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Human-Centered Automated Proof Search.

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Title: Human-Centered Automated Proof Search.
Authors: Sieg, Wilfried1 sieg@cmu.edu, Derakhshan, Farzaneh1
Source: Journal of Automated Reasoning. Dec2021, Vol. 65 Issue 8, p1153-1190. 38p.
Subjects: Mathematical proofs, Automatic theorem proving, Natural deduction (Logic), Mathematical logic, Calculus
Abstract: Human-centered automated proof search aims to capture structures of ordinary mathematical proofs and discover human strategies that are used (implicitly) in their construction. We analyze the ways of two theorem provers for approaching that goal. One, the G&G-prover, is presented in Ganesalingam and Gowers (J Autom Reason 58(2):253–291, 2017); the other, Sieg's AProS system, is described in Sieg and Walsh (Rev Symb Logic 1-35, 2019). Both systems make explicit, via their underlying logical calculi, the goal-directedness and bi-directionality of proof construction. However, the calculus for the G&G-prover is a weak fragment of minimal first-order logic, whereas AProS uses complete calculi for intuitionist and classical first-order logic. The strategies for the construction of proofs are dramatically different as well. The G&G-prover uses a waterfall strategy and is thus restricted to problems that can be solved without backtracking. The AProS strategies, by contrast, support a complete search procedure with backtracking. These divergences are rooted in the fact that the concrete goals of the systems are different: The G&G-prover is to yield write-ups indistinguishable from good mathematical writing; AProS is to yield humanly intelligible formal proofs by logically and mathematically motivated strategies. In our final Programmatic remarks, we sketch a plausible, but difficult project for achieving more fully G&G's broad goals by radically separating proof search from proof translation: one could use AProS for the proof search and then exploit the strategic structure of the completed proof as the deterministic underpinning for its translation into a natural language. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Human-Centered Automated Proof Search.
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Automated+Reasoning%22">Journal of Automated Reasoning</searchLink>. Dec2021, Vol. 65 Issue 8, p1153-1190. 38p.
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  Data: <searchLink fieldCode="DE" term="%22Mathematical+proofs%22">Mathematical proofs</searchLink><br /><searchLink fieldCode="DE" term="%22Automatic+theorem+proving%22">Automatic theorem proving</searchLink><br /><searchLink fieldCode="DE" term="%22Natural+deduction+%28Logic%29%22">Natural deduction (Logic)</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+logic%22">Mathematical logic</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus%22">Calculus</searchLink>
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  Data: Human-centered automated proof search aims to capture structures of ordinary mathematical proofs and discover human strategies that are used (implicitly) in their construction. We analyze the ways of two theorem provers for approaching that goal. One, the G&G-prover, is presented in Ganesalingam and Gowers (J Autom Reason 58(2):253–291, 2017); the other, Sieg's AProS system, is described in Sieg and Walsh (Rev Symb Logic 1-35, 2019). Both systems make explicit, via their underlying logical calculi, the goal-directedness and bi-directionality of proof construction. However, the calculus for the G&G-prover is a weak fragment of minimal first-order logic, whereas AProS uses complete calculi for intuitionist and classical first-order logic. The strategies for the construction of proofs are dramatically different as well. The G&G-prover uses a waterfall strategy and is thus restricted to problems that can be solved without backtracking. The AProS strategies, by contrast, support a complete search procedure with backtracking. These divergences are rooted in the fact that the concrete goals of the systems are different: The G&G-prover is to yield write-ups indistinguishable from good mathematical writing; AProS is to yield humanly intelligible formal proofs by logically and mathematically motivated strategies. In our final Programmatic remarks, we sketch a plausible, but difficult project for achieving more fully G&G's broad goals by radically separating proof search from proof translation: one could use AProS for the proof search and then exploit the strategic structure of the completed proof as the deterministic underpinning for its translation into a natural language. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10817-021-09594-z
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      – Code: eng
        Text: English
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        PageCount: 38
        StartPage: 1153
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        Type: general
      – SubjectFull: Automatic theorem proving
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      – SubjectFull: Natural deduction (Logic)
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      – SubjectFull: Mathematical logic
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      – SubjectFull: Calculus
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              M: 12
              Text: Dec2021
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              Y: 2021
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