The 12 Axes of the Logic Spectrum

An ultra-fine-grained model adding dimensions of paraconsistency, relevance, and computation. Building on the 8 Axes, we add: Axis 9: Explosive-Paraconsistent (contradiction entails everything vs. contradictions can be contained). Axis 10: Relevant-Irrelevant (premises must be relevant to conclusion vs. relevance not required). Axis 11: Computational-Noncomputational (logic has effective decision procedure vs. undecidable). Axis 12: Static-Dynamic (logic of static propositions vs. logic of change/action). These twelve axes generate 4096 logical positions. Paraconsistent logic is formal, nonclassical, deductive, monotonic or nonmonotonic, bivalent or many-valued, truth-preserving, any order, extensional or intensional, paraconsistent (non-explosive), can be relevant or not, often decidable, static typically. Dynamic logic is formal, nonclassical, deductive, monotonic, bivalent, truth-preserving, higher-order, intensional, explosive, relevant-ish, decidable often, dynamic (explicitly about change). The 12 Axes reveal that logical pluralism isn't optional—different problems require different logical tools, and the axes help you find the right one.

The 12 Axes of the Logic Spectrum "You want a logic for contradictions in legal reasoning. The 12 Axes ask: explosive (standard logic) would destroy everything. Paraconsistent contains them. Relevant ensures the contradiction matters. Dynamic handles changing laws. Twelve axes, twelve design choices. Your 'simple logic' is just the one you're used to—not the one you need."

by Dumu The Void February 25, 2026