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...tifiers, and formulas are built from propositional variables using logical connectives. In this context, a valuation begins with an assignment of a truth value to ...ation symbols. Formulas are built out of [[atomic formula]]s using logical connectives and quantifiers. A [[structure (mathematical logic)|structure]] consists o ...

...'''IMPLY gate''' is an informal digital [[logic gate]] that implements a [[logical conditional]]. ...it is equivalent to [[Material_conditional|material implication]], and the logical expression ¬A v B. ...

...sions. Logically, it is equivalent to [[material nonimplication]], and the logical expression A ∧ ¬B. {{Logical connectives}} ...

...countably]] many [[propositional variable]]s and the following primitive [[logical connective]]s: * '''Bottom''' <math>\bot</math> ([[nullary]] — a [[Logical constant|propositional constant]]); <math>0</math> or <math>\overline{0}</m ...

{{Short description|Range of application for a quantifier or connective in a logical formula}} In [[logic]], the '''scope''' of a [[Quantifier (logic)|quantifier]] or [[Logical connective|connective]] is the shortest formula in which it occurs,<ref nam ...

...=1991 |title=Logic, Language, and Meaning, Volume 2: Intensional Logic and Logical Grammar|publisher=University of Chicago Press |page=101}}</ref><ref>Grant, ...d by themselves were dubbed syncategorematic, (i.e., prepositions, logical connectives, etc.). [[Priscian]] in his ''Institutiones grammaticae''<ref>Priscian, ''I ...

{{Short description|Properties linking logical conjunction and disjunction}} {{Logical connectives sidebar}} ...

...diagram''' that represents the logical statement <math>P \lor Q</math> ([[Logical disjunction|disjunction]]).]] A '''Randolph diagram''' ('''R-diagram''') is a simple way to visualize logical expressions and combinations of sets. Randolph diagrams were created by mat ...

...es]]), and in the exact complete choice of axioms over the chosen basis of connectives. ...d negation <math>\{\to,\neg\}</math> as functionally complete set of basic connectives. Every logic system requires at least one non-nullary [[rule of inference]] ...

...order language are the [[Accessibility relation|accessible worlds]]. The [[logical connective]]s from [[propositional logic]] remain untouched and the modal o ...> is false but the whole formula is [[Vacuous truth|vacuously true]]: an [[Logical implication|implication]] is also true when the [[Antecedent (logic)|antece ...

...higher order logics one can define propositional connectives in terms of [[logical equivalence]] and quantifiers, in 1963 Henkin developed a formulation of '' ...put it, '''ST''' is "logic-free" in the sense that it contains no logical connectives or quantifiers in its formulae.<ref>P.T. Johnstone, ''Sketches of an elepha ...

...ath> are formulas, then <math>(\theta \and \xi)</math> is a formula (the [[logical conjunction|conjunction]] of <math>\theta</math> and <math>\xi</math>). It is possible to express the missing [[logical connectives]] in this language. For instance: ...

{{short description|Characteristic of some logical systems}} Completeness, as a quality of logical systems, is closely related to [[consistency]]. A formal system is consiste ...

...us]]), chosen to be as short as possible. For example, an axiom with six [[Logical NAND|NAND]] operations and three variables is equivalent to Boolean algebra where the vertical bar represents the NAND logical operation (also known as the [[Sheffer stroke]]). ...

Inquisitive propositions encode informational content via the region of logical space that their information states cover. For instance, the inquisitive pr ...opositions can be used to provide a semantics for the [[logical connective|connectives]] of [[propositional logic]] since they form a [[Heyting algebra]] when ord ...

* the [[logical connective|logical operators]] ¬ and ∨, and ...h as &lt;, &le;, =, &ge; or &gt;.{{clarify|reason=Since the set of logical connectives is chosen minimal (without e.g. \lor), the same could be done here. If time ...

{{Redirect|Logical implication|the binary connective|Material conditional}} ...provide accounts of the nature of logical consequence and the nature of [[logical truth]].<ref>[[Willard Van Orman Quine|Quine, Willard Van Orman]], ''Philos ...

...assertibles can be built up from simple ones through the use of [[logical connectives]]. The resulting syllogistic was grounded on five basic indemonstrable argu ...ars|2006|p=55}}</ref> To achieve a happy life—a life worth living—requires logical thought.<ref name="shenefeltwhite74"/> The Stoics held that an understandin ...

...metimes also been used to denote logic systems with a restricted number of connectives. [[logical implication|implication]] <math>\to</math>, ...

...ure]] consisting of only the equality relation symbol, and includes no non-logical axioms at all.<ref>{{Cite book| last1=Monk | first1=J. Donald | title=Mathe ...ex formulas can be built as usual in first-order logic using propositional connectives such as <math>\land, \lor, \lnot</math> and quantifiers <math>\forall,\exi ...