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Theme One Program • Appendices

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Author: Jon Awbrey



Appendices

Table 1. 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.


Rooted Node.jpg
Rooted Edge.jpg
Cactus A Big.jpg
Cactus (A) Big.jpg
Cactus ABC Big.jpg
Cactus ((A)(B)(C)) Big.jpg
Cactus (A(B)) Big.jpg

Cactus (A,B) Big.jpg

Cactus ((A,B)) Big.jpg

Cactus (A,B,C) Big.jpg

Cactus ((A),(B),(C)) Big.jpg

Cactus (A,(B,C)) Big.jpg


Cactus (X,(A),(B),(C)) Big.jpg


Table A. Existential Interpretation

Table A illustrates the existential interpretation of cactus graphs and cactus expressions by providing English translations for a few of the most basic and commonly occurring forms.


Cactus Graph Node Big.jpg
Cactus Graph Spike Big.jpg
Cactus A Big.jpg
Cactus (A) Big.jpg

Cactus ABC Big.jpg

Cactus ((A)(B)(C)) Big.jpg

Cactus (A(B)) Big.jpg

Cactus (A,B) Big.jpg

Cactus ((A,B)) Big.jpg

Cactus (A,B,C) Big.jpg

Cactus ((A),(B),(C)) Big.jpg

Cactus (A,(B),(C)) Big.jpg


Table B. Entitative Interpretation

Table B illustrates the entitative interpretation of cactus graphs and cactus expressions by providing English translations for a few of the most basic and commonly occurring forms.


Cactus Graph Node Big.jpg
Cactus Graph Spike Big.jpg
Cactus A Big.jpg
Cactus (A) Big.jpg

Cactus ABC Big.jpg

Cactus ((A)(B)(C)) Big.jpg

Cactus (A)B Big.jpg

Cactus (A,B) Big.jpg

Cactus ((A,B)) Big.jpg

Cactus (A,B,C) Big.jpg

Cactus ((A,B,C)) Big.jpg

Cactus (((A),B,C)) Big.jpg


Table C. Dual Interpretations


Cactus Graph Node Big.jpg
Cactus Graph Spike Big.jpg
Cactus A Big.jpg
Cactus (A) Big.jpg
Cactus ABC Big.jpg
Cactus ((A)(B)(C)) Big.jpg
Cactus (A(B)) Big.jpg  
Cactus (A)B Big.jpg  
Cactus (A,B) Big.jpg
Cactus ((A,B)) Big.jpg
Cactus (A,B,C) Big.jpg

Cactus ((A),(B),(C)) Big.jpg

Cactus ((A,B,C)) Big.jpg

Cactus (((A),(B),(C))) Big.jpg

Cactus (A,(B),(C)) Big.jpg

 
Cactus (((A),B,C)) Big.jpg