Math logic versus Semantic Web use of predicate

When I see any sort of mathematical logic treatment of a predicate, it typically says something like $G(x)$ where $G$ stands for, e.g. "is the color blue" and the $x$ will be the subject or variable that, when evaluated, becomes a proposition either true or false.

However, the Semantic Web's semantic triple goes beyond "subject-predicate" and into "subject-predicate-object." For example, The sky is the color blue would have sky the subject, is the color the predicate, and blue as the object. Confusing is how the standard math logic I've seen doesn't seem to have the object part, e.g., the subject above would be sky and the predicate would just be the entire is the color blue, i.e., the object is subsumed by the predicate. Have I simply not found the right logic text -- or is this a real difference not to be overcome?

Solution 1:

The distinction between "subject" and "object" does not exist in mathematics.

The distinction between subject and object is rather fluid even in natural language. For example, in English, you might say "I like tacos". The subject is "I", and the object is "tacos". In Spanish, the most direct translation of this is "Me gustan los tacos". Here, the subject and the object are flipped; it's actually the thing being liked (the tacos) that is the subject, and the liker (me) which is the object.

In predicate logic, one would simply define a two-place predicate $Likes$, with the semantics that $Likes(a, b)$ means that $a$ likes $b$. There is no grammatical notion in mathematics of one thing "acting on" another; the tacos and I would be treated evenhandedly (we could have just as easily defined $Likes'(a, b) :\equiv Likes(b, a)$).