The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes...

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

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

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

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

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...

This distinguishes it from propositional logic, which does not use quantifiers or relations;: 161  in this sense, propositional logic is the foundation of...

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

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...

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

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...

In propositional calculus and proof complexity a propositional proof system (pps), also called a Cook–Reckhow propositional proof system, is a system for...

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

rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions...

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

the modal μ-calculus (Lμ, Lμ, sometimes just μ-calculus, although this can have a more general meaning) is an extension of propositional modal logic (with...

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...

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...

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

to a General Theory of Elementary Propositions", extended his proof of the consistency of the propositional calculus (i.e. the logic) beyond that of Principia...

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,...

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

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

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

schemata and modus ponens, one can prove all tautologies of the propositional calculus. It can also be shown that no pair of these schemata is sufficient...

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

Propositional logic is not concerned with the concrete meaning of propositions other than their truth values. Key rules of inference in propositional...

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

Aristotelian syllogisms alone. Taking propositional logic as given, every formula in the monadic predicate calculus expresses something that can likewise...