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

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

mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence...

logic, an atomic formula (also known as an atom or a prime formula) is a formula with no deeper propositional structure, that is, a formula that contains...

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

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

nested within an OR In classical logic each propositional formula can be converted to an equivalent formula that is in CNF. This transformation is based...

whole formula and after every universal quantifier. This procedure exactly reduces to the propositional translation whenever φ is propositional. Thirdly...

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

D))} , since an OR is nested within an AND In classical logic each propositional formula can be converted to DNF ... The conversion involves using logical...

negative literals, forming the body of the clause. A Horn formula is a propositional formula formed by conjunction of Horn clauses. Horn satisfiability...

to be a propositional formula we can also take ¬ {\displaystyle \neg } Φ to be a formula; if we take Φ and Ψ to be a propositional formulas we can also...

calculus. This is similar to a way of axiomatizing classical propositional logic. In propositional logic, the inference rule is modus ponens MP: from ϕ → ψ...

as a propositional formula in k {\displaystyle k} variables x 1 , . . . , x k {\displaystyle x_{1},...,x_{k}} , and two propositional formulas are logically...

of propositional logic correspond to equational theorems of Boolean algebra. Syntactically, every Boolean term corresponds to a propositional formula of...

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

particularization to the propositional case is easier to define. Given a propositional formula T {\displaystyle T} , its circumscription is the formula having only...

program is, from this point of view, alternative notation for the propositional formula p ∧ ¬ q → s . {\displaystyle p\land \neg q\rightarrow s.} If we...

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...

Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example, the propositional logic...

the positive propositional calculus, the questions of validity and satisfiability may be unrelated. In the case of the positive propositional calculus, the...

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

programming) – Representation of an argument in a function definition Propositional function Type signature – Defines the inputs and outputs for a function...

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

a term that does not contain any variables. Similarly, a ground formula is a formula that does not contain any variables. In first-order logic with identity...

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

theorems can be written in a completely symbolic form (e.g., as propositions in propositional calculus), they are often expressed informally in a natural...

closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition, something...

Skeptical entailment deciding whether a propositional default theory skeptically entails a propositional formula is Π 2 P {\displaystyle \Pi _{2}^{P}} -complete;...