Definition of Conditional proof

1. Noun. (logic) A style of proof which proceeds as follows: (1) start with some premise(s) and assumption(s), (2) derive a desired conclusion from the premise(s) and assumption(s), (3) apply the deduction theorem to state the tautology that the premise(s) imply that the assumption(s) imply the conclusion (or just the contingency that the assumption(s) imply the conclusion, contingent implicitly upon the truth of the premise(s)). (''Note:'' a conditional proof can be embedded (i.e., be a subproof) within a larger, "ambient" proof, in which case its premises are formulas which it "inherits" from the ambient proof, whereas its assumptions are formulas which it hypothesizes ''in situ'' and whose scope is limited to the subproof and do not spill over to the ambient proof. A conditional proof can also be stand-alone in which case it has no premises, only assumptions, and the proof proceeds as follows: (1) start with assumption(s), (2) derive a conclusion from the assumption(s), (3) apply the deduction theorem to state the tautology that the assumption(s) imply the conclusion.) ¹

¹ Source: wiktionary.com

Lexicographical Neighbors of Conditional Proof

condition
condition precedent
conditionable
conditional
conditional-lethal mutant
conditional agreement
conditional contract
conditional entropy
conditional mood
conditional moods
conditional mutation
conditional perfect
conditional probability
conditional proof (current term)
conditional reaction
conditional reflex
conditional relation
conditional response
conditional sale
conditional sentence
conditional sentences
conditional tense
conditional tenses
conditional use permit
conditionalisation
conditionalisations
conditionalism
conditionalist

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