How can the word “is” express predication in formal logic?

In formal logic, the word "is" is often considered ambiguous because natural language uses it to express several distinct logical concepts, including identity, existence, subsumption, and predication.1

To avoid this ambiguity, formal logical systems replace the natural language "is" with specific symbolic structures. In the context of predication, the goal is to attribute a characteristic (a predicate) to a subject (an argument). For example, the statement "This dish is warm" is symbolized as Wd, where W represents the predicate "warm" and d represents the subject "dish".2

When the subject is indefinite, logicians use a variable, such as x, to create a propositional function like Wx ("x is warm"). By applying quantifiers such as "for every" ($\forall x$) or "there exists" ($\exists x$), this function is transformed into a general or particular proposition. Consequently, formal logic treats predication not as a simple verb of being, but as a functional relationship between a subject and a property.21