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Axiomatics of Restricted Choices by Linear Orders of Sets with Minimum as Fallback

Created by
  • Haebom

Author

Kai Sauerwald, Kenneth Skiba, Eduardo Ferm e, Thomas Meyer

Outline

This paper explores how linear ordering can be used to implement a selection function with a restricted set of choices (a limited set of possible choices, not a complete subset). In restricted settings, constructing a selection function through relationships between alternatives is not always feasible. However, this paper demonstrates that a linear ordering of the alternative set can always construct a selection function, where the fallback value is encoded as the minimum element in the linear ordering. We present an axiom system for this selection function for the general case and for the case of union-closed input restrictions. Restricted choice structures have applications in knowledge representation and reasoning, and this paper discusses applications to theory change and abstract argumentation.

Takeaways, Limitations

Takeaways: We present a novel construction method (using linear ordering) for selection functions with limited choice sets and provide an axiom system for it. Its applications are likely to be in the fields of knowledge representation and reasoning, particularly theory change and abstract argumentation.
Limitations: There is a lack of detailed analysis of specific application cases. There is no analysis of the computational complexity of constructing selection functions using linear ordering, and there is a lack of review of the efficiency of applying it to real-world problems.
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