Implementation of FDE^→_cmi

logic_details(fdeCmi,
[fdeCmi,
 tvs(['$true','$both','$neither','$false']),
 dtvs(['$true','$both']),
 conns([('~'/1)-common_not,
        ('|'/2)-common_or,
        ('&'/2)-common_and,
        ('=>'/2)-cmi_implies])
]).

connective_table(common_not,[
['$true']    > '$false',
['$both']    > '$both',
['$neither'] > '$neither',
['$false']   > '$true']).

connective_table(common_or,[
['$true','$true']       > '$true',
['$true','$both']       > '$true',
['$true','$neither']    > '$true',
['$true','$false']      > '$true',
['$both','$true']       > '$true',
['$both','$both']       > '$both',
['$both','$neither']    > '$true',
['$both','$false']      > '$both',
['$neither','$true']    > '$true',
['$neither','$both']    > '$true',
['$neither','$neither'] > '$neither',
['$neither','$false']   > '$neither',
['$false','$true']      > '$true',
['$false','$both']      > '$both',
['$false','$neither']   > '$neither',
['$false','$false']     > '$false'
]).

connective_table(common_and,[
['$true','$true']       > '$true',
['$true','$both']       > '$both',
['$true','$neither']    > '$neither',
['$true','$false']      > '$false',
['$both','$true']       > '$both',
['$both','$both']       > '$both',
['$both','$neither']    > '$false',
['$both','$false']      > '$false',
['$neither','$true']    > '$neither',
['$neither','$both']    > '$false',
['$neither','$neither'] > '$neither',
['$neither','$false']   > '$false',
['$false','$true']      > '$false',
['$false','$both']      > '$false',
['$false','$neither']   > '$false',
['$false','$false']     > '$false'
]).

connective_table(cmi_implies,[
['$true','$true']       > '$true',
['$true','$both']       > '$both',
['$true','$neither']    > '$neither',
['$true','$false']      > '$false',
['$both','$true']       > '$true',
['$both','$both']       > '$both',
['$both','$neither']    > '$neither',
['$both','$false']      > '$false',
['$neither','$true']    > '$true',
['$neither','$both']    > '$true',
['$neither','$neither'] > '$true',
['$neither','$false']   > '$true',
['$false','$true']      > '$true',
['$false','$both']      > '$true',
['$false','$neither']   > '$true',
['$false','$false']     > '$true'
]).