Automating Satisfiability Proofs for First-Order Logic
First-order logic can be used to aximatize essentially all of math, through set theory.
Goal: a procedure such that if is a first-order formula (or an enumerable sequence of formulas i.e. sequence where we can compute -the element for each ), then we can detect in finite amount of time the case when is unsatisfiable
- to prove is valid, we show is unsatisfiable
- to show that is true in an axiomatization given as an enumerable sequence , we check that the sequence ; is unsatisfiable
- given a well-defined mathematical statement, we can detect in finite amount of time if this statement follows from a well-defined set of axioms
Countable Models for Quantified First-Order Logic
Compactness Theorem for Propositional Logic