Constructive Sets with Non-binary Inclusion
نویسنده
چکیده
In this thesis we outline how to represent rough and fuzzy sets in intuitionistic type theory. The inherent meaning of such constructs are valuable when it comes to representing certainty in complex data structures to be used and reasoned on within the context of computer science. We ask fundamental questions regarding how to represent and understand non-binary inclusion within the constructive framework outlined by Martin-Löf and further illustrate the implied limitations and problems associated with the required high level of explicity. While it is possible to simulate non-countable collections, we concern ourselves with sets that are bijective to N as to showcase the design principle of representation; extendable to more complex collections.
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