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| | In [[modal logic]], the '''window operator''' <math>\triangle</math> is a [[modal operator]] with the following [[semantic]] definition: |
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| | <math>M,w\models\triangle\phi \iff \forall u, M,u\models\phi\Rightarrow Rwu</math> |
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| | for <math>M=(W,R,f)</math> a [[Kripke model]] and <math>w,u\in W</math>. Informally, it says that ''w'' "sees" every [[φ]]-world (or every φ-world is seen by ''w''). This operator is not definable in the basic modal logic (i.e. some propositional non-modal language together with a single primitive "necessity" (universal) operator, often denoted by '<math>\square</math>', or its existential dual, often denoted by '<math>\Diamond</math>'). Notice that its [[truth condition]] is the [[converse (logic)|converse]] of the truth condition for the standard "necessity" operator. |
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| | For references to some of its applications, see the References section. |
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| | == References == |
| | *{{cite book|last1=Blackburn|first1=P|last2=de Rijke|first2=M|last3=Venema|first3=Y|title=Modal Logic|publisher=Cambridge University Press|year=2002}} |
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| | [[Category:Logic]] |
| | [[Category:Modal logic]] |
Latest revision as of 19:35, 17 October 2013
Template:Orphan
In modal logic, the window operator is a modal operator with the following semantic definition:
for a Kripke model and . Informally, it says that w "sees" every φ-world (or every φ-world is seen by w). This operator is not definable in the basic modal logic (i.e. some propositional non-modal language together with a single primitive "necessity" (universal) operator, often denoted by '', or its existential dual, often denoted by ''). Notice that its truth condition is the converse of the truth condition for the standard "necessity" operator.
For references to some of its applications, see the References section.
References
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