What question did this study set out to answer?

The aim is to determine if the Hamilton product of quaternions can establish a non-commutative conjunction within a specific lattice framework.

April 16, 2026Open Access

Toward a Non-Commutative Residuated Lattice from Quaternion Multiplication

View Full Paper

Ask AI

Bookmark

The aim is to determine if the Hamilton product of quaternions can establish a non-commutative conjunction within a specific lattice framework.
Introduced the quaternionic G-lattice with component-wise min as monoidal operation.
Analyzed the Hamilton product's properties within the space V = [0,1] × [-1,1]^3.
Examined implications derived from quaternionic division and the compatibility with commutative restrictions.
Demonstrated the emergence of non-commutativity only in the full four-dimensional space.
Verified that the Hamilton product satisfies bilateral identity, annihilation, and associativity.
Showed that the product reduces to standard t-norm under commutative restrictions.
Identified four obstructions to compatible lattice orders within quaternionic structures.
Established a trilemma for any monoidal operation on V about the compatibility of associativity, non-commutativity, and lattice order.

Authors

No takes yet. Share an insight, caveat, or question.

Investigates the Hamilton product's role in non-commutative conjunction in quaternionic frameworks, highlighting implications for lattice structures.

J. Arturo Ornelas Brand (2026) studied this question.

View Full Paper

Ask AI

Bookmark

Investigates the Hamilton product's role in non-commutative conjunction in quaternionic frameworks, highlighting implications for lattice structures.