The absence of polyadic relation symbols severely restricts what can be expressed in the monadic predicate calculus.
It is so weak that, unlike the full predicate calculus, it is decidable—there is a decision procedure that determines whether a given formula of monadic predicate calculus is logically valid (true for all nonempty domains).
Inferences in term logic can all be represented in the monadic predicate calculus.
denote the predicates[clarification needed] of being, respectively, a dog, a mammal, and a bird.
Conversely, monadic predicate calculus is not significantly more expressive than term logic.
Reasoning about such statements can, however, still be handled within the framework of term logic, although not by the 19 classical Aristotelian syllogisms alone.
On the other hand, a modern view of the problem of multiple generality in traditional logic concludes that quantifiers cannot nest usefully if there are no polyadic predicates to relate the bound variables.
Allowing monadic function symbols changes the logic only superficially[citation needed][clarification needed], whereas admitting even a single binary function symbol results in an undecidable logic.