A monadic formula of first-order logic is one for which all nonlogical symbols are one-place predicates.

Theorem. If

is a monadic sentence that is satisfiable, then

is true in some interpretation whose domain contains at most

members, where

is the number of one-place predicate letters and

is the number of variables in

.

Therefore there is an effective procedure for deciding whether or not a monadic sentence is valid [1, p. 250].

Syllogistic forms are monadic sentences if considered as sentences of the form

with predicate letters

,

, and

.

[1] G. S. Boolos and R. C. Jeffrey,

*Computability and Logic*, Cambridge, UK: Cambridge University Press, 1974.

[2] L. Carroll,

*Symbolic Logic and The Game of Logic*, New York: Dover Publications, 1958.

[3] I. M. Copi and C. Cohen,

*Introduction to Logic*, 9th ed., New York: Macmillan Publishers, 1994 pp. 214–218.

[4] J. M. Bocheński,

*A History of Formal Logic*, 2nd ed. (I. Thomas, trans. and ed.), New York: Chelsea Publishing Company, 1970 p. 235.

[7] J. Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings,"

*Philosophical Magazine Series 5*,

**10**(59), 1880 pp. 1–18.

doi:10.1080/14786448008626877.