Substitutions for predicate variables and functional variables.

The Monotonous Elimination of Predicate Variables

I describe an algorithm which when given a sentence ? involving universally quantiied predicate variables, rst reduces this sentence to a normal form ? and then, if ? satisses certain extra restrictions, eliminates the predicate variables of ? to produce a predicate-free equivalent of ?. This process may involve the introduction of skolem functions but in many cases does not (and so produces a ...

Predicate Logic with Sequence Variables and Sequence Function Symbols

We extend first-order logic with sequence variables and sequence functions. We describe syntax, semantics and inference system for the extension, define an inductive theory with sequence variables and formulate induction rules. The calculus forms a basis for the top-down systematic theory exploration paradigm.

Functional Dependencies between Variables

Itisa standard practice to de ne the truth conditionsfora rst-orderform ula with a quanti erin term sofassignm entsto individualvariables. For exam ple,letM be a m odeland s a function (assignm ent)which assignsto variableselem entsin thedom ain ofM .Then a formula 9x (x)istruein M undersi thereisan assignm entswhich di ersfrom satm ostin thevalue itassignsto x,such that (x)istrue on M unders. ...

Dominated Convergence for Fuzzy Random Variables

SOME PROBABILISTIC INEQUALITIES FOR FUZZY RANDOM VARIABLES

In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequ...