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Reports on Mathematical Logic

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No. 39

Gemma Robles, José M. Méndez and Francisco Salto

**MINIMAL
NEGATION IN THE TERNARY RELATIONAL SEMANTICS
**

A b s t r a c t. Minimal Negation is defined within the
basic positive relevance logic in the relational ternary semantics: *B*+.
Thus, by defining a number of subminimal negations in the *B*+
context, principles of weak negation are shown to be isolable. Complete ternary
semantics are offered for minimal negation in *B*+. Certain forms of
reductio are conjectured to be undefinable (in ternary frames) without extending
the positive logic. Complete semantics for such kinds of reductio in a properly
extended positive logic are offered.

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