation algebras with off-the-shelf automated theorem provers. They form a basic calculus from which more advanced applications can be explored. We also present two autom...

We propose an automated deduction method which allows us to produce proofs close to the human intuition and practice. This method is based on tableaux, which generate more natural proofs than similar methods relying on clausal forms, and uses the principles of superdeduction, among which the theory is used to enrich the deduction system with new deduction rules. We present two implementations o...

using a generalized spherical mean operator, we obtain the generalizationof titchmarsh's theorem for the dunkl transform for functions satisfyingthe lipschitz condition in l2(rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.