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A Calculus of Inconsistency I: Sentential Logic | | Dan Seabold
; Stefan Waner
; Steve Warner
; | | Date: |
2 Sep 2004 | | Subject: | Logic | math.LO | | Abstract: | 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. | | Source: | arXiv, math.LO/0409034 | | Services: | Forum | Review | PDF | Favorites | |
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