Open AccessProceedings Article
Mechanizing inductive reasoning
Emmanuel Kounalis,Michaël Rusinowitch +1 more
- 29 Jul 1990
- pp 240-245
TL;DR: This work presents a new method to prove (and disprove) automatically inductive properties, which avoids completion and explicit induction but retains their positive features, namely the completeness of the former and the robustness of the latter.
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Abstract: Automating proofs by induction is important in many computer science and artificial intelligence applications, in particular in program verification and specification systems We present a new method to prove (and disprove) automatically inductive properties Given a set of axioms, a well-suited induction scheme is constructed automatically We call such a scheme a test-set Then, for proving a property, we just instanciate it with terms from the test-set and apply pure algebraic simplification to the result This method avoids completion and explicit induction However it retains their positive features, namely the completeness of the former and the robustness of the latter
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Citations
Automated Theorem Proving by Test Set Induction
TL;DR: This work presents a procedure for proof by test set induction which is refutationally complete for a larger class of specifications than has been shown in previous work.
66
A General Framework to Build Contextual Cover Set Induction Provers
TL;DR: This paper presents an abstract inference system uniformly defined in terms of contextual cover sets as a general framework to build implicit induction provers and shows that it generalizes existing cover set induction procedures.
56
On Notions of Inductive Validity for First-Oder Equational Clauses
Claus-Peter Wirth,Bernhard Gramlich +1 more
- 26 Jun 1994
TL;DR: This work defines and discusses various conceivable notions of inductive validity for first-order equational clauses within the framework of constructor-based positive/negative conditional equational specifications which permits to treat negation and incomplete function definitions in an adequate and natural fashion.
27
A Unified View of Induction Reasoning for First-Order Logic.
Sorin Stratulat
- 22 Jun 2012
TL;DR: A new cycle-based induction method that keeps their best features, i.e., performs local and non-reductive reasoning, and naturally fits for mutual and lazy induction.
•Proceedings Article
Automatic case analysis in proof by induction
Adel Bouhoula,Michaël Rusinowitch +1 more
- 28 Aug 1993
TL;DR: A new procedure for proof by induction in conditional theories where case analysis is simulated by term rewriting, which reduces considerably the number of variables of a conjecture to be considered for applying induction schemes (inductive positions).
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