Aquarius is a distributed theorem prover for first order logic with equality, developed for a network of workstations. Given as input a theorem proving problem and a number n of active nodes, Aquarius creates n deductive processes, one on each workstation, which work cooperatively toward the solution of the problem. Aquarius realizes a number of variants of a general methodology for distributed...

We study generalized deduction rules of cut and weakening in the context of equational fragment of Pavelkastyle fuzzy logic using complete residuated lattices as the structures of truth degrees. The deduction rules in question are parameterized by a truth stresser, an additional unary operation on the structure of truth degrees. It is shown that the deductive system of fuzzy Horn logic can be r...

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a non-associative generalization of FL (which we call SL) has been studied by Galatos and Ono as the logics of lattice-ordered residuated unital groupoids. This paper is based on an alternative...

We overview recent results related to Herbrand's theorem and tableau-like methods of automated deduction. Based on an analysis and discussion of these results, open problems are posed and new research directions are suggested.

In this paper, we introduce a semantics of realisability for the classical propositional natural deduction and we prove a correctness theorem. This allows to characterize the operational behaviour of some typed terms.

We present the canonical Gröbner Cover method for discussing parametric polynomial systems of equations. Its objective is to decompose the parameter space into subsets (segments) for which it exists a generalized reduced Gröbner basis in the whole segment with fixed set of leading power products on it. Wibmer’s Theorem guarantees its existence. The Gröbner Cover is designed in a joint paper of ...

Muscadet is a knowledge-based theorem prover based on natural deduction. Its results show its complementarity with regard to resolution-based provers. This paper presents some Muscadet results and points out some of its characteristics.

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