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- AKA: Logical System.
- See: Formal Model, Scientific Theory, Mathematical Theorem, Logical Consequence Relation, Proof Theory.
- (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.
- (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.