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Single Idea 10896

[filed under theme 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives ]

Full Idea

In propositional logic, any set containing ¬ and at least one of ∧, ∨ and → is expressively complete.

Gist of Idea

Propositional logic just needs ¬, and one of ∧, ∨ and →

Source

José L. Zalabardo (Introduction to the Theory of Logic [2000], §2.8)

Book Ref

Zalabardo,José L.: 'Introduction to the Theory of Logic' [Westview 2000], p.71

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The 3 ideas with the same theme [minimal connectives needed for a logic system]:

14105

There seem to be eight or nine logical constants [Russell]

10762

In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]

10896

Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]