A
logical graphIn mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges...
is a special type of diagramatic structure in any one of several systems of graphical
syntaxIn logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them...
that Charles Sanders Peirce developed for
logicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
.
In his papers on
qualitative logic,
entitative graphAn entitative graph is an element of the graphical syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880's, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned...
s, and
existential graphAn existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote his first paper on graphical logic in 1882, and continued to develop the method until his death in 1914.-The graphs:...
s, Peirce developed several versions of a graphical
formalismIn logic, a formal system consists of a formal language together with a deductive system which consists of...
, or a graph-theoretic
formal languageA formal language is a set of words, i.e. finite strings of letters, symbols, or tokens. The set from which these letters are taken is called the alphabet over which the language is defined...
, designed to be interpreted for logic.
In the century since Peirce initiated this line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graph-theoretic structures.
Discussion
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A
logical graphIn mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges...
is a special type of diagramatic structure in any one of several systems of graphical
syntaxIn logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them...
that Charles Sanders Peirce developed for
logicLogic, from the Greek λογική is the art and science of reasoning. More specifically, it is defined by the Penguin Encyclopedia to be "The formal systematic study of the principles of valid inference and correct reasoning". As a discipline, logic dates back to Aristotle, who established its...
.
In his papers on
qualitative logic,
entitative graphAn entitative graph is an element of the graphical syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880's, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned...
s, and
existential graphAn existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote his first paper on graphical logic in 1882, and continued to develop the method until his death in 1914.-The graphs:...
s, Peirce developed several versions of a graphical
formalismIn logic, a formal system consists of a formal language together with a deductive system which consists of...
, or a graph-theoretic
formal languageA formal language is a set of words, i.e. finite strings of letters, symbols, or tokens. The set from which these letters are taken is called the alphabet over which the language is defined...
, designed to be interpreted for logic.
In the century since Peirce initiated this line of development, a variety of formal systems have branched out from what is abstractly the same formal base of graph-theoretic structures.
See also
- Charles Sanders Peirce bibliography
This Charles Sanders Peirce bibliography consolidates numerous references to Charles Sanders Peirce's writings, including letters, manuscripts, publications, and Nachlass...
- Conceptual graph
A conceptual graph is a notation for logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. In the first published paper on CGs, John F. Sowa used them to represent the conceptual schemas used in database systems...
- Laws of Form
Laws of Form is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and of philosophy...
- Minimal negation operator
In logic and mathematics, the minimal negation operator is a multigrade operator where each is a k-ary boolean function defined in such a way that if and only if exactly one of the arguments is 0....
- Peirce's law
Peirce's law in logic is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic.In propositional calculus, Peirce's law says that →P...
- Propositional calculus
In logic and mathematics, a propositional calculus or logic is a formal system in which formulae representing propositions can be formed by combining atomic propositions using logical connectives, and a system of formal proof rules allows certain formulae to be established as theorems.-...
- Truth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—to compute the functional values of logical expressions on each of their functional arguments, that is, on each combination of values taken by their...
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