Non provable formulas

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(First list of non provable formulas.)
 
(Added some exponential cases (in relation with the Lattice of exponential modalities))
 
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<math>(A\tens B)\parr C \not\limp A\tens (B\parr C)</math>
 
<math>(A\tens B)\parr C \not\limp A\tens (B\parr C)</math>
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<math>A \not\limp \oc{A}</math>
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<math>\oc{\wn{\oc{A}}} \not\limp A</math>
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<math>\oc{\wn{\oc{A}}} \not\limp \oc{A}</math>
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<math>\oc{\wn{A}} \not\limp \wn{\oc{A}}</math>
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<math>\wn{\oc{A}} \not\limp \oc{\wn{A}}</math>

Latest revision as of 16:21, 31 August 2012

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A \with (B\plus C) \not\limp (A\with B)\plus (A\with C)

(A\plus B)\with (A\plus C) \not\limp A\plus (B\with C)

(A\tens B)\parr C \not\limp A\tens (B\parr C)

A \not\limp \oc{A}

\oc{\wn{\oc{A}}} \not\limp A

\oc{\wn{\oc{A}}} \not\limp \oc{A}

\oc{\wn{A}} \not\limp \wn{\oc{A}}

\wn{\oc{A}} \not\limp \oc{\wn{A}}

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