Displaying similar documents to “A general deduction theorem.”

Metric similarities in the logic of approximation.

Michael Katz (1982)

Stochastica

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We describe restricted and extended versions of the logic of approximation which is meant to handle formally the problems of measurement error and of deduction under conditions of uncertainty. We apply the logic to the foundations of social and behavioral inquiry, axiomatizing in it an inexact similarity predicate which behaves like a metric approximation to identity. In the restricted version of the logic we formulate conditions for the imbeddability of similarity models in the real...

A semantical hierarchy for modal formulas.

Salvatore Guccione, Roberto Tortora (1982)

Stochastica

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In this paper a semantical partition, relative to Kripke models, is introduced for sets of formulas. Secondly, this partition is used to generate a semantical hierarchy for modal formulas. In particular some results are given for the propositional calculi T and S4.

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

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Equation [1] f(x+y) + f (f(x)+f(y)) = f (f(x+f(y)) + f(f(x)+y)) has been proposed by C. Alsina in the class of continuous and decreasing involutions of (0,+∞). General solution of [1] is not known yet. Nevertheless we give solutions of the following equations which may be derived from [1]: [2] f(x+1) + f (f(x)+1) = 1, [3] f(2x) + f(2f(x)) = f(2f(x + f(x))). Equation [3] leads to a Cauchy functional equation: ...

On the extension of Rosenbrock's theory in algebraic design on multivariable controllers.

Manuel de la Sen (1986)

Stochastica

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System similarity and system strict equivalence concepts from Rosenbrock's theory on linear systems are used to establish algebraic conditions of model matching as well as an algebraic method for design of centralized compensators. The ideas seem to be extensible without difficulty to a class of decentralized control.