## Local consecuence in modal logic [closed]

which means the local consecuence? in a modal logic

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@ariel: You should explain more specifically what you would like to know about local consequence, and what your motivation is. mathoverflow.net/howtoask – Ed Dean Jan 18 2012 at 23:51
Hi ariel: I expect that your question will be closed soon. If you edit it into a good MO question, after having read carefully mathoverflow.net/howtoask, you should flag it for moderator attention and/or post a thread at meta.mathoverflow.net asking that it be reopened. – Theo Johnson-Freyd Jan 19 2012 at 3:20
For sure this is not a "research" question. You can find the definition, for instance, in plato.stanford.edu/entries/consequence-algebraic – boumol Jan 19 2012 at 9:25
The SEP entry is fine, but the original definition (which explains the terminology) is model-theoretic: a formula $\phi$ is a local consequence of a set of formulas $\Gamma$ if for every point $x$ in every Kripke model $W$, if $W,x\models\Gamma$, then $W,x\models\phi$. In contrast, $\phi$ is a global consequence of $\Gamma$ if for every model $W$: if $W,x\models\Gamma$ for every $x\in W$, then $W,x\models\phi$ for every $x\in W$. – Emil Jeřábek Jan 19 2012 at 11:33