A note on generalized generalization

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F25%3A10510631" target="_blank" >RIV/00216208:11210/25:10510631 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8auEtkueFx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8auEtkueFx</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14712/24647055.2025.5" target="_blank" >10.14712/24647055.2025.5</a>

Result language
angličtina
Original language name
A note on generalized generalization
Original language description
The generalization rules of sequent calculi allow, under some restrictions, to derive a formula THERE EXISTS χφ or FOR ALL χφ from a formula φχ (γ), i.e. from the formula obtained by substituting a variable γ for all free occurrences of χ in φ. We introduce modified generalization rules that make it possible to derive THERE EXISTS χφ or FOR ALL χφ from φχ (t) even in some cases where t is a complex term. These modified rules were invented in connection with attempts to prove the interpolation theorem for classical predicate logic without equality but with function symbols. This theorem seems (and remains) to be an unresolved case in the literature.
Czech name
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Czech description
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Type
J<sub>ost</sub> - Miscellaneous article in a specialist periodical
CEP classification
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OECD FORD branch
60301 - Philosophy, History and Philosophy of science and technology

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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