MHB What is the meaning of consequence in logic?

Thread starter hossam killua
Start date Nov 12, 2014
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Logic

Nov 12, 2014

hossam killua

what is the defintion of consequence in logic

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Nov 13, 2014

Evgeny.Makarov

Gold Member

MHB

There are a couple of different kinds. You can look at material implication and logical consequence. (In my experience, though, most textbooks use the latter term to refer to what the article calls semantic consequence.)

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

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