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An Incompleteness Theorem via Abstraction
, 1996
"... ion Alan Bundy 1 , Fausto Giunchiglia 2;3 , Adolfo Villafiorita 4;5 and Toby Walsh 2;5 1. Mathematical Reasoning Group, Dept of AI, University of Edinburgh 2. Mechanized Reasoning Group, IRST 3. DISA, University of Trento 4. Istituto di Informatica, University of Ancona 5. Mechanized Re ..."
Abstract

Cited by 6 (4 self)
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ion Alan Bundy 1 , Fausto Giunchiglia 2;3 , Adolfo Villafiorita 4;5 and Toby Walsh 2;5 1. Mathematical Reasoning Group, Dept of AI, University of Edinburgh 2. Mechanized Reasoning Group, IRST 3. DISA, University of Trento 4. Istituto di Informatica, University of Ancona 5. Mechanized Reasoning Group, DIST, University of Genoa April 13, 1996 Abstract We demonstrate the use of abstraction in aiding the construction of an interesting and difficult example in a proof checking system. This experiment demonstrates that abstraction can make proofs easier to comprehend and to verify mechanically. To support such proof checking, we have developed a formal theory of abstraction and added facilities for using abstraction to the GETFOL proof checking system. 1 Introduction This paper describes an experiment in which we use abstraction to aid the construction of a simplified proof of Godel's first incompleteness theorem. We show that this use of abstraction makes the proof more ac...
A Many Sorted Natural Deduction
, 1994
"... The goal of this paper is to motivate and define yet another sorted logic, called SND. All the previous sorted logics which can be found in the Artificial Intelligence literature have been designed to be used in (completely) automated deduction. SND has been designed to be used in interactive theor ..."
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The goal of this paper is to motivate and define yet another sorted logic, called SND. All the previous sorted logics which can be found in the Artificial Intelligence literature have been designed to be used in (completely) automated deduction. SND has been designed to be used in interactive theorem proving. Because of this shift of focus, SND has been designed to satisfy three innovative design requirements; that is: it is defined on top of a natural deduction calculus, and in a way to be a definitional extension of such calculus; and it is implemented on top of its implementation. In turn, because of this fact, SND has various innovative technical properties; among them: it allows us to deal with free variables, it has no notion of wellsortedness and of wellsortedness being a prerequisite of wellformedness, its implementation is such that, in the default mode, the system behaves exactly as with the original unsorted calculus. The formal system presented here was originally defin...