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).
@RossGayler@Heterokromia@cogsci to me it seems you need to be more clear on your requirements. Are your non-negative and multidimensional requirements independent, as far as you can tell?
If so, a multidimensional (do you know how many dimensions/animals you have?) modulo space sounds a viable solution. That'd be something denoted as https://www.HostMath.com/Show.aspx?Code=%5Cmathbb%7BZ%7D_k%5En , with k being the cardinality of one dimension (would they need to have different cardinalities?), and n being the number of dimensions.
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