Is is that a common way to present a proof system in the field of Logic and Automated Reasoning is to present a system of inference rules, without having to formally describe a particular algorithm or procedure to find proofs in this system?I notice that phenomenon in both textbook as well as conference or journal papers of this field.This can be seen in classic topics like: the Natural Deduction calculus, Hilbert calculus where only inference rules is presented.In modern researches, I am studying about Separation Logic, thus, I would like to take some papers from this field to illustrate this observation:Automated Cyclic Entailment Proofs in Separation LogicSymbolic Execution with Separation Logic
Why do presenttations of proof systems in logic and automated reasoning not include the algorithm that finds proofs?
logic;automated theorem proving