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A '''logical graph''' is a [[graph theory|graph-theoretic]] structure in one of the systems of graphical [[syntax]] that [[Charles Sanders Peirce]] developed for [[logic]].
A '''logical graph''' is a [[graph theory|graph-theoretic]] structure in one of the systems of graphical [[syntax]] that [http://mywikibiz.com/Charles_Sanders_Peirce Charles Sanders Peirce] developed for [[logic]].
In his papers on ''[[qualitative logic]]'', ''[[entitative graph]]s'', and ''[[existential graph]]s'', Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.
In his papers on ''[[qualitative logic]]'', ''[[entitative graph]]s'', and ''[[existential graph]]s'', Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.
====C<sub>2</sub>. Generation theorem====
====C<sub>2</sub>. Generation theorem====
One theorem of frequent use goes under the nickname of the ''weed and seed theorem'' (WAST). The proof is just an exercise in mathematical induction, once a suitable basis is laid down, and it will be left as an exercise for the reader. What the WAST says is that a label can be freely distributed or freely erased anywhere in a subtree whose root is labeled with that label. The second in our list of frequently used theorems is in fact the base case of this weed and seed theorem. In LOF, it goes by the names of ''Consequence 2'' <math>(C_2)\!</math> or ''Generation''.
One frequently used theorem goes under the nickname of the ''weed and seed theorem'' (WAST). The proof is just an exercise in mathematical induction, once a suitable basis is laid down, and it will be left as an exercise for the reader. What the WAST says is that a label can be freely distributed or freely erased anywhere in a subtree whose root is labeled with that label. The second in our list of frequently used theorems is in fact the base case of this weed and seed theorem. In LOF, it goes by the names of ''Consequence 2'' <math>(C_2)\!</math> or ''Generation''.
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* [[George Spencer Brown|Spencer Brown, George]] (1969), ''[[Laws of Form]]'', George Allen and Unwin, London, UK.
* [[George Spencer Brown|Spencer Brown, George]] (1969), ''[[Laws of Form]]'', George Allen and Unwin, London, UK.
==See also==
==Related articles==
* [http://mywikibiz.com/Directory:Jon_Awbrey/Papers/Propositional_Equation_Reasoning_Systems Jon Awbrey, “Propositional Equation Reasoning Systems”]
==Related topics==
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* Shoup, Richard (ed.), [http://www.lawsofform.org/ Laws of Form Web Site]
* Shoup, Richard (ed.), [http://www.lawsofform.org/ Laws of Form Web Site]
** Spencer-Brown, George (1973), [http://www.lawsofform.org/aum/session1.html Transcript Session One], [http://www.lawsofform.org/aum/ AUM Conference], Esalen, CA.
** Spencer-Brown, George (1973), [http://www.lawsofform.org/aum/session1.html Transcript Session One], [http://www.lawsofform.org/aum/ AUM Conference], Esalen, CA.
==Translations==
* [http://pt.wikipedia.org/wiki/Grafo_l%C3%B3gico Grafo lógico], [http://pt.wikipedia.org/ Portuguese Wikipedia].
==Document history==
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
* [http://mywikibiz.com/Logical_graph Logical Graph], [http://mywikibiz.com/ MyWikiBiz].
* [http://www.getwiki.net/-Logical_Graph Logical Graph], [http://www.getwiki.net/ GetWiki].
* [http://www.wikinfo.org/index.php/Logical_graph Logical Graph], [http://www.wikinfo.org/ Wikinfo].
* [http://en.wikipedia.org/wiki/Logical_graph Logical Graph], [http://en.wikipedia.org/ Wikipedia].
[[Category:Artificial Intelligence]]
[[Category:Artificial Intelligence]]
