1994 WhatIsALogicalSystem

(Gabbay, 1994) ⇒ Dov M. Gabbay. (1994). “What is a Logical System?.” Oxford University Press. ISBN:0198538596

Subject Headings: Logical System.

Notes

This superb collection of papers focuses on a fundamental question in logic and computation: What is a logical system? With contributions from leading researchers-- including Ian Hacking, Robert Kowalski, Jim Lambek, Neil Tennent, Arnon Avron, L. Farinas del Cerro, Kosta Dosen, and Solomon Feferman- - the book presents a wide range of views on how to answer such a question, reflecting current, mainstream approaches to logic and its applications. Written to appeal to a diverse audience of readers, What is a Logical System? will excite discussion among students, teachers, and researchers in mathematics, logic, computer science, philosophy, and linguistics.

A consequence relation is a binary relation on finite sets of formulas, Δ and Γ written as Δ |~ Γ, satisfying certain conditions, namely reflexivity, monotonicity and cut.
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The notion of a proof system is not well defined in the literature. There are some recognized methodologies such as 'Gentzen formulations', 'tableaux', 'Hilbert style' but these are not sharply defined. For our purpose, let us agree that a proof system is any algorithmic system for generating |~ using rules of the form: … and 'axioms' of the form: … The axioms are the initial list of … So a proof system is a particular way of generating |~.
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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_|~).
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A logical system is a pair (|~, S_|~), where |~ is a structured-consequence, and S_|~ is an algorithmic system for it.

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
1994 WhatIsALogicalSystem	Dov M. Gabbay			What is a Logical System?			http://books.google.com/books?id=XqCu4XjHrIQC			1994