List of equivalences
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<math> |
<math> |
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\begin{array}{rcccl} |
\begin{array}{rcccl} |
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| − | A &\linequiv& A \tens (A\orth\parr A) &\linequiv& (A\tens A\orth)\parr A \\ |
+ | A &\linequiv& A \tens (A\orth\parr A) &\linequiv& (A\tens A\orth)\parr A |
| − | & & A\parr A\orth &\linequiv& (A\parr A\orth)\tens(A\parr A\orth) |
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\end{array} |
\end{array} |
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</math> |
</math> |
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<math> |
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\begin{array}{rcl} |
\begin{array}{rcl} |
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| − | \zero &\linequiv& \oc{\zero} \\ |
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| − | \top &\linequiv& \wn{\top} \\ |
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| − | \\ |
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| − | \one &\linequiv& \oc{(A\orth\parr A)} \\ |
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| − | \bot &\linequiv& \wn{(A\orth\tens A)} \\ |
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| − | \\ |
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\oc{\wn{(\oc{A}\with\oc{B})}} &\linequiv& \oc{(\wn{\oc{A}}\with\wn{\oc{B}})} \\ |
\oc{\wn{(\oc{A}\with\oc{B})}} &\linequiv& \oc{(\wn{\oc{A}}\with\wn{\oc{B}})} \\ |
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\wn{\oc{(\wn{A}\plus\wn{B})}} &\linequiv& \wn{(\oc{\wn{A}}\plus\oc{\wn{B}})} |
\wn{\oc{(\wn{A}\plus\wn{B})}} &\linequiv& \wn{(\oc{\wn{A}}\plus\oc{\wn{B}})} |
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Revision as of 20:55, 27 July 2017
Each isomorphism gives an equivalence of formulas. The following equivalences are not isomorphisms.
Contents |
Multiplicatives
Additives
Quantifiers
Exponentials
Some of these equivalences are related with the lattice of exponential modalities.
Polarities
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(N negative) |
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(P positive) |
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(R regular) |
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(L co-regular) |
Second order encodings
Miscellaneous
