PropositionalLogic

Propositional logic instantiates Popper’s Basis III: a formula’s atoms and connectives fix a truth table, and Basis III’s abstract deducibility becomes semantic entailment between formulas. Under this instance, conjunction, disjunction, and negation satisfy Popper’s own characterizing properties for a conjunction, a disjunction, and a classical negation.

• Formula
  • Difficulty: easy (3 definitions, 1 abbreviations, 0 lemmas, 0 theorems)
  • Examples: 0
  • Total complexity: 55
• FunctionalCompleteness
  • Difficulty: optional (7 definitions, 2 abbreviations, 8 lemmas, 0 theorems)
  • Examples: 0
  • Total complexity: 67189
• Sheffer
  • Difficulty: moderate (5 definitions, 0 abbreviations, 1 lemmas, 2 theorems)
  • Examples: 0
  • Total complexity: 18117
• Hilbert
  • Difficulty: optional (6 definitions, 0 abbreviations, 14 lemmas, 17 theorems)
  • Examples: 0
  • Total complexity: 34046
• Popper
  • Difficulty: hard (2 definitions, 0 abbreviations, 18 lemmas, 4 theorems)
  • Examples: 0
  • Total complexity: 22080
• Completeness
  • Difficulty: hard (1 definitions, 0 abbreviations, 7 lemmas, 1 theorems)
  • Examples: 0
  • Total complexity: 171273