In this paper a uniform methodology to perform Natural Deduction over the family of linear, relevance and intuitionistic logics is proposed. The methodology follows the Labelled Deductive Systems (LDS) discipline, where the deductive process manipulates declarative units { formulas labelled according to a labelling algebra. In the system described here, labels are either ground terms or variabl...

A new predicate calculus deduction system based on production rules is proposed. The system combines several developments in Artificial Intelligence and Automatic Theorem Proving research including the use of domain-specific inference rules and separate mechanisms for forward and backward reasoning. It has a clean separation between the data base, the production rules, and the control system. G...

this paper presents an indirect adaptive system based on neuro-fuzzy approximators for the speed control of induction motors. the uncertainty including parametric variations, the external load disturbance and unmodeled dynamics is estimated and compensated by designing neuro-fuzzy systems. the contribution of this paper is presenting a stability analysis for neuro-fuzzy speed control of inducti...

In this manuscript, we introduce  a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and   propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between  the fuzzy solution set of a  fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtain...

in this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. numerical examples are presented to illustrate the proposed method.

Deduction chains represent a syntactic and in a certain sense constructive method for proving completeness of a formal system S with respect to the class of S-structures. Given a formula A, the deduction chains of A are built up by systematically decomposing A into its subformulae. In the case where A is a valid formula, the decomposition yields a (usually cut-free) proof of A in the system S. ...

Meaning negotiation (MN) is the general process with which agents reach an agreement about the meaning of a set of terms. We give here a general model of MN for two agents, in which each agent discusses with the other one her viewpoint by exhibiting it in an actual set of constraints on the meaning of the negotiated terms. We call this presentation of individual viewpoints an angle. The two age...

This paper is concerned with the problem of how to construct a natural deduction system for nonmonotonic reasoning. Three possible constructions are investigated, the ones which consists of (1) pure nonmonotonic inference rules; (2) nonmonotonic inference rules plus a nonmonotonic tautology base; or (3) nonmonotonic inference rules plus a nonmonotonic conditional assertion base. Based on a fram...

Deduction modulo is a paradigm which consists in applying the inference rules of a deductive system—such as for instance natural deduction—modulo a rewrite system over terms and propositions. It has been shown that higher-order logic can be simulated into the first-order natural deduction modulo. However, a theorem stated by Gödel and proved by Parikh expresses that proofs in second-order arith...

In the papers [1, 2, 4–6, 8] the similarities and differences between systems of sequents and systems of natural deduction for some fragments of intuitionistic logic were presented. The main goal of almost all of these papers was to study the connection between cut-free derivations and normal derivations. It is a well-known property that the natural deduction image of a cut-free derivation is a...