n this article, we prove An Lp-Lq-version of Morgan’s theorem for the generalized Bessel transform.

ALGEBRAIC LOGIC AND THE DEDUCTION THEOREM W. J. BLOK AND D. PIGOZZI

In this paper we give a natural deduction formulation of hybrid logic. Our natural deduction system can be extended with additional inference rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give natural deduction systems in a uniform way for a wide class of hybrid logics which appears to be impossible in the context of ordinar...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

We prove that no logic (i.e.consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6).

We introduce a new encoding of the set theory of the B method based on deduction modulo. The theory of deduction modulo is an extension of predicate calculus that includes rewriting on both terms and propositions, which is well suited for proof search in axiomatic theories, as it turns many axioms into rewrite rules. We also present Zenon Modulo and iProver Modulo, two automated theorem provers...

Automated deduction, or automated theorem proving is a branch of science that deals with automatic search for a proof. The contribution of Kanger to automated deduction is well-recognized. His monograph 1957] introduced a calculus LC, which was one of the rst calculi intended for automated proof-search. His article 1963] was later republished as Kanger 1983] in the collection of \classical pape...