Is the deducutive apparatus of a formal system necessarily a set of inference rules?

Question

In the book "Logic" by Paul Tomassi, the author uses the term deductive apparatus to refer to the set of inference rules in propositional logic and first-order logic. The use of this term seems to suggest a formal system may contain another kind of deductive apparatus besides a set of inference rules. Is this the case, or is a set of inference rules the only type of deductive apparatus and the term "deductive apparatus" is simply synonymous with "inference rules?" If indeed other types of deductive apparatuses exist, could someone name them and point me in a direction where I could learn more? Thanks!

Answer 1

On page $7$ of Metalogic: An Introduction to the Metatheory of Standard First Order Logic by Geoffrey Hunter, the deductive apparatus of a formal system consists of at least one of the following:

$(a)$ a non-empty set of axioms

$(b)$ a non-empty set of inference rules

I have found this text to be an excellent bridge into Metalogic after reading Logic by Paul Tomassi.

Answer 2

I am not sure what Tomassi has in mind when talking about 'formal systems' or 'deductive apparatus', but there are certainly ways to demonstrate that some claim or argument is deductively valid without the use of formal inference rules. For example: Truth-tables and truth trees (tableaux)