Adequacy (logic)

In logic, adequacy denotes the property of a calculus to be complete and correct . Adequacy is a relationship between a semantically defined inference operator and a syntactically defined inference or derivability operator , which states that everything that can be syntactically inferred can also be inferred semantically, and vice versa: ${\displaystyle \models }$ ${\displaystyle \vdash }$

${\displaystyle \Gamma \models G\quad }$ exactly when ${\displaystyle \quad \Gamma \vdash G}$

This means that “the terms of provability and deducibility in the calculus coincide with the respective terms of general validity and logical conclusion”. Every tautology is then also a theorem , and vice versa.

Individual evidence

1. ↑ Hoyningen-Huene, Logic (1998), p. 270