The propositional calculus is a branch of logic. It is also called (first-order) propositional logic, statement logic, sentential calculus, sentential...

the much simpler rules of propositional calculus. In a typical argument, quantifiers are eliminated, then propositional calculus is applied to unquantified...

those built up from propositional variables using Boolean operations. Instantiation is still possible within propositional calculus, but only by instantiating...

false) of a truth function. Propositional variables are the basic building-blocks of propositional formulas, used in propositional logic and higher-order logics...

mathematical logic, the implicational propositional calculus is a version of classical propositional calculus that uses only one connective, called implication...

propositional logic, a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula...

following Hilbert-style calculus. This is similar to a way[broken anchor] of axiomatizing classical propositional logic. In propositional logic, the inference...

Two key uses of formulas are in propositional logic and predicate logic. A key use of formulas is in propositional logic and predicate logic such as...

needed] In relation to the mind, propositions are discussed primarily as they fit into propositional attitudes. Propositional attitudes are simply attitudes...

{\displaystyle {\frac {\neg \neg P}{P}}} or as a tautology (plain propositional calculus sentence): P → ¬ ¬ P {\displaystyle P\to \neg \neg P} and ¬ ¬ P...

in connection with the classical propositional logic and with the so-called protothetic or quantified propositional logic; in both cases the law of non-contradiction...

other expressions. Propositional and predicate calculi are examples of formal systems. The formation rules of a propositional calculus may, for instance...

formal language for classical propositional logic can be expressed using just negation (¬), implication (→) and propositional symbols. A well-known axiomatization...

logic is called complete.[citation needed] The completeness of the propositional calculus was proved by Paul Bernays in 1918[citation needed] and Emil Post...

Implicational propositional calculus Laws of Form Logical graph Logical equivalence Material implication (rule of inference) Peirce's law Propositional calculus Sole...

refutation-complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution...

the last 2000 years, with the propositional Stoic logic. The two were sometimes seen as irreconcilable. Leibniz's calculus ratiocinator can be seen as foreshadowing...

W. M. "Propositional logic" (PDF). It describes (among others) a specific Hilbert-style proof system (that is restricted to propositional calculus)....

This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order...

then, the negation of a propositional function's existential quantification is a universal quantification of that propositional function's negation; symbolically...

valid formulas of propositional logic. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing...

co-NP complete. In the case of classical propositional logic, satisfiability is decidable for propositional formulae. In particular, satisfiability is...

1938, Zuse discovered that the calculus he had independently devised already existed and was known as propositional calculus.: 3  What Zuse had in mind,...

as argument are usually given by truth tables. Truth-functional propositional calculus is a formal system whose formulae may be interpreted as either true...

be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective ∨ {\displaystyle \lor } can be used to...

specified – see § Propositional inference rules (Suppes–Lemmon style). This section defines the formal syntax for a propositional logic language, contrasting...

In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation...

Hilbert-style deductive systems for propositional logics. Classical propositional calculus is the standard propositional logic. Its intended semantics is...

expression from premises Propositional calculus, specifies the rules of inference governing the logic of propositions Predicate calculus, specifies the rules...

which can be either true (1), or false (0). In a classical propositional calculus, each proposition will be assigned a truth value of either true or false...