MECHANIZATION OF MALTINGS

The Mechanization of Mathematics

The mechanization of mathematics refers to the use of computers to find, or to help find, mathematical proofs. Turing showed that a complete reduction of mathematics to computation is not possible, but nevertheless the art and science of automated deduction has made progress. This paper describes some of the history and surveys the state of the art.

A Mechanization of Type Theory

A r e f u t a t i o n a l sys tem o f l o g i c f o r a l a n g u a g e o f o r d e r w i a p r e s e n t e d . T h i s langage i s a s l i g h t m o d i f i c a t i o n o f C h u r c h ' s \ c a l c u l u s w i t h t y p e s . The sys tem i s c o m p l e t e , i n the sense t h a t a r e f u t a t i o n o f a s e t o f sen tences e x i s t s i f and o n l y i f t h i s s e t does n o t possess...

A Mechanization of Phylogenetic Trees

Structural Embeddings: Mechanization with Method

The most powerful tools for analysis of formal speci cations are general-purpose theorem provers and model checkers, but these tools provide scant methodological support. Conversely, those approaches that do provide a well-developed method generally have less powerful automation. It is natural, therefore, to try to combine the better-developed methods with the more powerful general-purpose tool...

Mechanization of Analytic Reasoning About Sets

Resolution reasoners, when applied to set theory problems, typically suffer from “lack of focus.” MARS is a program that attempts to rectify this difficulty by exploiting the definition-like character of the set theory axioms. As in the case of its predecessor, SLIM, it employs a tableau proof procedure based on binary resolution, but MARS IS enhanced by an equality substitution rule and a devi...