Maths/CogSci/MathPsych lazyweb: Are there any algebras in which you have subtraction but don't have negative values? Pointers appreciated. I am hoping that the abstract maths might shed some light on a problem in cognitive modelling.
The context is that I am interested in formal models of cognitive representations and I want to represent things (e.g. cats), don't believe that we should be able to represent negated things (i.e. I don't think it should be able to represent anti-cats), but it makes sense to subtract representations (e.g. remove the representation of a cat from the representation of a cat and a dog, leaving only the representation of the dog).
Most of the Artificial Neural Net simulation research I have seen (say, at venues like NeurIPS) seems to take a very simple conceptual approach to analysis of simulation results - just treat everything as independent observations with fixed effects conditions, when it might be better conceptualised as random effects and repeated measures. Do other people think this? Does anyone have views on whether it would be worthwhile doing more complex analyses and whether the typical publication venues would accept those more complex analyses? Are there any guides to appropriate analyses for simulation results, e.g what to do with the results coming from multi-fold cross-validation (I presume the results are not independent across folds because they share cases).