Definition:Corresponding Conditional
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Definition
Let $p_1, p_2, p_3, \ldots, p_n \vdash q$ be a sequent of propositional logic.
It can be expressed as a theorem as follows:
- $\vdash p_1 \implies \paren {p_2 \implies \paren {p_3 \implies \paren {\ldots \implies \paren {p_n \implies q} \ldots } } }$
This is known as the sequent's corresponding conditional.
Also see
- Extended Rule of Implication, where the validity of this construction is proved.
Work In Progress In particular: This pertains probably to the classical interpretation of propositional calculus, and needs to be reformulated and put in the correct category in due time You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by completing it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{WIP}} from the code. |