I just finished an article with the above title. Abstract below.
Since it hasn't yet been published, I put it in a temporary directory:
http://jfsowa.com/temp/diagram.pdf
Section 1 summarizes existential graphs in 4 pages, and Section 2
summarizes Common Logic and the Existential Graph Interchange Format
in another 3 pages. Those two sections are the prerequisites.
Anyone who is familiar with those topics can skip them or skim them.
But note that page 7 cites the Heterogeneous Tool Set (HeTS), which
includes theorem provers for Common Logic and its many subsets,
including first-order logic and Peirce's version of higher-order logic.
Since EGIF can express the full semantics of Common Logic, it can serve
as a bridge between EGs and many computational systems, including the
software for the Semantic Web.
Section 3 introduces the IKL extensions to Common Logic, which can
support Peirce's use of EGs to express metalanguage. These topics
are important for supporting the semantics of natural languages.
Section 4 is the longest (5 pages) and the most relevant to the
title. It begins with quotations by Peirce and others about
diagrammatic reasoning. It continues with Peirce's classification
of the sciences (which we have discussed on Peirce-L) and shows
how Peirce relates diagrammatic reasoning to that classification.
Pages 12 and 13 show how the operations of observation and
imagination, which Peirce discussed informally, can be stated
formally in terms of his rules of inference for EGs.
Formal proofs with the rules of observation and imagination
are possible with diagrams that are as precisely defined as
Euclid's. But informal reasoning can be done with any images.
There is a continuum from commonsense reasoning to the most
complex math, science, and engineering.
The references include some introductory and some more advanced
articles. Most of them have URLs.
John
______________________________________________________________________
Diagrammatic Reasoning With EGs and EGIF
John F. Sowa
Abstract. Diagrammatic reasoning dominated mathematics until algebraic
methods became popular in the 17th century. Although Peirce developed
the algebraic notation for predicate calculus in 1885, he kept searching
for a more iconic graph-based logic. In 1897, he developed existential
graphs (EGs), which have the full expressive power of the ISO standard
for Common Logic (CL). In the last two decades of his life, Peirce
wrote extensively about diagrammatic reasoning as a general theory and
EGs as the formal representation. They are two aspects of the same
theory. Peirce’s rules of inference for EGs can be generalized to any
notation for logic, linear or graphic. Two additional rules, which he
described informally, are observation and imagination. For precisely
defined diagrams, as in Euclid’s geometry, those operations can be
defined formally. To bridge the gap between algebra and diagrams, the
Existential Graph Interchange Format (EGIF) has a formal mapping to EGs
and to Common Logic. When the rules of observation and imagination are
defined in terms of EGIF, they enable any software developed for Common
Logic to be used in diagrammatic reasoning.
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