MUSCADET is a knowledge-based theorem prover based on natural deduction. It has participated in CADE Automated theorem proving System Competitions. The results show its complementarity with regard to resolution-based provers. This paper presents some of its crucial methods and gives some examples of MUSCADET proofs from the last competition (CASC-JC in IJCAR 2001).

Using a Bessel generalized translation, we obtain an analog of Titchmarsh's theorem for the Bessel transform for functions satisfying the Lipschitz condition in the space $mathrm{L}_{p,alpha}(mathbb{R}_{+})$, where $alpha>-frac{1}{2}$ and $1

In 1981, Paris and Wilkie [21] indicated it was an open question whether IΣ0 would satisfy the Second Incompleteness Theorem for Herbrand deduction. We will show that IΣ0 will both obey and defy the Herbrandized version of the Second Incompleteness Theorem, depending on which of several equivalent definitions of IΣ0 one examines.

This paper presents a new proof-assistant based approach to program verification: programs are translated, via fully-automatic deduction, into tail-recursive function defined in the logic of a theorem prover. This approach improves on well-established methods based on Hoare logic and verification condition generation (VCG) by removing the need to annotate programs with assertions, making the pr...

in this paper, we deal with molaei’s generalized groups. we definethe notion of a fuzzy generalized subgroup with respect to a t-norm (ort-fuzzy generalized subgroup) and give some related properties. especially,we state and prove the representation theorem for these fuzzy generalizedsubgroups. next, using the concept of continuity of t-norms we obtain a correspondencebetween tf(g), the set of ...

In this paper, using a generalized Jacobi-Dunkl translation operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the Lipschitz Jacobi-Dunkl condition in the space Lp.

The aim of this paper is to prove new quantitative uncertainty principle for the generalized Fourier transform connected with a Dunkl type operator on the real line. More precisely we prove An Lp-Lq-version of Morgan's theorem.

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.

Linear logic (LL) [9], [10](see Appendix A, B) is the logical foundation of some typetheoretic languages and also of environments for specification and theorem proving. In this paper, we consider the Multiplicative fragment of Linear Logic (MLL) from an automated deduction point of view. We propose an automated deduction (Automatic Proof Nets Construction and its implementation) based on the no...