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{{About|the rule of inference|the formula of absolute truth|Tautology (logic)|other uses|Tautology (disambiguation)}} ...and [[Logical conjunction|conjunctions]] when they occur in [[formal proof|logical proofs]]. They are: ...

......, <math>P_n</math>) in a [[formal proof|proof]] with respect to some [[logical system]] if one is [[Validity (logic)|validly]] able to introduce the propo ...opositions (<math>P_1</math>, <math>P_2</math>, ..., <math>P_n</math>) the truth table also assigns "T" to <math>Q</math>. ...

...alue]]s to [[propositional variable]]s, with a corresponding assignment of truth values to all [[propositional formula]]s with those variables. ...rpretation (logic)|interpretation]]) and the corresponding assignment of a truth value to each sentence in the language for that structure (the valuation pr ...

...ath>P</math> and <math>Q</math>. The rule makes it possible to introduce [[Logical conjunction|conjunctions]] to [[formal proof|proofs]]. It is called the law ...ic consequence]] of <math>(P \rightarrow Q)</math> in some [[formal system|logical system]]; ...

...8), pp. 338–353.</ref> whose [[membership function]]s are defined by the [[truth value]] of a fuzzy [[propositional function]].<ref>Zimmermann, H.-J. (2000) ...math>. Here, <math display="inline">\tilde{T}</math> is the set of fuzzy [[truth value]]s, i.e., the [[unit interval]] <math display="inline">[0,1]</math>. ...

...).</ref> but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by ...'' of an argument can be tested, proved or disproved, and depends on its [[logical form]].<ref name=":0" /> ...

...ements having conditional [[consequent]]s and vice versa in [[formal proof|logical proofs]]. It is the rule that: ...c equivalent]] of <math>((P \land Q) \to R)</math> in some [[formal system|logical system]]; ...

...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 ...

...or "is stronger than".<ref>{{cite book |last=Nederpelt |first=Rob |title=Logical Reasoning: A First Course |publisher=King's College Publications|year=2004| ...the single-barred [[turnstile (symbol)|turnstile]] symbol which denotes [[logical consequence#Syntactic consequence|syntactic consequence]]. ...

...n [[Information retrieval]]. This formalization is a [[logical consequence|logical implication]] with an attached measure of uncertainty. ...certainty]] of a document ''d'' to a query ''q'' be the probability of its logical implication, i.e.: ...

...=1991 |title=Logic, Language, and Meaning, Volume 2: Intensional Logic and Logical Grammar|publisher=University of Chicago Press |page=101}}</ref><ref>Grant, ...not stand by themselves were dubbed syncategorematic, (i.e., prepositions, logical connectives, etc.). [[Priscian]] in his ''Institutiones grammaticae''<ref>P ...

...amut |date=1991 |title= Logic, Language and Meaning: Intensional Logic and Logical Grammar |publisher= University of Chicago Press |pages=245–249 |isbn=0-226- ...valuating the truth of the [[determiner phrase]] as a whole. For instance, truth of the first sentence above does not depend on which biting non-aardvarks e ...

* ({0,1}, ∧) (where "∧" is the [[logical connective]] "[[Logical conjunction|and]]"), or equivalently the set {0,1} under multiplication: th ...ub>" is "addition modulo 2"), or equivalently ({0,1}, ⊕) (where "⊕" is the logical connective "[[exclusive or|xor]]"), or equivalently the set {−1,1} under mu ...

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

{{Logical connectives sidebar}} ...eir logical variables]].<ref>{{harvnb|Enderton|2001}}</ref> In particular, truth tables can be used to show whether a propositional expression is true for a ...

{{short description|Many-valued logic in which truth values comprise a continuous range}} ...edLogic.html}}</ref> and is an example of [[finite-valued logic]] in which truth values are discrete, rather than continuous. Infinite-valued logic comprise ...

...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 ...

...n [[Matrix (mathematics)|matrix algebra]]. Vector logic assumes that the [[truth value]]s map on [[Vector (mathematics and physics)|vectors]], and that the ...false]]''. A two-valued vector logic requires a correspondence between the truth-values ''true'' (t) and ''false'' (f), and two ''q''-dimensional normalized ...

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

*<math>+</math> is [[logical disjunction|disjunction]] (logical "or"). *<math>\cdot</math> is [[logical conjunction|conjunction]] (logical "and"). ...