A Calculus of Inconsistency I: Sentential Logic

Details A Calculus of Inconsistency I: Sentential Logic A Calculus of Inconsistency I: Sentential Logic

2004-09-02

arxiv.org/abs/math/0409034v1

Mathematics

Logic

Scientific paper

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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