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Differential Propositional Calculus • Overview
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• Overview • Part 1 • Part 2 • Appendices • References •
A differential propositional calculus is a propositional calculus extended by a set of terms for describing aspects of change and difference, for example, processes taking place in a universe of discourse or transformations mapping a source universe to a target universe.
Casual Introduction
Cactus Calculus
Formal Development
Elementary Notions
Special Classes of Propositions
Linear Propositions
Positive Propositions
Singular Propositions
Differential Extensions
Appendices
Appendix 1. Propositional Forms and Differential Expansions
Table A1. Propositional Forms on Two Variables
Table A2. Propositional Forms on Two Variables
Table A3. Ef Expanded Over Differential Features
Table A4. Df Expanded Over Differential Features
Table A5. Ef Expanded Over Ordinary Features
Table A6. Df Expanded Over Ordinary Features
Appendix 2. Differential Forms
Table A7. Differential Forms Expanded on a Logical Basis
Table A8. Differential Forms Expanded on an Algebraic Basis
Table A9. Tangent Proposition as Pointwise Linear Approximation
Table A10. Taylor Series Expansion Df = df + d²f
Table A11. Partial Differentials and Relative Differentials
Table A12. Detail of Calculation for the Difference Map
Appendix 3. Computational Details
Operator Maps for the Logical Conjunction f8(u, v)
Computation of εf8
Computation of Ef8
Computation of Df8
Computation of df8
Computation of rf8
Computation Summary for Conjunction
Operator Maps for the Logical Equality f9(u, v)
Computation of εf9
Computation of Ef9
Computation of Df9
Computation of df9
Computation of rf9
Computation Summary for Equality
Operator Maps for the Logical Implication f11(u, v)
Computation of εf11
Computation of Ef11
Computation of Df11
Computation of df11
Computation of rf11
Computation Summary for Implication
Operator Maps for the Logical Disjunction f14(u, v)
Computation of εf14
Computation of Ef14
Computation of Df14
Computation of df14
Computation of rf14
Computation Summary for Disjunction
Appendix 4. Source Materials
Appendix 5. Various Definitions of the Tangent Vector
References
• Overview • Part 1 • Part 2 • Appendices • References •
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