The validity degree vectors of formulae in two-valued predicate logic

DOI

10.1080/18756891.2015.1063245How to use a DOI?

Keywords

two-valued predicate logic, -validity degree, validity degree vector, consistency theorem

Abstract

By means of infinite product of uniformly distributed probability spaces of cardinal , the concept of -validity degrees and validity degree vectors of formulae in two-valued predicate logic are introduced. It is proved that the validity degree vectors of formulae can preserve the logical relation between formulae. Moreover, a consistency theorem is obtained which says that the -validity degree () of the quantifierfree first-order formula without any repeated predicate symbols or terms is independent of the natural number , and is a constant equal to the validity degree () of the corresponding proposition 0 in classical propositional logic.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Xiaoyan Qin
AU  - Yang Xu
AU  - Yi Liu
PY  - 2015
DA  - 2015/09/01
TI  - The validity degree vectors of formulae in two-valued predicate logic
JO  - International Journal of Computational Intelligence Systems
SP  - 829
EP  - 840
VL  - 8
IS  - 5
SN  - 1875-6883
UR  - https://doi.org/10.1080/18756891.2015.1063245
DO  - 10.1080/18756891.2015.1063245
ID  - Qin2015
ER  -