- Have you ever done any statistical analysis of data, or any of the statistical sciences such as the Theory of Error, Experimental Psychology, Thermodynamics, Quantum Theory? These handle what you are calling differential logic using probability distribution functions of various types over various knowledge domains. If you are heading toward logic based on vague or imprecise statements, then there is the well established science and application of Fuzzy Logic.
Yes, been there done that. On top of the usual theory courses in Probability and Statistics, Measure Theory, etc. contributing to a master’s in math (1980) and the canonical year of “Advanced Psychometrics”, really a quaint legacy term for what had long since morphed into statistical methods for experimental design and analysis, sine qua non for a master’s in psych (1989), there was a raft of short courses on statistical computing packages which always seemed to get me a lot more bucks for the head-banging than anything else as the years wore on.
- Survey of Differential Logic
- Survey of Theme One Program
- Theme One • A Program Of Inquiry
- Introduction • Program Overview and User Guide (pdf)
- Linear Topics • Differential Theory of Qualitative Equations (pdf)