Difference between revisions of "Modal Logic"
From Wiki Notes @ WuJiewen.com, by Jiewen Wu
(→Syntax) |
(→Syntax) |
||
| Line 5: | Line 5: | ||
, | , | ||
| − | where p ranges over elements of <math>\,\Phi</math>. A dual operator of <math>\,\Box</math> is <math>\,\Diamond</math>: <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> |
==Semantics== | ==Semantics== | ||
Revision as of 13:24, 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>
