These logics often require calculational devices quite distinct from propositional calculus. These sentences may contain quantifiers, unlike sentences of propositional logic. Variants of the theorem hold for other logics, such as propositional logic. However, alternative propositional logics are possible. "Commutativity" is a property of some logical connectives of truth functional propositional logic. Most reasoning systems implement variations of propositional and symbolic (predicate) logic. "Distributivity" is a property of some logical connectives of truth-functional propositional logic. "Associativity" is a property of some logical connectives of truth-functional propositional logic. The semantics of propositional logic rely on truth assignments. The question whether a sentence in propositional logic is satisfiable is a decidable problem. Mathematicians sometimes distinguish between propositional constants, propositional variables, and schemata. Our propositional calculus has eleven inference rules. Absorption is a valid argument form and rule of inference of propositional logic. A literal is a propositional variable or the negation of a propositional variable. The fundamental definition of a tautology is in the context of propositional logic.