Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences

Title: Fuzzy Truth Value Assignment for Collections of Self-Referential Sentences

Research Question: How can we assign consistent fuzzy truth values to collections of self-referential sentences, such as the Liar paradox, to resolve the inherent contradictions?

Methodology: The authors propose a fuzzy truth value assignment method for collections of self-referential sentences. They reduce the problem to solving a system of nonlinear equations. They prove that under mild conditions, there always exists a solution, and that the "mid-point" solution is consistent. They also present several algorithms for truth value assignment, arguing that these can be understood as generalized sequential reasoning.

Results: The authors provide several examples of self-referential collections, including the Liar and the Strengthened Liar, and solve the corresponding truth value equations analytically and/or numerically. They demonstrate that their method can consistently assign truth values to these collections, thereby resolving the paradoxes.

Implications: The authors' work has significant implications for the study of self-referential paradoxes. By using fuzzy logic, they provide a systematic approach to assigning truth values to self-referential sentences, which can help resolve the inherent contradictions. This work also contributes to the field of computational logic and artificial intelligence, as it may have applications in modeling and reasoning with ambiguous or uncertain information.

Link to Article: https://arxiv.org/abs/0309046v1 Authors: arXiv ID: 0309046v1