Abstract
AbstractThis paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions with a term forming operator. In the final section rules for I for negative free and classical logic are also mentioned.
Funder
Alexander von Humboldt-Stiftung
Publisher
Springer Science and Business Media LLC
Subject
History and Philosophy of Science,Logic
Reference26 articles.
1. Bencivenga, E., Free logics, in D. Gabbay, and F. Guenther, (eds.), Handbook of Philosophical Logic. Volume III: Alternatives to Classical Logic, Springer, Dortrecht, 1986, pp. 373–426.
2. Bostock, D., Intermediate Logic, Clarendon Press, Oxford, 1997.
3. Czermak, J., A logical calculus with definite descriptions, Journal of Philosophical Logic 3(3): 211–228, 1974.
4. Dummett, M., Frege. Philosophy of Language, 2 ed., Duckworth, London, 1981.
5. Fitting, M., and R. L. Mendelsohn, First-Order Modal Logic. Kluwer, Dordrecht, Boston, London, 1998.
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献