What question did this study set out to answer?

To introduce Relational Logic and Axiomatic Context as generalized mathematical frameworks that extend truth-value spaces to the extended real line and unify classical logical systems.

August 19, 2026Open Access

Relational Logic (RL) and Axiomatic Context (AC) : Extending the Boundaries of Boolean and Fuzzy Paradigms

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Authors

SYSermsak Yingsomsuk

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Implication

Mathematical modeling reveals extended real-number logic systems encompass classical paradigms, highlighting paraconsistent contradiction handling.

Key Points

To introduce Relational Logic and Axiomatic Context as generalized mathematical frameworks that extend truth-value spaces to the extended real line and unify classical logical systems.
Expanded truth-value domains from discrete sets and closed intervals to the extended real line using order comparisons rather than strict equality.
Formalized the Axiomatic Context framework using continuous scalar field theory, unbounded measure spaces, and algebraic decoupling proofs.
Demonstrated that classical Boolean logic and Zadeh's Fuzzy Logic are bounded sub-domains corresponding to {-1, +1} and [-1, 1], respectively.
Proved that the framework exhibits paraconsistency, absorbing contradictions as measurable dissonance signals without causing system-wide collapse.
Established that the non-associativity of signed composition operators is restricted to causal contextual transitions while field totalization remains globally convergent.

Cite This Study

Sermsak Yingsomsuk (2026) studied this question.

synapsesocial.com/papers/6a8563eb03308d306e2d74da https://doi.org/10.5281/zenodo.21979943

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Implication

Mathematical modeling reveals extended real-number logic systems encompass classical paradigms, highlighting paraconsistent contradiction handling.

Relational Logic (RL) and Axiomatic Context (AC) : Extending the Boundaries of Boolean and Fuzzy Paradigms

Discussion

Member takes

Implication

Key Points

Cite This Study

Relational Logic (RL) and Axiomatic Context (AC) : Extending the Boundaries of Boolean and Fuzzy Paradigms

Discussion

Member takes

Implication

Key Points

Cite This Study

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