A Calculus of Inconsistency I: Sentential Logic

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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.

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Logic

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http://salesiana.dossiersoluciones.com/handle/123456789/72349

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409034
 http://arxiv.org/abs/math/0409034

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arXiv