Non-deterministic Matrices in Action: Expansions, Refinements, and Rexpansions

The operations of expansion and refinement on nondeterministic matrices (Nmatrices) are composed to form a new operation called rexpansion. Properties of this operation are investigated, together with their effects on the induced consequence relations. A semantic method for obtaining conservative extensions of matrix-defined logics is introduced and applied to fragments of the classical two-valued matrix, as well as to other well-known many-valued matrices. The central application of rexpansion that we present is the construction of truth-preserving paraconsistent conservative extensions of Godel fuzzy logic.