A Calculus of Inconsistency I: Sentential Logic
逻辑
2007-05-23 v1
摘要
We describe a graph-theoretic syntax for self-referential formulas as well as a four-valued logic to include contradictory and independent formulas. We then explore the degree to which generalized truth tables can be realized in our theory, and go on to describe a model theory for sentential calculus, wherein models are allowed to include contradictions (such as the ``Liar'') and formulas that result from them as an integral part of their structure. This sets the groundwork for a sequel in which we construct models of set theory that include contradictions.
引用
@article{arxiv.math/0409034,
title = {A Calculus of Inconsistency I: Sentential Logic},
author = {Dan Seabold and Stefan Waner and Steve Warner},
journal= {arXiv preprint arXiv:math/0409034},
year = {2007}
}