The SAD System: Deductive Assistance in an Intelligent Linguistic Environment

Formal methods are widely used in the computer science community. Formal verification and certification is an important component of any formal approach. Such a work can not be done by hand, hence the software that can do a part of it is rather required. The verification methods are often based on a deductive system and "verify" means "prove". Corresponding software is called proof assistant. We describe in this paper the System for Automated Deduction (SAD): its architecture, input language, and reasoning facilities. We show how to use SAD as a proof assistant. We outline specific features of SAD - a handy input language, powerful reasoning strategy, opportunity to use various low level inference engines. Examples and results of some experiments are also given

[1]  Xin Yu,et al.  MetaPRL - A Modular Logical Environment , 2003, TPHOLs.

[2]  Bruno Buchberger,et al.  A survey of the Theorema project , 1997, ISSAC.

[3]  Andrei Voronkov,et al.  The design and implementation of VAMPIRE , 2002, AI Commun..

[4]  Stephen J. Garland,et al.  A Guide to LP, The Larch Prover , 1991 .

[5]  de Ng Dick Bruijn,et al.  The mathematical language AUTOMATH, its usage, and some of its extensions , 1970 .

[6]  Hugo Herbelin,et al.  The Coq proof assistant : reference manual, version 6.1 , 1997 .

[7]  Christoph Weidenbach,et al.  S PASS Version 2.0 , 2002, CADE.

[8]  Konstantin Verchinine,et al.  On verification tools implemented in the System for Automated Deduction , 2022 .

[9]  Geoff Sutcliffe,et al.  The TPTP Problem Library , 1994, Journal of Automated Reasoning.

[10]  Jean-Pierre Serre Cours d'arithmétique , 1971 .

[11]  Reinhold Letz,et al.  Model Elimination and Connection Tableau Procedures , 2001, Handbook of Automated Reasoning.

[12]  Daniel Brand,et al.  Proving Theorems with the Modification Method , 1975, SIAM J. Comput..

[13]  Andrzej Trybulec,et al.  Computer Assisted Reasoning with MIZAR , 1985, IJCAI.

[14]  Markus Wenzel,et al.  Isar - A Generic Interpretative Approach to Readable Formal Proof Documents , 1999, TPHOLs.

[15]  Frank G. Garvan,et al.  The MAPLE Book , 2001 .

[16]  J. Strother Moore,et al.  An Industrial Strength Theorem Prover for a Logic Based on Common Lisp , 1997, IEEE Trans. Software Eng..

[17]  A. C. Hearn,et al.  REDUCE: a user-oriented interactive system for algebraic simplification , 1967, Symposium on Interactive Systems for Experimental Applied Mathematics.

[18]  Richard D. Jenks,et al.  AXIOM: the scientific computation system , 1992 .

[19]  Volker Sorge,et al.  ΩMEGA : Towards a mathematical assistant , 1997 .

[20]  Volker Sorge,et al.  Omega: Towards a Mathematical Assistant , 1997, CADE.

[21]  William McCune,et al.  OTTER 3.0 Reference Manual and Guide , 1994 .

[22]  Hao Wang,et al.  Toward Mechanical Mathematics , 1960, IBM J. Res. Dev..

[23]  Tobias Nipkow,et al.  A Proof Assistant for Higher-Order Logic , 2002 .

[24]  Tobias Nipkow,et al.  Isabelle/HOL , 2002, Lecture Notes in Computer Science.

[25]  Natarajan Shankar,et al.  PVS: A Prototype Verification System , 1992, CADE.

[26]  Konstantin Verchinine,et al.  SAD as a mathematical assistant - how should we go from here to there? , 2006, J. Appl. Log..

[27]  Amel Mammar Un environnement formel pour le développement d'applications bases de données , 2002 .

[28]  Konstantin Verchinine,et al.  Theorem Proving and Proof Verification in the System SAD , 2004, MKM.

[29]  William M. Farmer,et al.  IMPS: An interactive mathematical proof system , 1990, Journal of Automated Reasoning.

[30]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[31]  Freek Wiedijk,et al.  The Seventeen Provers of the World , 2006 .

[32]  Ronald L. Graham,et al.  Rudiments of Ramsey theory , 1981 .