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Proving FirstOrder Equality Theorems with HyperLinking
, 1995
"... Lee and Plaisted recently developed a new automated theorem proving strategy called hyperlinking. As part of his dissertation, Lee developed a roundbyround implementation of the hyperlinking strategy, which competes well with other automated theorem provers on a wide range of theorem proving p ..."
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Lee and Plaisted recently developed a new automated theorem proving strategy called hyperlinking. As part of his dissertation, Lee developed a roundbyround implementation of the hyperlinking strategy, which competes well with other automated theorem provers on a wide range of theorem proving problems. However, Lee's roundbyround implementation of hyperlinking is not particularly well suited for the addition of special methods in support of equality. In this dissertation, we describe, as alternative to the roundbyround hyperlinking implementation of Lee, a smallest instance first implementation of hyperlinking which addresses many of the inefficiencies of roundbyround hyperlinking encountered when adding special methods in support of equality. Smallest instance first hyperlinking is based on the formalization of generating smallest clauses first, a heuristic widely used in other automated theorem provers. We prove both the soundness and logical completeness of smallest instance first hyperlinking and show that it always generates smallest clauses first under
Historical Projects in Discrete Mathematics and Computer Science
"... A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itse ..."
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A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development
On Coquand's "An Analysis of Girard's Paradox"
"... In his paper "An Analysis of Girard's Paradox" [3], Coquand presents a result of Girard that minimal higherorder logic extended with quantification over types is inconsistent. Using Girard's idea, he shows that some other extensions of minimal higherorder logic, several extensions of the calcul ..."
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In his paper "An Analysis of Girard's Paradox" [3], Coquand presents a result of Girard that minimal higherorder logic extended with quantification over types is inconsistent. Using Girard's idea, he shows that some other extensions of minimal higherorder logic, several extensions of the calculus of constructions, and an early calculus of MartinLof with type:type are also inconsistent. He also presents several consistent extensions of minimal higherorder logic and the calculus of constructions. In this paper, I survey relevant background material and present two of Coquand's proofs of inconsistency. 1 Background In this section, I present some material that is relevant for understanding Coquand's results. Readers familiar with this material may wish to skip to section 2 and refer to this section later as necessary. 1.1 Styles of Axiomatization There are two styles commonly used for axiomatizing various logics; the style of natural deduction and the style of Hilbert. Syst...
A Study of Logic and Programming via Turing Machines
"... Let's first study a few excerpts from Turing's original paper [13, p. 231234], and then design a few machines to perform certain tasks. ..."
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Let's first study a few excerpts from Turing's original paper [13, p. 231234], and then design a few machines to perform certain tasks.