Hoping for the Truth - A Survey of the TPTP Logics

This paper compares features of the classical logics that are commonly used in the TPTP-based automated reasoning community for representing chosen aspects of “the world”, and the consequent implications for reasoning about these representations. The paper argues that increases in complexity in terms of representation and reasoning force users to compromise between the reliability of the representation and the reliability of the reasoning.

[1]  Richard Statman,et al.  Lambda Calculus with Types , 2013, Perspectives in logic.

[2]  Francesco M. Donini,et al.  Complexity of Reasoning , 2003, Description Logic Handbook.

[3]  Francis Jeffry Pelletier The Philosophy of Automated Theorem Proving , 1991, IJCAI.

[4]  Reiner Hähnle,et al.  Tableaux and Related Methods , 2001, Handbook of Automated Reasoning.

[5]  Toby Walsh,et al.  Handbook of satisfiability , 2009 .

[6]  Christoph Weidenbach,et al.  SPASS Version 3.5 , 2009, CADE.

[7]  Tobias Nipkow Linear Quantifier Elimination , 2008, IJCAR.

[8]  Clark W. Barrett,et al.  The SMT-LIB Standard Version 2.0 , 2010 .

[9]  William M. Farmer,et al.  The seven virtues of simple type theory , 2008, J. Appl. Log..

[10]  Konstantin Korovin Instantiation-Based Automated Reasoning: From Theory to Practice , 2009, CADE.

[11]  Christoph Walther,et al.  A Many-Sorted Calculus Based on Resolution and Paramodulation , 1982, IJCAI.

[12]  Andrei Voronkov,et al.  Logic for Programming, Artificial Intelligence, and Reasoning , 2013, Lecture Notes in Computer Science.

[13]  Peter Baumgartner,et al.  Hierarchic Superposition with Weak Abstraction , 2013, CADE.

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

[15]  Geoff Sutcliffe,et al.  The TPTP World - Infrastructure for Automated Reasoning , 2010, LPAR.

[16]  Simon Cruanes,et al.  Extending Superposition with Integer Arithmetic, Structural Induction, and Beyond. (Extensions de la Superposition pour l'Arithmétique Linéaire Entière, l'Induction Structurelle, et bien plus encore) , 2015 .

[17]  Andrei Voronkov,et al.  First-Order Theorem Proving and Vampire , 2013, CAV.

[18]  Cesare Tinelli,et al.  DPLL( T): Fast Decision Procedures , 2004, CAV.

[19]  Christoph Weidenbach,et al.  Combining Superposition, Sorts and Splitting , 2001, Handbook of Automated Reasoning.

[20]  Jean-Yves Béziau,et al.  Logica Universalis: Towards a General Theory of Logic , 2007 .

[21]  Christoph Weidenbach,et al.  Computing Small Clause Normal Forms , 2001, Handbook of Automated Reasoning.

[22]  Geoff Sutcliffe,et al.  The state of CASC , 2006, AI Commun..

[23]  Anthony G. Cohn,et al.  A more expressive formulation of many sorted logic , 1987, Journal of Automated Reasoning.

[24]  Birte Glimm,et al.  Konclude: System description , 2014, J. Web Semant..

[25]  George A. Robinson,et al.  AUTOMATIC GENERATION OF PROOFS IN THE LANGUAGE OF MATHEMATICS , 2000 .

[26]  Alan Robinson,et al.  The Inverse Method , 2001, Handbook of Automated Reasoning.

[27]  Dominique Pastre,et al.  MUSCADET 2.3: A Knowledge-Based Theorem Prover Based on Natural Deduction , 2001, IJCAR.

[28]  Stephan Schulz,et al.  E - a brainiac theorem prover , 2002, AI Commun..

[29]  Sylvain Conchon,et al.  Implementing polymorphism in SMT solvers , 2008, SMT '08/BPR '08.

[30]  Volker Sorge,et al.  Combined reasoning by automated cooperation , 2008, J. Appl. Log..

[31]  Chad E. Brown,et al.  Satallax: An Automatic Higher-Order Prover , 2012, IJCAR.

[32]  Harald Ganzinger,et al.  Resolution Theorem Proving , 2001, Handbook of Automated Reasoning.

[33]  Stephan Schulz A Comparison of Different Techniques for Grounding Near-Propositional CNF Formulae , 2002, FLAIRS Conference.

[34]  Yves Bertot,et al.  Interactive Theorem Proving and Program Development: Coq'Art The Calculus of Inductive Constructions , 2010 .

[35]  Harald Ganzinger,et al.  New directions in instantiation-based theorem proving , 2003, 18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings..

[36]  Monty Newborn Automated theorem proving - theory and practice , 2000 .

[37]  Damien Doligez,et al.  Zenon Modulo: When Achilles Outruns the Tortoise Using Deduction Modulo , 2013, LPAR.

[38]  Sylvain Conchon,et al.  A Collaborative Framework for Non-Linear Integer Arithmetic Reasoning in Alt-Ergo , 2013, 2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing.