Dear Yaozhi,

What do you exactly mean by ?

Thanks for your answer. Marc.

Dear Marc Carvallo,

Binary true-valued function is Boolean algebra, i.e. valued on the two discrete values of 0 and 1, multiple true-valued function is valued on several discreate values of a,b,~,i, 0

Dear Yaozhi,

Your answer is not upon my question (of a day ago), and leads me now to question you by another question: how can discreteness become ? Please answer both questions (of now and a day ago). Thanks for your answers. Marc.

Dear Marc Cavarllo:

This is based on a difinition which can include the binary true-valued function and multiple true-valued function into continuons true-valued function valued on close interval[-1,+1]. With another word, we can make the binary true-valued function and multiple true-valued function as subsets belong to continuons true-valued function valued on close interval [-1,+1].

Thanks for Marc Cavarllo!

Dear Yaozhi,

Can any multiplication of logic effect the continuousness? Marc.

Dear Marc Carvallo:

I just said multiple true-valued function of logic is a subset of continuous true-valued function. Because of multiple true-valued function is also discrete, as same as set X={0.2, 0.3,~,0.7} is a subset of close interval [-1,+1].

Thanks for Marc Carvallo.

Dear Yaozhi,

Again, can any multiplication of logic and sets and discretenesses result in continousness? Thanks for your answer. Marc.

Dear Marc Carvallo:

The first, true-and-false of logic is defined by true-valued function,. The second, binary true-valued function and multiple true-valued function, the two all are discrete functions, of that all belong to the continuons true-valued function and therefor become into subsets of continuons true-valued function which valued on close interval [-1,+1] , not that all result in continuonsness.

Thanks for Mac Cavallo.

n-valued logics (where n is a positive integer) all have a finite number of discrete values. If you want a continuous non-discrete range of values (i.e. an infinite-valued logic), why not just use probabilities?

Also, you'd have to decide which are the designated values that are to be preserved in valid inferences. Where would you locate the "neither-true-nor-false" or the "indeterminate" value of a 3-valued logic on a continuous range of values? Once you start thinking about the values as standing for some actual concept of English (or other natural language) instead of as just a formal uninterpreted symbol or as just a number, it may be difficult to regard the values as subsets whose elements can be intuitively and nonarbitrarily located in your continuous range of values.

To Dear Karl Pfeifer,

Your opinion is involved an important topic in dialectical logic, contradiction. A contradiction, we say, is a state that two or many factors exist to depand on each other and , at same time, struggle each other, for instance, one-postive factor +A and one-negative factor -A, the two factors are combined into one proposition system of dialectical logic. This proposition system of dialectical logic is defined by a continuous true-valued function F belongs to closed interval [-1,+1]. the continuous true-valued function is used for express the two factors which is superiorty, and especially the two factors all are continuous variables. For example, +A=0.4, -A=-0.2, its continuous true-valued function can be defined as F=1/2(0.4-0.2)=+0.1, thus we can say the true-valued function, of that the postive factor is superior than negative factor, is +0.1, etc.

Best regards!