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    Home/Original/inverse
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    Inverse View

    It is not the case that Hoare logic is a true logic of programs, not merely a proof method

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.A genuine logic requires a semantics that determines truth conditions independently of any particular computational model or execution mechanism.
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    • 2.Hoare triples derive their validity from the operational or denotational semantics of the underlying programming language, not from logical axioms alone.
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    • 3.A system whose well-formedness conditions are parasitic on an external semantic theory is a proof calculus, not an autonomous logic in Frege's sense.
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    Reason for 2 of 2
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    • 1.Cook's 1978 incompleteness result shows that Hoare logic is relatively complete only by importing expressive power from the underlying data theory.
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    • 2.Any system requiring an oracle for first-order arithmetic to achieve completeness lacks the self-contained inferential closure definitive of a logic.
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    • 3.This expressibility dependence reveals that Hoare logic is a structured proof method systematically indexed to a metalanguage, not a freestanding logical system.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.The Floyd-Naur inductive assertion method was a way to prove program correctness using logic, but was not itself a logic in the strict sense
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    • 2.Hoare exploited the syntactic structure of imperative programs to derive compositional proof rules
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    • 3.Hoare introduced Hoare triples of the form {P}S{Q} as formal assertions, giving the system the character of a genuine logic
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