As it is well-known, Lukasiewicz developed in [2] the many-valued propositional calculi based on two primitive connectives, negation N and implication C, which were defined semantically. Complete axiomatizations followed later on. Among the works on this argument, we mention Wajsberg [9], Rosser and Turquette [8], Mc Naughton [3], Rose and Rosser [7], Meredith [4], Chang [1], Rose [5], [6]. It ...

Cirquent calculus is a recent approach to proof theory, whose characteristic feature is being based on circuit-style structures (called cirquents) instead of the traditional formulas or sequents. In this paper we prove the deduction theorem for the symmetric version of cirquent calculus, and show that the derivation in the deduction theorem will be at most polynomially longer than the proof of ...

We present the certifying part of the Zenon Modulo automated theorem prover, which is an extension of the Zenon tableau-based first order automated theorem prover to deduction modulo. The theory of deduction modulo is an extension of predicate calculus, which allows us to rewrite terms as well as propositions, and which is well suited for proof search in axiomatic theories, as it turns axioms i...

in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.

in this paper, by modifying cheng-yau$'$s technique to complete hypersurfaces in $s^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [h. li, hypersurfaces with constant scalar curvature in space forms, {em math. ann.} {305} (1996), 665--672].

a characteriation of continuity of the $p$-$lambda$-variation function is given and the helly's selection principle for $lambda bv^{(p)}$ functions is established. a characterization of the inclusion of waterman-shiba classes into classes of functions with given integral modulus of continuity is given. a useful estimate on modulus of variation of functions of class $lambda bv^{(p)}$ is found.

We prove in HOL that three proof systems for classical rst-order predicate logic, the Hilbertian axiomatization, the system of natural deduction, and a variant of sequent calculus, are isomorphic. The isomorphism is in the sense that provability of a conclusion from hypotheses in one of these proof systems is equivalent to provability of this conclusion from the same hypotheses in the others. P...

The goal of this paper is to show how modal logic may be conceived as recording the derived rules of a logical system in the system itself. This conception of modal logic was propounded by Dana Scott in the early seventies. Here, similar ideas are pursued in a context less classical than Scott's. First a family of propositional logical systems is considered, which is obtained by gradually addin...

of the Dissertation Distributed Automated Deduction by Maria Paola Bonacina Doctor of Philosophy in Computer Science State University of New York at Stony Brook 1992 This thesis comprises four main contributions: an abstract framework for theorem proving, a methodology for parallel theorem proving in a distributed environment, termed deduction by Clause-Diffusion, a study of special topics in d...

An automated forward deduction system for entailment calculus is an indispensable component of many application systems – such as theorem finding, active database, knowledge discovery systems – that require an autonomous reasoning engine. The performance of an automated forward deduction system is crucial to its applicability. In this paper, we present some parallel forward deduction algorithms...