Translating English to Logic

Mathematical Logic · Axiom Academy

LESSON Translating English to Logic Master the art of converting natural language statements into precise predicate logic formulas 1. Identifying Predicates in English Sentences A predicate is a property or relationship that can be true or false about objects. The first step in translation is identifying what properties and relationships your sentence discusses. Verbs: "is even", "divides", "loves", "is greater than" Adjectives: "prime", "red", "happy", "tall" Relational phrases: "is the parent of", "is between" 2. Choosing Appropriate Domains The domain of discourse (or universe) is the set of all objects we're considering. Choosing the right domain simplifies translations dramatically. Broad domain: Requires explicit predicates for object types Restricted domain: Simpler formulas, but must be clearly stated Translation: "All students work hard" can be expressed either way, but the restricted domain is simpler. 3. Translating "All", "Some", "None", "Not All" Quantifiers are the heart of predicate logic. Master these four fundamental patterns: "All A are B": Uses universal quantifier with implication "Some A are B": Uses existential quantifier with conjunction "No A are B": Universal quantification of negation "Not all A are B": Negation of universal statement 4. Handling "Only", "Unless", "Except" These tricky words require careful translation. They often reverse the direction of implication! "Only A are B" means "If B, then A" (reverses!)

This is the written version of the interactive lesson above. See the full Mathematical Logic course.