# Formal System

A Formal System is a formal specification of 1) a formal language and 2) a finite set of formal operations.

**AKA:**Logical System.**Context:**- It can be
- 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

### 2018

- (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.

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### 1994

- (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.

- 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 (|~,