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Satisfaction relation

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Summary

The relation MβŠ¨Ο†M\models\varphi stating that a structure MM makes a formula or sentence Ο†\varphi true under a specified variable assignment when one is needed.

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First-order structureSatisfaction relation

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

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.

How to interpret this relation type

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.

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Satisfaction relationSemantic consequence

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Semantic consequence is defined by universal satisfaction: Ξ“βŠ¨Ο†\Gamma\models\varphi when every structure satisfying all sentences in Ξ“\Gamma also satisfies Ο†\varphi.

How to interpret this relation type

The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.

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