Inductionless Induction (aka Implicit Induction or Proof by Consistency): A Literature Survey
نویسنده
چکیده
منابع مشابه
History and Future of Implicit and Inductionless Induction: Beware the Old Jade and the Zombie!
In this survey on implicit induction I recollect some memories on the history of implicit induction as it is relevant for future research on computer-assisted theorem proving, esp. memories that significantly differ from the presentation in a recent handbook article on “inductionless induction”. Moreover, the important references excluded there are provided here. In order to clear the fog a lit...
متن کاملARTIFICIAL INTELLIGENCE Proof by Consistency*
Advances of the past decade in methods and computer programs for showing consistency of proof systems based on first-order equations have made it feasible, in some settings, to use proof by consistency as an alternative to conventional rules of inference. Musser described the method applied to proof of properties of inductively defined objects. Refinements of this inductionless induction method...
متن کاملAutomating Inductionless Induction Using Test Sets
The inductionless induction (also called proof by consistency) approach for proving equations by induction from an equational theory, requires a consistency check for equational theories. A new method using test sets for checking consistency of an equational theory is proposed. Using this method, a variation of the Knuth-Bendix completion procedure can be used for automatically proving equation...
متن کاملDeduction versus Computation: The Case of Induction
The fundamental difference and the essential complementarity between computation and deduction are central in computer algebra, automated deduction, proof assistants and in frameworks making them cooperating. In this work we show that the fundamental proof method of induction can be understood and implemented as either computation or deduction. Inductive proofs can be built either explicitly by...
متن کاملInduction as Deduction Modulo
Inductive proofs can be built either explicitly by making use of an induction principle or implicitly by using the so-called induction by rewriting and inductionless induction methods. When mechanizing proof construction, explicit induction is used in proof assistants and implicit induction is used in rewrite based automated theorem provers. The two approaches are clearly complementary but up t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007