Formal System

AKA: Logical System.
Context:
- It can be
  - an Arithmetic Formal System.
  - a Set Formal System.
  - a Mathematical Formal System.
  - a Logic Formal System.
  - a Natural Language Formal System.
- It can have a Closed Form. ??
- It can be an Input to Simulation Task.
- It can have a degree of certainty (high to low). (e.g. Evolution Theory)
Example(s):
Counter-Example(s):
- a Model (that abides by some Formal System).
See: Formal Model, Scientific Theory, Mathematical Theorem, Logical Consequence Relation, Proof Theory.

References

(Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Formal_system Retrieved:2018-11-3.
- A formal system is the name of a logic system usually defined in the mathematical way. Logical calculus is carried out in the system. It can represent a well-defined system of abstract thought. Spinoza's Ethics imitates the form of Euclid's Elements. Spinoza employed Euclidean elements such as “axioms" or “primitive truths", rules of inferences, etc., so that a calculus can be built using these.
  Some theoristsuse the term formalism as a rough synonym for formal system, but the term is also used to refer to a particular styleof notation, for example, Paul Dirac's bra–ket notation.

(Gabbay, 1994) ⇒ Dov M. Gabbay. (1994). “What is a Logical System?." Oxford University Press. ISBN:0198538596
- The central role which proof theoretical methodologies play in generating logics compels us to put forward the view that a logical system is a pair (|~, S_|~), where S_|~ is a proof theory for |~. In other words, we are saying that it is not enough to know |~ to 'understand' the logic, but we must also know how it is presented (i.e. S_|~).
- A logical system is a pair (|~, S_|~), where |~ is a structured-consequence, and S_|~ is an algorithmic system for it.