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A nonempty carrier together with interpretations of every symbol in a first-order signature.
The signature and carrier are separate inputs; interpretations are additional data on that pair.
wp-structure-logicopenlogic-model-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Assign operations, relations, and constants of the prescribed arities.
Feed several structures into a construction junction and impose compatibility between them.
wp-structure-logicopenlogic-model-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Supply a structure in the same signature.
Feed several structures into a construction junction and impose compatibility between them.
wp-model-theoryopenlogic-model-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
The recursively defined satisfaction relation evaluates terms and formulas in a first-order structure after an interpretation of the nonlogical symbols and, for open formulas, a variable assignment are fixed.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
openlogic-model-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
A first-order structure whose signature has only function symbols (including constants as nullary operations) is exactly an -algebra.
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
wp-universal-algebranlab-universal-algebraburris-universal-algebra