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    Hoare logic is a true logic of programs, not merely a pro... — Carmelics
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    Hoare logic is a true logic of programs, not merely a proof method

    Philosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

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    Reason for
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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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    Reasons Against

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    Reason against 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 against 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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    Related

    A genuine logic requires a semantics that determines truth conditions independen...A system whose well-formedness conditions are parasitic on an external semantic ...Any system requiring an oracle for first-order arithmetic to achieve completenes...Cook's 1978 incompleteness result shows that Hoare logic is relatively complete ...
    +5 moreShow less
    Hoare exploited the syntactic structure of imperative programs to derive composi...Hoare introduced Hoare triples of the form {P}S{Q} as formal assertions, giving ...Hoare triples derive their validity from the operational or denotational semanti...The Floyd-Naur inductive assertion method was a way to prove program correctness...This expressibility dependence reveals that Hoare logic is a structured proof me...

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    Program verification has a long history. Already since the inception of the computer and its programming researchers started to think of ways of analyzing programs to be sure they did what they were supposed to do. In the 60s the development of a true mathematical theory of program correctness began to take serious shape (de Bakker 1980, 466). Remarkably, the work of John McCarthy who we will also encounter later on when we turn to the field of artificial intelligence played an important role he
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    Details

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    Perspectives
    3 (1 for, 2 against)
    Edits
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