# Monthly Archives: August 2020

## Survey of Theme One Program • 3

This is a Survey of blog and wiki posts relating to the Theme One Program I worked on all through the 1980s.  The aim was to develop fundamental algorithms and data structures for integrating empirical learning with logical reasoning.  I … Continue reading

## Animated Logical Graphs • 38

Re: Richard J. Lipton • Logical Complexity Of Proofs Three examples of propositional proofs in logical graphs using equational inference rules can be found at the following location. Propositional Equation Reasoning Systems • Exemplary Proofs Animated proofs of the three … Continue reading

## Survey of Animated Logical Graphs • 3

This is one of several Survey posts I’ll be drafting from time to time, starting with minimal stubs and collecting links to the better variations on persistent themes I’ve worked on over the years.  After that I’ll look to organizing … Continue reading

## Animated Logical Graphs • 37

Re: Richard J. Lipton • Logical Complexity Of Proofs Another dimension of proof style has to do with how much information is kept or lost as the argument develops.  For the moment let’s focus on classical deductive reasoning at the … Continue reading

## Animated Logical Graphs • 36

Re: Richard J. Lipton • Logical Complexity Of Proofs Dear Dick, You asked, “Is this measure, the logical flow of a proof, of any interest?” I was not sure how you define the measure of flow in a proof — … Continue reading

## Animated Logical Graphs • 35

Re: Richard J. Lipton • Logical Complexity Of Proofs The smoothest way I know to do propositional calculus is by using minimal negation operators as primitives, parsing propositional formulas into (painted and rooted) cactus graphs, and using the appropriate extension … Continue reading

## Mathematical Method • Discussion 7

Re: Ontolog Forum • Alex Shkotin Dear Alex, You raised the following point: AS: One important usage of a sign is as an element of a language, especially a formal one, i.e. with a formal grammar. For context you cited … Continue reading

## Mathematical Method • Discussion 6

Re: Ontolog Forum • Alex Shkotin Dear Alex, Thanks for the very apt segue from Jon Barwise — Modern mathematics might be described as the science of abstract objects, be they real numbers, functions, surfaces, algebraic structures or whatever.  Mathematical … Continue reading

## Animated Logical Graphs • 34

Re: Ontolog Forum • John Sowa Re: Peirce List • John Sowa Dear John, I can’t imagine why anyone would bother with Peirce’s logic if it’s just Frege and Russell in a different syntax, which has been the opinion I … Continue reading

## Mathematical Method • Discussion 5

Re: Ontolog Forum • Paul Tyson Dear Paul, “How We Think” is a topic for the descriptive science of psychology, and its ways are legion beyond definitive or exhaustive description. “How We Ought To Think” if we wish to succeed … Continue reading