LeoPARD - A Generic Platform for the Implementation of Higher-Order Reasoners

LeoPARD supports the implementation of knowledge representation and reasoning tools for higher-order logic(s). It combines a sophisticated data structure layer (polymorphically typed {\lambda}-calculus with nameless spine notation, explicit substitutions, and perfect term sharing) with an ambitious multi-agent blackboard architecture (supporting prover parallelism at the term, clause, and search level). Further features of LeoPARD include a parser for all TPTP dialects, a command line interpreter, and generic means for the integration of external reasoners.

[1]  I. V. Ramakrishnan,et al.  Term Indexing , 1995, Lecture Notes in Computer Science.

[2]  Geoff Sutcliffe,et al.  Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure , 2010, J. Formaliz. Reason..

[3]  Gopalan Nadathur,et al.  System description : Teyjus : A compiler and abstract machine based implementation of λprolog , 1999 .

[4]  Frank Pfenning,et al.  System Description: Twelf - A Meta-Logical Framework for Deductive Systems , 1999, CADE.

[5]  Geoff Sutcliffe.  The TPTP Problem Library and Associated Infrastructure , 2009, Journal of Automated Reasoning.

[6]  Gerhard Weiss,et al.  Multiagent Systems , 1999 .

[7]  Volker Sorge,et al.  &Ω-ANTS- combining interactive and automated theorem proving , 2001 .

[8]  Andrew Gacek.  The Abella Interactive Theorem Prover (System Description) , 2008, IJCAR.

[9]  Maria Paola Bonacina,et al.  A taxonomy of parallel strategies for deduction , 2001, Annals of Mathematics and Artificial Intelligence.

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

[11]  Alexander Steen,et al.  Efficient Data Structures for Automated Theorem Proving in Expressive Higher-Order Logics , 2014 .

[12]  Lawrence C. Paulson,et al.  Extending Sledgehammer with SMT Solvers , 2011, Journal of Automated Reasoning.

[13]  A. Riazanov.  Implementing an Efficient Theorem Prover , 2003 .

[14]  Frank Pfenning,et al.  A Linear Spine Calculus , 2003, J. Log. Comput..

[15]  Lawrence C. Paulson,et al.  LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description) , 2008, IJCAR.

[16]  de Ng Dick Bruijn,et al.  Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem , 1972 .

[17]  Hendrik Pieter Barendregt,et al.  Introduction to generalized type systems , 1991, Journal of Functional Programming.

[18]  John C. Reynolds,et al.  Towards a theory of type structure , 1974, Symposium on Programming.

[19]  Gopalan Nadathur,et al.  System Description: Teyjus - A Compiler and Abstract Machine Based Implementation of lambda-Prolog , 1999, CADE.

[20]  Jerzy Tiuryn,et al.  Alpha-Conversion and Typability , 1999, Inf. Comput..

[21]  Martín Abadi,et al.  Explicit substitutions , 1989, POPL '90.

[22]  Christoph Benzmüller,et al.  Agent-based Blackboard Architecture for a Higher-Order Theorem Prover , 2014 .

[23]  Christoph Benzmüller,et al.  System Description: LEO - A Higher-Order Theorem Prover , 1998, CADE.

[24]  I. V. Ramakrishnan,et al.  Term Indexing , 2001, Handbook of Automated Reasoning.

[25]  L. A. Goodman,et al.  Social Choice and Individual Values , 1951 .

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

[27]  J. Y. Girard,et al.  Interpretation fonctionelle et elimination des coupures dans l'aritmetique d'ordre superieur , 1972 .