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Diagram 1 represents my attempt to present the main components of classical predicate logic in a simple diagrammatic form. Diagram 1 is about logic, not in a particular logic, hence the term metalogical. This diagram is divided in into two sections, representing the syntax and semantics.

The taxonomic hierarchy represents is part-of relation, e.g. the symbols, syntax, and proof theory are part of a given logic.

The dotted horizontal line represent a dependency between components e.g. without syntax proof would not be possible.

The green line represents the correspondence between syntactic and model theoretic proof.

Diagram 1 (updated)

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Is this presentation reasonable? Should the domain of discourse be totally on the semantic side?

Patrick Browne
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    Maybe Formation rules are not at the level of formulas, because we use Formation rules to produce: *terms* (names) and *formulas* (phrases). And maybe you have to move "vdash" (the turnstile) under Inference rules, calling it Derivability. – Mauro ALLEGRANZA Mar 28 '22 at 14:56
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    In this way you can map Semantics on Syntax and Interpretation will map terms on objects of the Domain and sentences on "meaning" (truth values?). – Mauro ALLEGRANZA Mar 28 '22 at 14:57
  • @Mauro ALLEGRANZA Hopefully the updated diagram incorporates your suggestions. – Patrick Browne Mar 28 '22 at 19:22
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    1. You may wish to distinguish the logical symbols from the non-logical symbols (the signature). 2. The domain is usually considered to be part of the interpretation, rather than separate from it. – Bumble Mar 28 '22 at 23:41
  • @Bumble I have incorporated your suggestions in the updated diagram. – Patrick Browne Mar 29 '22 at 06:38

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