Many-Valued Intuitionistic Implication and Inference Closure in a Bilattice-Based Logic

Authors:
Zoran Majkic
Affiliations:
UMIACS, University of Maryland, College Park, MD
Venue:
ISMVL '05 Proceedings of the 35th International Symposium on Multiple-Valued Logic
Year:
2005

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Abstract

In this paper we present a many-valued logic programming, based on reinterpreted Belnap's 4-valued bilattice: we introduce the new semantics for a 4-valued implication by relative pseudo-complement, used for intuitionistic logics. This kind of logic programming is particularly useful for data integration with possibly incomplete and inconsistent information.We define an ontological encapsulation of the epistemic many-valued logic programs with negation, based on this bilattice, into 2-valued meta logic programs. Obtained 2-valued logic semantically reflects original epistemic many-valued logic, and can be used in order to define many-valued logic entailment and inference closure for many-valued truth assignments.