The 6 Axes of the Logic Spectrum

A comprehensive model adding dimensions of truth and inference. Axis 1: Formal-Informal. Axis 2: Classical-Nonclassical. Axis 3: Deductive-Inductive. Axis 4: Monotonic-Nonmonotonic. Axis 5: Bivalent-Many-Valued (two truth values vs. many). Axis 6: Truth-Preserving-Information-Preserving (logic keeps truth vs. logic keeps information). These six axes generate sixty-four logical positions. Relevance logic is formal, nonclassical, deductive, monotonic, bivalent, but demands relevance between premises and conclusion—it preserves relevance, not just truth. Fuzzy logic is formal, nonclassical, can be deductive or inductive, monotonic typically, many-valued (degrees of truth), truth-preserving (of degrees). The 6 Axes reveal that logical systems are designed for different goals—some prioritize certainty, others nuance, others relevance.

The 6 Axes of the Logic Spectrum "You want a logic that handles uncertainty. The 6 Axes ask: uncertainty as degrees of truth (fuzzy) or as probability (inductive)? Many-valued or probabilistic? Both are nonclassical, but they're different nonclassical. The axes help you choose the right tool, not just any tool labeled 'logic for uncertainty.'"

The 6 Axes of the Logic Spectrum by Dumu The Void February 25, 2026