Protothetic

definition

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[pq]:p.q.≡.[f].f(pq)≡f(q1)

p	q	p.q
False	False	False
False	True	False
True	False	False
True	True	True

Leśniewski's protothetic is an extended propositional calculus in which all Boolean functions can be defined. The theory also includes a universal quantifier. In 1922, Alfred Tarski established that by employing functional variables and quantifiers, all the functions of propositional calculus can be defined using equivalence as the sole primitive function.