Difference between revisions of "Modal Logic"
From Wiki Notes @ WuJiewen.com, by Jiewen Wu
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<math>\phi := p\mid\perp\mid\neg\phi\mid\phi\wedge\phi\mid\Box\phi</math> | <math>\phi := p\mid\perp\mid\neg\phi\mid\phi\wedge\phi\mid\Box\phi</math> | ||
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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>\,\Daimond\phi\equiv\neg\Box\neg\phi</math> | ||
==Semantics== | ==Semantics== |
Revision as of 13:23, 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>\,\Daimond\phi\equiv\neg\Box\neg\phi</math>