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PREFACE
INTRODUCTION
Symbols of the Existential Graphs
Transformations in the Existential Graphs
The Continuity Interpretation
Chapter I
THE ALPHA SYSTEMS
1.1
The Set of Alpha Graphs
1.2
The Alpha Graphs and the WFFS of the CPC
1.3
Alpha as a Logic
1.31
Theorem generation in alpha
1.32
The logic alpha in the system
P
_{r}
1.33
The system
P
_{w}
in the logic alpha
Chapter II
THE BETA SYSTEM
2.1
The Set of Beta Graphs
2.2
The Beta Graphs and the WFFS of Classical Predicate Calculi
2.21
The systems
F
_{r}
and
F
_{w}
2.22
The translation function
f
¢
2.23
The translation function
g
¢
2.3
Beta as a Logic
2.31
Theorem generation in beta
2.32
The logic beta in the system
F
_{r}
2.33
The system
F
_{w}
in the logic beta
2.34
The completeness of beta
2.35
The intertranslatability of beta and the first-order calculus with identity
Chapter III.
THE GAMMA SYSTEMS
3.1
Remarks on on Some Standard Modal Systems
3.2
The Broken Cut Systems
3.21
Gamma-MR: Broken cuts with minimal restrictions
3.22
Gamma-4: A "classical" broken cut system
3.23
Gamma-4.2: Another "Lewis-modal" broken cut system
3.24
Gamma-5: The limiting "Lewis-modal" broken cut system
3.25
A summary of the broken cut systems here presented
3.3
Cleaning Up
APPENDIX -- The Deduction Theoerem in S4, S4.2, and S5
BIBLIOGRAPHY
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NOTES