Helmut, List, The bracket notation of the form (x1, x2, ..., xk) a text rendition of a "minimal negation operator" on k logical variables x1, x2, ..., xk. This is an operator which gives the result 1 (= true) if and only if exactly one of the k variables is 0 (= false).
So the 0-ary operator, or the empty form ( ), is equivalent to the constant 0 (= false) since there can't be just one variable false if there aren't any variables at all in the argument list. The 1-ary operator (x) means the same thing as "not x". The 2-ary operator (x, y) means the same thing as "x XOR y". And so on ... At any rate, this is how things are in the "existential interpretation". Here's a link to a brief article on minimal negation operators: https://oeis.org/wiki/Minimal_negation_operator Regards, Jon On 2/24/2020 3:35 PM, Helmut Raulien wrote:
Jon, List, does the comma mean having something in common, so "y XOR x" = "(y,x)" , meaning that something that is x cannot be y, so that it its not so, that "x" and "y" have anything in common? I was thinking about possibility and probability. Is it so, that possibility means "x OR NOT x", written ""x(x)" in entitative Graph, which would be written in EG and DPC like ((x)x): "NOT(NOT x AND x)". It implies that from x follows x (tautology). Probability is possibility with values (is that so?), and maybe with a time range for this possibility, so I was thinking how can you write probability in a calculus. Maybe like e.g. "dx" has the probability of one third to happen in one hour, one may write it like "d/h((1/3x) 2/3x) = d/3h((x)2x). Maybe this is completely wrong, I am not good with mathematics, but maybe something like that? Best, Helmut
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