Automated Deduction: Looking Ahead

In this article, the body of a report on automated deduction is presented that notes some significant achievements and takes a studied look at the future of the field.

[1]  Larry Wos,et al.  Efficiency and Completeness of the Set of Support Strategy in Theorem Proving , 1965, JACM.

[2]  Robert S. Boyer,et al.  The QED Manifesto , 1994, CADE.

[3]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[4]  Stephen Owen,et al.  Analogy for automated reasoning , 1990, Perspectives in artificial intelligence.

[5]  Robin Milner,et al.  Definition of standard ML , 1990 .

[6]  Lawrence Charles Paulson,et al.  Isabelle: A Generic Theorem Prover , 1994 .

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

[8]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[9]  J. A. NEWELLt,et al.  Empirical Explorations of the Logic Theory Machine : A Case Study in Heuristic , .

[10]  J. S. Moore,et al.  ACL2: an industrial strength version of Nqthm , 1996, Proceedings of 11th Annual Conference on Computer Assurance. COMPASS '96.

[11]  Sentot Kromodimoeljo,et al.  EVES: An Overview , 1991, VDM Europe.

[12]  Thomas A. Henzinger,et al.  HYTECH: The Cornell HYbrid TECHnology Tool , 1994, Hybrid Systems.

[13]  Ingo Dahn,et al.  Natural Language Presentation and Combination of Automatically Generated Proofs , 1996, FroCoS.

[14]  Randal E. Bryant,et al.  Formally Verifying a Microprocessor Using a Simulation Methodology , 1994, 31st Design Automation Conference.

[15]  Dave Barker-Plummer,et al.  Graphical Theorem Proving: An Approach to Reasoning with the Help of Diagrams , 1992, ECAI.

[16]  D. Loveland,et al.  Empirical explorations of the geometry-theorem proving machine , 1995 .

[17]  Rodney J. Douglas KIDS: A Semi-Automatic Program Development System , 1990 .

[18]  C PaulsonLawrence Set theory for verification. I , 1993 .

[19]  Xiaorong Huang,et al.  Presenting Machine-Found Proofs , 1996, CADE.

[20]  M. Gordon,et al.  Introduction to HOL: a theorem proving environment for higher order logic , 1993 .

[21]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[22]  Bart Selman,et al.  Pushing the Envelope: Planning, Propositional Logic and Stochastic Search , 1996, AAAI/IAAI, Vol. 2.

[23]  Patrick Suppes,et al.  Student use of an interactive theorem prover , 1984 .

[24]  Rina Dechter,et al.  Network-Based Heuristics for Constraint-Satisfaction Problems , 1987, Artif. Intell..

[25]  Donald W. Loveland,et al.  A Simplified Format for the Model Elimination Theorem-Proving Procedure , 1969, J. ACM.

[26]  Chetan R. Murthy An evaluation semantics for classical proofs , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[27]  Bart Selman,et al.  Encoding Plans in Propositional Logic , 1996, KR.

[28]  Gopalan Nadathur,et al.  An Overview of Lambda-PROLOG , 1988, ICLP/SLP.

[29]  S. Chou Mechanical Geometry Theorem Proving , 1987 .

[30]  Kenneth Kunen,et al.  Quasigroups, Loops, and Associative Laws , 1996 .

[31]  Helen Murray Roberts,et al.  Elements of mathematics , 1956 .

[32]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[33]  Toby Walsh,et al.  The Use of Proof Plans to Sum Series , 1992, CADE.

[34]  Frank van Harmelen,et al.  Rippling: A Heuristic for Guiding Inductive Proofs , 1993, Artif. Intell..

[35]  Donald W. Loveland,et al.  Automated theorem proving: a quarter-century review , 1984 .

[36]  J. Barwise,et al.  The language of first-order logic , 1991 .

[37]  Deepak Kapur,et al.  Mechanically Verifying a Family of Multiplier Circuits , 1996, CAV.

[38]  Hector J. Levesque,et al.  GOLOG: A Logic Programming Language for Dynamic Domains , 1997, J. Log. Program..

[39]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[40]  Douglas J. Howe The Computational Behaviour of Girard's Paradox , 1987, LICS.

[41]  Edmund M. Clarke,et al.  Combining Symbolic Computation and Theorem Proving: Some Problems of Ramanujan , 1994, CADE.

[42]  Ingo Dahn,et al.  Integration of Automated and Interactive Theorem Proving in ILP , 1997, CADE.

[43]  Peter B. Andrews Transforming Matings into Natural Deduction Proofs , 1980, CADE.

[44]  Robert S. Boyer,et al.  A computational logic handbook , 1979, Perspectives in computing.

[45]  Rina Dechter,et al.  Directional Resolution: The Davis-Putnam Procedure, Revisited , 1994, KR.

[46]  J. A. Robinson,et al.  Logic and logic programming , 1992, CACM.

[47]  Edmund M. Clarke,et al.  Analytica - A Theorem Prover in Mathematica , 1992, CADE.

[48]  Dale Miller,et al.  Expansion Tree Proofs and Their Conversion to Natural Deduction Proofs , 1984, CADE.

[49]  Douglas J. Howe Importing Mathematics from HOL into Nuprl , 1996, TPHOLs.

[50]  Sentot Kromodimoeljo,et al.  Eves System Description , 1992, CADE.

[51]  -. DaveBarker,et al.  Diagrams and Mathematics , 1995 .

[52]  Mark E. Stickel A Complete Unification Algorithm for Associative-Commutative Functions , 1975, IJCAI.

[53]  Geoff Sutcliffe,et al.  The Design of the CADE-13 ATP System Competition , 1996, CADE.

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

[55]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[56]  John McCarthy,et al.  Programs with common sense , 1960 .

[57]  Gábor Péli,et al.  The logic of propagation strategies : Axiomatizing a fragment of organizational ecology in first-order logic , 1997 .

[58]  Donald MacKenzie,et al.  The automation of proof: a historical and sociological exploration , 1995, IEEE Ann. Hist. Comput..

[59]  M. Stickel,et al.  Automated reasoning and exhaustive search: Quasigroup existence problems☆ , 1995 .

[60]  Wayne Snyder,et al.  Basic Paramodulation and Superposition , 1992, CADE.

[61]  L. Wos,et al.  Automated generation of models and counterexamples and its application to open questions in Ternary Boolean algebra , 1978, MVL '78.

[62]  Jörg Denzinger,et al.  Learning Domain Knowledge to Improve Theorem Proving , 1996, CADE.

[63]  Thierry Coquand,et al.  The Calculus of Constructions , 1988, Inf. Comput..

[64]  Ivan Bratko,et al.  Applications of inductive logic programming , 1995, CACM.

[65]  Larry M. Hines Str+ve and Integers , 1994, CADE.

[66]  Rance Cleaveland,et al.  Implementing mathematics with the Nuprl proof development system , 1986 .

[67]  Masayuki Fujita,et al.  Automatic Generation of Some Results in Finite Algebra , 1993, IJCAI.

[68]  Michael R. Lowry,et al.  Deductive Composition of Astronomical Software from Subroutine Libraries , 1994, CADE.

[69]  H. Gelernter,et al.  Realization of a geometry theorem proving machine , 1995, IFIP Congress.

[70]  Zohar Manna,et al.  A Deductive Approach to Program Synthesis , 1979, TOPL.

[71]  Ingo Br,et al.  Prolog programming for artificial intelligence , 1990 .

[72]  Patrick Brézillon,et al.  Lecture Notes in Artificial Intelligence , 1999 .

[73]  Jeroen Bruggeman,et al.  A logical approach to formalizing organization ecology , 1994 .

[74]  Chetan R. Murthy,et al.  Finding computational content in classical proofs , 1991 .

[75]  E. Feigenbaum,et al.  Computers and Thought , 1963 .

[76]  Larry Wos,et al.  The Concept of Demodulation in Theorem Proving , 1967, JACM.

[77]  Jon Whittle,et al.  Internal Analogy in Theorem Proving , 1996, CADE.

[78]  Donald E. Knuth,et al.  Simple Word Problems in Universal Algebras††The work reported in this paper was supported in part by the U.S. Office of Naval Research. , 1970 .

[79]  Hantao Zhang,et al.  An overview of Rewrite Rule Laboratory (RRL) , 1995 .

[80]  Yves Deville,et al.  Logic programming - systematic program development , 1990, International series in logic programming.

[81]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[82]  William McCune,et al.  33 basic test problems: a practical evaluation of some paramodulation strategies , 1997 .

[83]  W. W. Bledsoe,et al.  Variable Elimination and Chaining in a Resolution-based Prover for Inequalities , 1980, CADE.

[84]  Richard Bornat,et al.  A Review of Several Programs for the Teaching of Logic , 1993, Comput. J..