User:Jon Awbrey/Figures and Tables
Contents
Logical Graphs
Old Versions
Example 1
oo    o o o o o o   \       o o o o o o o o o   \/ \/ /    @ = @ = @ = @    oo    (()())(())() = (())(())() = (())() = ( )    oo 
Example 2
oooo  Object  Sign  Interpretant  oooo      Falsity  "(()())(())()"  "(())(())()"       Falsity  "(())(())()"  "(())()"       Falsity  "(())()"  "()"      oooo 
Example 3
oooo  Object  Sign  Interpretant  oooo      Falsity  "(()())(())()"  "(()())(())()"       Falsity  "(()())(())()"  "(())(())()"       Falsity  "(()())(())()"  "(())()"       Falsity  "(()())(())()"  "()"      oooo      Falsity  "(())(())()"  "(()())(())()"       Falsity  "(())(())()"  "(())(())()"       Falsity  "(())(())()"  "(())()"       Falsity  "(())(())()"  "()"      oooo      Falsity  "(())()"  "(()())(())()"       Falsity  "(())()"  "(())(())()"       Falsity  "(())()"  "(())()"       Falsity  "(())()"  "()"      oooo      Falsity  "()"  "(()())(())()"       Falsity  "()"  "(())(())()"       Falsity  "()"  "(())()"       Falsity  "()"  "()"      oooo 
Example 4
oooo  a  b  (a , b)  oooo      blank  blank  cross       blank  cross  blank       cross  blank  blank       cross  cross  cross      oooo 
Example 5
ooooo  a  b  c  (a, b, c)  ooooo       blank  blank  blank  cross        blank  blank  cross  blank        blank  cross  blank  blank        blank  cross  cross  cross        cross  blank  blank  blank        cross  blank  cross  cross        cross  cross  blank  cross        cross  cross  cross  cross       ooooo 
Example 6
ooooo  a  b  c  (a, b, c)  ooooo       o  o  o          o  o    o        o    o  o        o                o  o  o          o                o                       ooooo 
New Versions
Example 1
…
Example 2a
Example 2b



Example 3












Example 4



Example 5




Example 6




Semiotic Equivalence Relations


Fourier Analysis

Sign Relations
Combinators
Composer

Transposer

Figures
Example 1
Example 2
Example 3
Tables
Appendices
Syntax and Semantics of a Calculus for Propositional Logic
Table 1 collects a sample of basic propositional forms as expressed in terms of cactus language connectives.


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Futures Of Logical Graphs
Reflective Series • Variant 1
Reflective Series • Variant 2
Higher Order Propositions
Higher Order Propositions (n = 1)
Version 1
0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  
0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  
0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1  
0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1 
Version 2
1 0  
0 0  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  
0 1  0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  
1 0  0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1  
1 1  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1 
Interpretive Categories (n = 1)
Version 1
Measure  Happening  Exactness  Existence  Linearity  Uniformity  Information 
Nothing happens  
Just false  Nothing exists  
Just not  
Nothing is  
Just  
Everything is  is linear  
is not uniform  is informed  
Not just true  
Just true  
is uniform  is not informed  
Something is not  is not linear  
Not just  
Something is  
Not just not  
Not just false  Something exists  
Anything happens 
Version 2
Measure  Happening  Exactness  Existence  Linearity  Uniformity  Information 
Nothing happens  
Just false  Nothing exists  
Just not  
Nothing is  
Just  
Everything is  is linear  
is not uniform  is informed  
Not just true  
Just true  
is uniform  is not informed  
Something is not  is not linear  
Not just  
Something is  
Not just not  
Not just false  Something exists  
Anything happens 
Higher Order Propositions (n = 2)
Version 1
0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  
0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  
0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1  
0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 
Version 2

1100 1010 

0000  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  0  1  
0001  0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  0  0  1  1  
0010  0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1  0  0  0  0  1  1  1  1  
0011  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  0  0  0  0  0  0  0  0  
0100  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  
0101  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0110  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
0111  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
1000  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
1001  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
1010  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
1011  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
1100  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
1101  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
1110  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  
1111  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 
Minimal Negation Operators
Table 3 is a truth table for the sixteen boolean functions of type whose fibers of 1 are either the boundaries of points in or the complements of those boundaries.
How It Used To Look
How It Looks Now








Test 1








Test 2








Test 3








Templates for Logical Operators
Exclusive disjunction
Exclusive disjunction, also known as logical inequality or symmetric difference, is an operation on two logical values, typically the values of two propositions, that produces a value of true just in case exactly one of its operands is true.
An exclusive disjunction of propositions and may be written in various ways. Among the most common are these:
A truth table for appears below:
The exclusive disjunction of two variables belongs to the family of minimal negation operators. Thus, we have the following equivalents:
A logical graph for is shown below:
The traversal string of this graph is The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means
A Venn diagram for indicates the region where is true by means of a distinctive color or shading. In this case the region is two single cells, as shown below:
Logical conjunction
Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are true.
A logical conjunction of propositions and may be written in various ways. Among the most common are these:
A truth table for appears below:
A logical graph for is drawn as two letters attached to a root node:
Written as a string, this is just the concatenation The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means
A Venn diagram for indicates the region where is true by means of a distinctive color or shading. In this case the region is a single cell, as shown below:
Logical disjunction
Logical disjunction, also called logical alternation, is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are false.
A logical disjunction of propositions and may be written in various ways. Among the most common are these:
A truth table for appears below:
A logical graph for is shown below:
The traversal string of this graph is The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means
A Venn diagram for indicates the region where is true by means of a distinctive color or shading. In this case the region consists of three adjacent cells, as shown below:
Logical equality
Logical equality is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true.
A logical equality of propositions and may be written in various ways. Among the most common are these:
A truth table for appears below:
A logical graph for is shown below:
The traversal string of this graph is The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means
A Venn diagram for indicates the region where is true by means of a distinctive color or shading. In this case the region consists of two single cells, as shown below:
Logical implication
The concept of logical implication encompasses a specific logical function, a specific logical relation, and the various symbols that are used to denote this function and this relation. In order to define the specific function, relation, and symbols in question it is first necessary to establish a few ideas about the connections among them.
Close approximations to the concept of logical implication are expressed in ordinary language by means of linguistic forms like the following:

Here and are propositional variables that stand for any propositions in a given language. In a statement of the form the first term, is called the antecedent and the second term, is called the consequent, while the statement as a whole is called either the conditional or the consequence. Assuming that the conditional statement is true, then the truth of the antecedent is a sufficient condition for the truth of the consequent, while the truth of the consequent is a necessary condition for the truth of the antecedent.
Note. Many writers draw a technical distinction between the form and the form In this usage, writing asserts the existence of a certain relation between the logical value of and the logical value of whereas writing merely forms a compound statement whose logical value is a function of the logical values of and This will be discussed in detail below.
The concept of logical implication is associated with an operation on two logical values, typically the values of two propositions, that produces a value of false just in case the first operand is true and the second operand is false.
In the interpretation where and , the truth table associated with the statement symbolized as appears below:
A logical graph for is shown below:
The traversal string of this graph is The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means
A Venn diagram for indicates the region where is true by means of a distinctive color or shading. In this case the region is three adjacent cells, as shown below:
Logical NAND
Logical NAND (“Not And”) is an operation on two logical values, typically the values of two propositions, that produces a value of false if and only if both of its operands are true. In other words, it produces a value of true if and only if at least one of its operands is false.
A logical NAND of propositions and may be written in various ways. Among the most common are these:
A truth table for appears below:
A logical graph for is drawn as two letters attached to the free node of a rooted edge:
The traversal string of this graph is The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means
A Venn diagram for indicates the region where is true by means of a distinctive color or shading. In this case the region consists of three adjacent cells, as shown below:
Logical NNOR
Logical NNOR (“Neither Nor”) is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are false. In other words, it produces a value of false if and only if at least one of its operands is true.
A logical NNOR of propositions and may be written in various ways. Among the most common are these:
A truth table for appears below:
A logical graph for is shown below:
The traversal string of this graph is The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means
A Venn diagram for indicates the region where is true by means of a distinctive color or shading. In this case the region is a single cell, as shown below:
Logical negation
Logical negation is an operation on one logical value, typically the value of a proposition, that produces a value of true when its operand is false and a value of false when its operand is true.
A truth table for also written appears below:
The negation of a proposition may be found notated in various ways in various contexts of application, often merely for typographical convenience. Among these variants are the following:
bar  
tilde  
prime complement  
bang 
A logical graph for is shown below:
The traversal string of this graph is The proposition may be taken as a Boolean function having the abstract type where is interpreted in such a way that means and means
A Venn diagram for indicates the region where is true by means of a distinctive color or shading. In this case the region is a single cell, as shown below:
Symbol Renderings
NAND



NNOR


