What question did this study set out to answer?

To introduce Relational Logic and Axiomatic Context as generalized mathematical frameworks that transcend Boolean and fuzzy logic by evaluating truth through order comparisons across the extended real number line.

August 16, 2026Open Access

Relational Logic and Axiomatic Context: Extending the Boundaries of Boolean and Fuzzy Paradigms

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Authors

SYSermsak Yingsomsuk

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Implication

Theoretical analysis reveals relational logic unifies classical and fuzzy paradigms over extended real numbers, highlighting paraconsistent handling of logical contradictions.

Key Points

To introduce Relational Logic and Axiomatic Context as generalized mathematical frameworks that transcend Boolean and fuzzy logic by evaluating truth through order comparisons across the extended real number line.
Expanded standard truth value spaces from discrete sets {0, 1} and closed intervals [0, 1] to the extended real number line.
Redefined logical evaluation criteria around relative order comparison rather than strict equivalence.
Demonstrated that classical Boolean logic and Zadeh's Fuzzy Logic function as bounded special cases within Relational Logic and Axiomatic Context.
Established paraconsistent properties within the system, allowing contradictions to register as measurable dissonance signals without causing systemic collapse.

Cite This Study

Sermsak Yingsomsuk (2026) studied this question.

synapsesocial.com/papers/6a817980f2fb91fc834acae3 https://doi.org/10.5281/zenodo.21935064

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Implication

Theoretical analysis reveals relational logic unifies classical and fuzzy paradigms over extended real numbers, highlighting paraconsistent handling of logical contradictions.

Relational Logic and Axiomatic Context: Extending the Boundaries of Boolean and Fuzzy Paradigms

Discussion

Member takes

Implication

Key Points

Cite This Study

Relational Logic and Axiomatic Context: Extending the Boundaries of Boolean and Fuzzy Paradigms

Discussion

Member takes

Implication

Key Points

Cite This Study

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