Nicod's axiom
Nicod's axiom (named after Jean Nicod) is an axiom in propositional calculus that can be used as a sole wff in a two-axiom formalization of zeroth-order logic.
The axiom states the following always has a true truth value.
- ((φ ⊼ (χ ⊼ ψ)) ⊼ ((τ ⊼ (τ ⊼ τ)) ⊼ ((θ ⊼ χ) ⊼ ((φ ⊼ θ) ⊼ (φ ⊼ θ))))[1]
To utilize this axiom, Nicod made a rule of inference, called Nicod's modus ponens.
1. φ
2. (φ ⊼ (χ ⊼ ψ))
∴ ψ[2]
In 1931, Mordechaj Wajsberg found an adequate, and easier-to-work-with alternative.
- ((φ ⊼ (ψ ⊼ χ)) ⊼ (((τ ⊼ χ) ⊼ ((φ ⊼ τ) ⊼ (φ ⊼ τ))) ⊼ (φ ⊼ (φ ⊼ ψ))))[3]
References
- ↑ http://us.metamath.org/mpegif/nic-ax.html
- ↑ http://us.metamath.org/mpegif/nic-mp.html
- ↑ http://www.wolframscience.com/nksonline/page-1151a-text
External links
Works related to A Reduction in the number of the Primitive Propositions of Logic at Wikisource
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