A paraconsistent 3-valued logic related to Godel logic G3

作者：Robles Gemma^*; Mendez Jose M

来源：Logic Journal of the IGPL, 2014, 22(4): 515-538.

DOI：10.1093/jigpal/jzt046

• Many-valued logic
• Godel 3-valued logic
• Bivalent under-determined and over-determined semantics
• paracon-sistent logics

The aim of the article is to introduce a paraconsistent logic, G3(L)(%26lt;), related to Godel 3-valued logic G3. In order to adequately explain G3(L)(%26lt;), the akin logics G3(L(FD)) and G3(L)(1) are also investigated. A Henkin-style completeness proof is provided for each one of these logics by endowing them with dually equivalent under-determined and over- determined bivalent semantics of the type defined by Dunn. G3(L(FD), G3(L)(1) and G3(L)(%26lt;) are related to %26apos;quasi relevant%26apos; logics such as R-Mingle or RM3, as well as to non-relevant logics such as Lukasiewicz L3 or some logics in the vicinity of intuitionistic logic. The logic G3(L)(%26lt;) belongs to the class of paraconsistent logics extending positive intuitionistic logic rather than positive classical logic.

• 出版日期2014-8