Truth-trees, also known as analytic tableaux, are a method for testing logical validity and consistency. They systematically break down complex…
Skolem Normal Form (SNF) simplifies first-order logic by eliminating existential quantifiers. It replaces them with Skolem functions, ensuring only universal…
Skolemization is a crucial technique in first-order logic for eliminating existential quantifiers. It involves introducing Skolem functions to preserve logical…
Sequent calculus is a formal system representing logical deductions. It uses sequences of formulas before and after a turnstile, signifying…
The semantic tableau method is a systematic proof technique in logic. It employs a tree structure to analyze the truth…
Proof theory is a branch of mathematical logic focused on the structure and properties of mathematical proofs. It formalizes reasoning,…
The matrix is the quantifier-free part of a formula after it's converted to prenex normal form. It's the core propositional…
A theorem stating that if A implies B is provable, a formula C exists using only common symbols. Both A…
An effectively decidable theory is a formal system where an algorithm can definitively prove any statement as either true or…
A decision procedure is a systematic algorithm that determines if statements are theorems or non-theorems within a logical system. It…