Science

Mathematical Symbols

The symbol |- is used to mean 'implies'

What does the symbol |= mean?

mikeyp Sun 08/05/05 16:34

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QmunkE
Sun 08/05/05
22:25

Indeed, the implication symbols I know look like

=>

Perhaps the other one you have is meant to be:

<==> which is equivalence or "if and only if" ?

magicdice
Sun 08/05/05
22:59

QmunkE i thought <==> meant that they were mutually implicit?

QmunkE
Mon 09/05/05
08:13

Apologies, the <==> is the "is-equivalent-to" connective, but is not the same as "logical equivalence" unless p <==> q is a tautology.

(p => q) ^ (q => p) = (p <=> q)

mikeyp
Tue 10/05/05
00:14

Question Author

Thanks for your effort guys. Yeah => can mean implies too. Basically, I can't figure out what the symbol means. I think i've managed to do what I need to despite it. I'm revising for an exam, and this came up on one of the lecture slides. I reckon I can answer around it, should be fine!

magicdice
Tue 10/05/05
08:23

sorry we couldn't be any more help. good luck with your exam!

Peter Pedant
Wed 11/05/05
23:15

Sorry mikey I am a bit late on this.

The first one is a turnstyle, first used by Frege i think, and means implies when used with axioms.

the second sign is a double turnstyle and means = logically valid or equivalent

Both terms are in Boolos and Jeffrey, Intro to computability and logic 3rd edition

you cannot imagine my shock at seeing this question - considering what I usually see, it was totally unexpected

Peter Pedant
Wed 11/05/05
23:27

We're in the country called first order logic, Corby

Sorry MIke the double turnstyle means 'satisfies'. I will use ~ - no no I've seen how to do I=

U satisfies w with assignment s is written U I= w(s)

I= is not a part of a first order language but is used to describe things about the language, and so is said to be metalanguage. Yup that's it

You havent just picked up the book have you? you should start at page 1. Boolos and J is a bit of a hard read, howver the OU do an excellent course on it MST 384 I think - Number Theory and Computability and Logic

Peter Pedant
Tue 24/05/05
00:02

How did the exam go, and did it come up?

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