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

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...

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...

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

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

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

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...

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

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...

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

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...

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

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

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

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

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

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...

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

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...

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

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

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

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...

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

function. The logical axioms of PRA are the: Tautologies of the propositional calculus; Usual axiomatization of equality as an equivalence relation. The...

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

simply the propositional calculus augmented by □, the rule N, and the axiom K. K is weak in that it fails to determine whether a proposition can be necessary...

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

disjunction Logical graph Negation Operation Peano–Russell notation Propositional calculus "2.2: Conjunctions and Disjunctions". Mathematics LibreTexts. 2019-08-13...