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### what's the difference between Syntactic consequence ⊢ and Semantic consequence ⊨ [duplicate]

Can you help me to differentiate the Syntactic consequence $\vdash$ and Semantic consequence $\vDash$ ? I think $A \vdash B$ means, "$A$ proves $B$" and $A \vDash B$ means , if $A$ is true, then ...
570 views

### How can you derive a formula without premises? [duplicate]

What is the difference between $\vdash A$ and $\models A$? I'm not asking about the general difference between syntactic entailment and semantic entailment. I specifically don't understand the ...
202 views

### Semantical and syntactical derivation notation [duplicate]

What do the following two notations mean: $$A \models$$ $$A \vdash$$ The first one would be saying that A is a contradiction? The second one that A is not a theorem? That doesn't sound right to ...
548 views

### Difference between implies and "turnstile" symbols (→ and ⊢) [duplicate]

According to Wikipedia's list of logic symbols: A → B means A → B is false when A is true and B is false but true otherwise. ...