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

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

Conditional quantifier Implicational propositional calculus Laws of Form Logical graph Logical equivalence Material implication (rule of inference) Peirce's...

inference), a logical rule of replacement Implicational propositional calculus, a version of classical propositional calculus that uses only the material conditional...

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

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

lambda calculus is closely related to the implicational fragment of propositional intuitionistic logic, i.e., the implicational propositional calculus, via...

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

logic, hypersequents, the calculus of structures, and bunched implication. Method of analytic tableaux Proof procedure Propositional proof system Resolution...

lambda calculus and the proofs of natural deduction. Below, the left-hand side formalizes intuitionistic implicational natural deduction as a calculus of...

1970, pp. 295–305) — (1950), On the System of Axioms of the Implicational Propositional Calculus (included in Łukasiewicz 1970, pp. 306–310) — (1938), On...

other logics avoid explosion: implicational propositional calculus, positive propositional calculus, equivalential calculus and minimal logic. The latter...

namely implication. In propositional calculus, Peirce's law says that ((P→Q)→P)→P. Written out, this means that P must be true if there is a proposition Q...

are propositions expressed in some formal system. An alternative form of hypothetical syllogism, more useful for classical propositional calculus systems...

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

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

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

logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each...

reasoning Logic gate Logical graph Peirce's law Probabilistic logic Propositional calculus Sole sufficient operator Strawson entailment Strict conditional...

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

in the simply typed lambda calculus with each natural-deduction proof in intuitionistic propositional logic. The calculus of constructions extends this...

falsity to propositions can be subject to fewer constraints. Intuitionistic logic Paraconsistent logic Implicational propositional calculus List of logic...

expressed in untyped lambda calculus, enriched by implicational propositional calculus. To cope with the lambda calculus's syntactic restrictions, m {\displaystyle...

truth-functional tautology or theorem of propositional logic. The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia...

converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q...

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...

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

the paradoxes of material implication. This fact counts strongly against beginning the treatment of the propositional calculus with the truth-table method...