A simple Henkin-style completeness proof for Gödel 3-valued logic G3
DOI:
https://doi.org/10.12775/LLP.2014.001Keywords
many-valued logic, Gödel 3-valued logic, bivalent under-determined and over-determined semanticsAbstract
A simple Henkin-style completeness proof for Gödel 3-valued propositional logic G3 is provided. The idea is to endow G3 with an under-determined semantics (u-semantics) of the type defined by Dunn. The key concept in u-semantics is that of “under-determined interpretation” (u-interpretation). It is shown that consistent prime theories built upon G3 can be understood as (canonical) u-interpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailment Logic.References
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