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

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

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...

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

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

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

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...

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...

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...

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

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

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

In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except...

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...

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

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

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

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

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

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

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

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

communicative. Thus Mentalese is best expressed through predicate and propositional calculus.[citation needed] Made up of discrete symbols; each symbol has a...

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

first two premises below: Deduction theorem Logical consequence Propositional calculus Robert L. Causey, Logic, sets, and recursion, Jones and Barlett...

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...

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