I have a doubt regarding the implications of Beckers' paper on abstractions. I am a lawyer by profession so I'm venturing pretty far afield here, and I hope my question will not be too trivial.
Given that every constructive abstraction is also a τ - abstraction, there must be some surjective function τU that is compatible with τ . Hence, for constructive abstractions, must there also be mappings τ1U,…,τnU such that, τU(→uL)=τ1U(→z1U)⋅…⋅τnU(→znU) , where →ziU is the projection of →uL onto the variables in →ZiU ? In other words, must there also be a partition of the low-level exogenous variables where each partition is mapped to a distinct high-level variable? I missed τU in the definition of constructive abstraction..
Thank you!
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Dear John Wentworth:
I have a doubt regarding the implications of Beckers' paper on abstractions. I am a lawyer by profession so I'm venturing pretty far afield here, and I hope my question will not be too trivial.
Given that every constructive abstraction is also a τ - abstraction, there must be some surjective function τU that is compatible with τ . Hence, for constructive abstractions, must there also be mappings τ1U,…,τnU such that, τU(→uL)=τ1U(→z1U)⋅…⋅τnU(→znU) , where →ziU is the projection of →uL onto the variables in →ZiU ? In other words, must there also be a partition of the low-level exogenous variables where each partition is mapped to a distinct high-level variable? I missed τU in the definition of constructive abstraction..
Thank you!