Foundations of Mathematics

Mathematical and Formal Logic

What is the atomic formula of predicate calculus?

The atomic formula of predicate calculus is when a predicate and special case of a subject (individual) are written together. For example, if M is the predicate “to be a human,” and b is the subject (individual) “Socrates,” then Mb means the assertion “Socrates is a human.” This atomic formula is phrased “b is the argument of M.” Thus, M, as the predicate, may be applied to any subject, and that subject is then an argument of M. But if c is the subject “Vermont,” then Mc is a false assertion, because Vermont is not a human. Some predicates require more than one argument, thus, you can have formulas such as Mxy.



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