Displaying similar documents to “A semantical hierarchy for modal formulas.”

Metric similarities in the logic of approximation.

Michael Katz (1982)

Stochastica

Similarity:

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 general deduction theorem.

Salvatore Guccione, Roberto Tortora (1980)

Stochastica

Similarity:

In this paper we present a very general deduction theorem which -based upon a uniform notion of proof from hypotheses- holds for a very large class of logical systems. Most of the known results for classical and modal logics, as well as new results, are immediate corollaries of this theorem.

Some problems of measure theory which are related to economic theory.

Heinz J. Skala (1982)

Stochastica

Similarity:

After a short discussion of the first application of measure theoretic tools to economics we show that it is consistent relative to the usual axioms of set theory that there exists no nonatomic probability space of power less than the continuum. This together with other results shows that Aumann's continuum-of-agents methodology provides a sound framework at least for the cooperative theory. There are, however, other problems in economics where, without further assumptions,...

Some remarks on a problem of C. Alsina.

J. Matkowski, M. Sablik (1986)

Stochastica

Similarity:

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 symmetries and parallelogram spaces.

Mirko Polonijo (1985)

Stochastica

Similarity:

The notion of a TST-space is introduced and its connection with a parallelogram space is given. The existence of a TST-space is equivalent to the existence of a parallelogram space, which is a new characterization of a parallelogram space. The structure of a TST-space is described in terms of an abelian group.

Representation of continuous associative functions.

Barbara Baccheli (1986)

Stochastica

Similarity:

Strengthened forms of Ling's representation theorem concerning a class of continuous associative functions are given: Firstly the monotonicity condition is removed. Then the associativity condition is replaced by the power associativity.