What does this research mean for the field?

Relational Logic (RL) and Axiomatic Context (AC) provide a generalized mathematical framework that embeds logical truth values into the extended real number line, encompassing Boolean and Fuzzy logic as bounded special cases while enabling paraconsistency. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

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 beyond discrete or bounded intervals to the extended real number line.

August 22, 2026Open Access

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

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Authors

SYSermsak Yingsomsuk

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Implication

Theoretical analysis reveals an unbounded relational logic framework across the extended real number line, indicating a continuous continuum capable of processing complex non-linear reasoning.

Key Points

To introduce Relational Logic and Axiomatic Context as generalized mathematical frameworks that extend truth value spaces beyond discrete or bounded intervals to the extended real number line.
Expanded truth value assignments and set memberships to the extended real number line using an order-theoretic comparison relation rather than strict equality.
Embedded logical structures into continuous scalar field theory and unbounded measure spaces using the Axiomatic Context Context-Field Total Magnitude.
Decoupled operational layers to ensure causal contextual state transitions operate alongside path-invariant and globally convergent spatial totalization.
Demonstrated that classical Boolean logic and Zadeh's Fuzzy Logic represent bounded sub-domains restricted to discrete and closed intervals within the generalized system.
Achieved paraconsistency, enabling the mathematical architecture to absorb logical contradictions as measurable dissonance signals without systemic collapse.

Cite This Study

Sermsak Yingsomsuk (2026) studied this question.

synapsesocial.com/papers/6a895eeeca7ade938187d179 https://doi.org/10.5281/zenodo.22014799

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Implication

Theoretical analysis reveals an unbounded relational logic framework across the extended real number line, indicating a continuous continuum capable of processing complex non-linear reasoning.

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

Discussion

Member takes

Implication

Key Points

Cite This Study

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

Discussion

Member takes

Implication

Key Points

Cite This Study

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