theory-derivation

Definition

A theory-derivation is a tuple \(\left( \boldsymbol{I}, \boldsymbol{\Phi} \right)\)

Where:

  • \(\boldsymbol{I}\) is a finite collection of inference-rules,

  • \(\boldsymbol{\Phi}\) is a finite sequence of formulas \(\boldsymbol{\phi_1}, \boldsymbol{\phi_1}, \ldots, \boldsymbol{\phi_n}\) each of which is either an axiom schema, an axiom, a definition, or a propositional formula inferred from previous formula (including theorems of other theories being extended by this derivation) by one of the inference-rule in \(\boldsymbol{I}\).

Bibliography