diff --git a/work_files/verum-nimply_logic.md b/work_files/verum-nimply_logic.md new file mode 100644 index 000000000..ff39d89a6 --- /dev/null +++ b/work_files/verum-nimply_logic.md @@ -0,0 +1,54 @@ +# Verum-Nimply Logic + +Verum-Nimply Logic is a logic system built upon a two gates which are functionally complete. + +## Atoms +### Verum (⊤) +Verum is a logic-gate modelling of the "Signal Source". +| Output | +|----| +| 1 | + +### Falsum (⊥) +Verum is a logic-gate modelling of the "Lack of Signal" or "No Connection". +| Output | +|----| +| 0 | + +### Nimply (↛) +Nimply is a logic-gate modelling of the "Signal Blocker". + +The source signal is connected to the Collector, and the blocking signal is connected to the Gate. The Nimply gate is not commutative. + +This document will use the convention where the Collector is placed on the lefthand side. + +| Collector | Gate | Emitter | +| ---- | ---- | ---- | +| 0 | 0 | 0 | +| 0 | 1 | 0 | +| 1 | 0 | 1 | +| 1 | 1 | 0 | + +## Derivations + +### Diode += (p ↛ ⊥) + +### NOT p += (⊤ ↛ p) + +### p AND q += (p ↛ (NOT q)) += (p ↛ (⊤ ↛ q)) + +### p NAND q += NOT (p AND q) += NOT (p ↛ (⊤ ↛ q)) += (⊤ ↛ (p ↛ (⊤ ↛ q))) + +### p OR q += NOT ( NOT(p) AND NOT(q) ) += NOT ( (⊤ ↛ p) AND (⊤ ↛ q) ) += NOT ( ( (⊤ ↛ p) ↛ (⊤ ↛ (⊤ ↛ p)) ) ) += (⊤ ↛ ( ( (⊤ ↛ p) ↛ (⊤ ↛ (⊤ ↛ p)) ) )) +Note: For the most cases, an OR gate can be substituted using merging wires and diodes.