A predicate is basically the rest of a proposition after the subject. For example, in "all men are mortal", "are mortal" is the predicate, while "all men" is the subject; and in "Socrates is a man", "Socrates" is the subject, and "is a man" is the predicate. The predicate is basically what a proposition is saying about the subject.

In contemporary predicate logic, the predicate is treated as a logical function, called the propositional function, and the subject of that predicate treated as its argument: the function upon that argument then yields a specific proposition. For example, the proposition "Socrates is mortal" might be decomposed into the function is-mortal() which indicates that whatever is put into it is mortal, and the subject Socrates, such that is-mortal(Socrates) means "Socrates is mortal". This can then be combined with quantification functions to encode a proposition like "all men are mortal" as ∀m(if is-man(m) then is-mortal(m)). Predicating something of a subject is usually taken as equivalent to saying that that thing is a member of some set, the set of all things that predicate is true of.

My proposal for improving this aspect of logic is the use of a single function to handle predicating membership in any set of any subject, a function that is also capable of predicating a fuzzy, non-binary degree of membership, thus allowing the expression of ideas appropriate to fuzzy logic, which deals with sets to which individuals can be members in degrees somewhere between fully members and not at all members. This is similar to simply separating the “is” out from those is-something() functions described above, but because in my entire system of logic we are dealing with ideas independently of the different kinds of attitudes we might have toward them, we want to encode not the idea that e.g. Socrates IS mortal, any more than we want to encode the idea that Socrates OUGHT to be mortal, but rather just the idea of Socrates BEING mortal.

So the function I propose is being(), and it again takes three functions: the first is a number from zero to one expressing the degree of membership in some set to be predicated of some subject, the second is the set to which that degree of membership is to be predicated, and the third is the subject of which it is to be predicated. So for example to encode the idea of Socrates being entirely mortal (and noting for ease of reading here that x% is an equivalent way of writing x/100, so 100% = 1 and 50% = 0.5), we might write being(100%,mortal,Socrates); while if we wanted to instead encode the idea of e.g. Hercules being only half-mortal (whatever that might mean), we might instead write being(50%,mortal,Hercules).