| MATERNA, Pavel. The Notion of Problem, Intuitionism and Partiality. Logic and logical philosophy. Torun, Poland: Nicholas Copernicus University Press, roč. 17, č. 17, s. 287-303. ISSN 1425-3305. 2008. |
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@article{871021,
author = {Materna, Pavel},
article_location = {Torun, Poland},
article_number = {17},
keywords = {abstract procedures; constructions; effective procedures; concepts; partiality},
language = {eng},
issn = {1425-3305},
journal = {Logic and logical philosophy},
title = {The Notion of Problem, Intuitionism and Partiality},
volume = {17},
year = {2008}
}
TY - JOUR
ID - 871021
AU - Materna, Pavel
PY - 2008
TI - The Notion of Problem, Intuitionism and Partiality
JF - Logic and logical philosophy
VL - 17
IS - 17
SP - 287-303
EP - 287-303
PB - Nicholas Copernicus University Press
SN - 14253305
KW - abstract procedures
KW - constructions
KW - effective procedures
KW - concepts
KW - partiality
N2 - Problems are defined as abstract procedures. An explication of procedures as used in Transparent Intensional Logic (TIL) and called constructions is presented and the subclass of constructions called concepts is defined. Concepts as closed constructions modulo alfa- and eta-conversion can be associated with meaningful expressions of a natural or professional language in harmony with Church's conception. Thus every meaningful expression expresses a concept. Since every problem can be unambiguously determined by a concept we can state that every problem is a concept and every concept can be viewed as a problem. Kolmogorov's idea of a connection between problems and Heyting's calculus is examined and the non-classical features of the latter are shown to be compatible with realistic logic using partial functions.
ER -
MATERNA, Pavel. The Notion of Problem, Intuitionism and Partiality. \textit{Logic and logical philosophy}. Torun, Poland: Nicholas Copernicus University Press, roč.~17, č.~17, s.~287-303. ISSN~1425-3305. 2008.
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