TY - GEN
T1 - A minimal computational theory of a minimal computational universe
AU - Avron, Arnon
AU - Cohen, Liron
N1 - Publisher Copyright:
© Springer International Publishing AG 2018.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - In [3] a general logical framework for formalizing set theories of different strength was suggested. We here employ that framework, focusing on the exploration of computational theories. That is, theories whose set of closed terms suffices for denoting every concrete set (including infinite ones) that might be needed in applications, as well as for computations with sets. We demonstrate that already the minimal computational level of the framework, in which only a minimal computational theory and a minimal computational universe are employed, suffices for developing large portions of scientifically applicable mathematics.
AB - In [3] a general logical framework for formalizing set theories of different strength was suggested. We here employ that framework, focusing on the exploration of computational theories. That is, theories whose set of closed terms suffices for denoting every concrete set (including infinite ones) that might be needed in applications, as well as for computations with sets. We demonstrate that already the minimal computational level of the framework, in which only a minimal computational theory and a minimal computational universe are employed, suffices for developing large portions of scientifically applicable mathematics.
KW - Computational theories
KW - Computational universes
KW - Formalized mathematics
KW - Rudimentary set theory
UR - http://www.scopus.com/inward/record.url?scp=85039420508&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-72056-2_3
DO - 10.1007/978-3-319-72056-2_3
M3 - Conference contribution
AN - SCOPUS:85039420508
SN - 9783319720555
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 37
EP - 54
BT - Logical Foundations of Computer Science - International Symposium, LFCS 2018, Proceedings
A2 - Nerode, Anil
A2 - Artemov, Sergei
PB - Springer Verlag
T2 - International Symposium on Logical Foundations of Computer Science, LFCS 2018
Y2 - 8 January 2018 through 11 January 2018
ER -