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A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart

Abstract

Routley–Meyer semantics (RM-semantics) is defined for Gödel 3-valued logic G3 and some logics related to it among which a paraconsistent one differing only from G3 in the interpretation of negation is to be remarked. The logics are defined in the Hilbert-style way and also by means of proof-theoretical and semantical consequence relations. The RM-semantics is defined upon the models for Routley and Meyer’s basic positive logic B+, the weakest positive RM-semantics. In this way, it is to be expected that the models defined can be adapted to other related many-valued logics.

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Correspondence to Gemma Robles.

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Robles, G. A Routley–Meyer Semantics for Gödel 3-Valued Logic and Its Paraconsistent Counterpart. Log. Univers. 7, 507–532 (2013) doi:10.1007/s11787-013-0088-7

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Mathematics Subject Classification (2010)

  • Primary 03B47
  • Secondary 03B55
  • 03B50
  • 03B53

Keywords

  • Many-valued logics
  • Gödel 3-valued logic
  • Routley–Meyer semantics
  • Paraconsistent logics