Theorems \ phi of classical or intuitionistic propositional calculus are translated as equations \ phi = 1 of Boolean or Heyting algebra respectively.
22.
Frege's propositional calculus is equivalent to any other classical propositional calculus, such as the " standard PC " with 11 axioms.
23.
Frege's propositional calculus is equivalent to any other classical propositional calculus, such as the " standard PC " with 11 axioms.
24.
Some examples include the first primitive recursive function that results in complexity, the smallest universal Turing Machine, and the shortest axiom for propositional calculus.
25.
A minimal set of operators that can express every statement expressible in the propositional calculus is called a " minimal functionally complete set ".
26.
In this sense, DT corresponds to the natural conditional proof inference rule which is part of the first version of propositional calculus introduced in this article.
27.
It can be shown that with only these three axiom schemata and " modus ponens ", one can prove all tautologies of the propositional calculus.
28.
Propositional variables should not be confused with the metavariables which appear in the typical axioms of propositional calculus; the latter effectively range over well-formed formulae.
29.
Although a propositional calculus originated with Aristotle, the notion of an " algebra " applied to propositions had to wait until the early 19th century.
30.
This ability to mix external implication \ vdash and internal implication ?! in the one logic is among the essential differences between sequent calculus and propositional calculus.
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