Difference between revisions of "Modal Logic"
From Wiki Notes @ WuJiewen.com, by Jiewen Wu
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− | where p ranges over elements of <math>\,\Phi</math>. A dual operator of <math>\,\Box</math> is <math>\,\Diamond</math>: <math>\,\Diamond\phi\equiv\neg\Box\neg\phi</math> | + | where p ranges over elements of <math>\,\Phi</math>. A dual operator of <math>\,\Box</math> is <math>\,\Diamond</math>: <math>\,\Diamond\phi\equiv\neg\Box\neg\phi</math>. |
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+ | The basic temporal language is an extension to the basic modal logic. It is defined using a set of unary operators F and P. F<math>\phi</math> is interpreted as '<math>\,\phi will be true at some future time</math>', while p<math>\,\phi</math> means '<math>\,\phi</math> was true at some past time.' | ||
==Semantics== | ==Semantics== |
Revision as of 13:30, 5 November 2009
Syntax
The basic modal logic is defined using a set of propositional letters <math>\,\Phi</math>, and a unary operator <math>\,\Box</math>. A well-formed formula is then given by the rule
<math>\phi := p\mid\perp\mid\neg\phi\mid\phi\wedge\phi\mid\Box\phi</math> ,
where p ranges over elements of <math>\,\Phi</math>. A dual operator of <math>\,\Box</math> is <math>\,\Diamond</math>: <math>\,\Diamond\phi\equiv\neg\Box\neg\phi</math>.
The basic temporal language is an extension to the basic modal logic. It is defined using a set of unary operators F and P. F<math>\phi</math> is interpreted as '<math>\,\phi will be true at some future time</math>', while p<math>\,\phi</math> means '<math>\,\phi</math> was true at some past time.'