| KUCHYŇKA, Petr and Jiří RACLAVSKÝ. Completeness in partial type theory. Journal of Logic and Computation. Oxford, UK: Oxford University Press, 2024, vol. 34, No 1, p. 1-32. ISSN 0955-792X. Available from: https://dx.doi.org/10.1093/logcom/exac089. |
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@article{2363117,
author = {Kuchyňka, Petr and Raclavský, Jiří},
article_location = {Oxford, UK},
article_number = {1},
doi = {http://dx.doi.org/10.1093/logcom/exac089},
keywords = {partial type theory; completeness proof; partiality; natural deduction; higher-order logic; hyperintensionality},
language = {eng},
issn = {0955-792X},
journal = {Journal of Logic and Computation},
note = {WOS:000936329300001},
title = {Completeness in partial type theory},
url = {https://doi.org/10.1093/logcom/exac089},
volume = {34},
year = {2024}
}
TY - JOUR
ID - 2363117
AU - Kuchyňka, Petr - Raclavský, Jiří
PY - 2024
TI - Completeness in partial type theory
JF - Journal of Logic and Computation
VL - 34
IS - 1
SP - 1-32
EP - 1-32
PB - Oxford University Press
SN - 0955792X
N1 - WOS:000936329300001
KW - partial type theory
KW - completeness proof
KW - partiality
KW - natural deduction
KW - higher-order logic
KW - hyperintensionality
UR - https://doi.org/10.1093/logcom/exac089
N2 - The present paper provides a completeness proof for a system of higher-order logic framed within partial type theory. The framework is a modification of Tichý’s extension of Church’s simple type theory, equipped with his innovative natural deduction system in sequent style. The system deals with both total and partial (multiargument) functions-as-mappings and also accommodates algorithmic computations arriving at various objects of the framework. The partiality of a function or a failure of a computation is not represented by a postulated null object such as the third truth value. The logical operators of the system are classical. Another welcome feature of this expressive system is that its consequence relation is monotonic.
ER -
KUCHYŇKA, Petr and Jiří RACLAVSKÝ. Completeness in partial type theory. \textit{Journal of Logic and Computation}. Oxford, UK: Oxford University Press, 2024, vol.~34, No~1, p.~1-32. ISSN~0955-792X. Available from: https://dx.doi.org/10.1093/logcom/exac089.
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