An exploration of formal reasoning through the lens of pixel precision and neon light. Every proposition mapped, every inference traced, every conclusion illuminated.
>_ formal systems rendered in 8px increments
The atomic units of logical reasoning. Every argument begins with a declarative statement that is either true or false -- never both, never neither.
>_ P, Q, RThe bridge from known to unknown. If the premises are true and the form is valid, the conclusion follows with the inevitability of gravity.
>_ P -> QThe simplest transformation. Every truth hides a falsehood; every falsehood, a truth. NOT inverts the world.
>_ NOT(A AND B)Two propositions that share the same truth value under all conditions. Logically indistinguishable yet semantically distinct -- the biconditional's elegant symmetry.
>_ P <-> QBegin with what you accept without proof. Axioms are the bedrock -- the starting position from which all deduction flows. Choose them wisely; everything depends on them.
Through valid inference, derive new truths from old. Each theorem stands on the shoulders of its axioms, a chain of reasoning forged link by careful link.
The chain holds. From axiom to theorem to conclusion, each step valid, each inference sound. The proof is not just correct -- it is beautiful.