Proof Support for Common Logic

We present an extension of the Heterogeneous Tool Set HETS that enables proof support for Common Logic. This is achieved via logic translations that relate Common Logic and some of its sublogics to already supported logics and automated theorem proving systems. We thus provide the first full theorem proving support for Common Logic, including the possibility of verifying meta-theoretical relationships between Common Logic theories.

[1]  Kurt Stenzel,et al.  KIV 3.0 for Provably Correct Systems , 1998, FM-Trends.

[2]  Till Mossakowski,et al.  Heterogeneous Specification and the Heterogeneous Tool Set , 2004 .

[3]  Christopher Menzel.  Knowledge representation, the World Wide Web, and the evolution of logic , 2009, Synthese.

[4]  James A. Hendler,et al.  The Semantic Web" in Scientific American , 2001 .

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

[6]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

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

[8]  Till Mossakowski,et al.  Carnap, Goguen, and the Hyperontologies: Logical Pluralism and Heterogeneous Structuring in Ontology Design , 2010, Logica Universalis.

[9]  Megan Katsumi,et al.  A Methodology for the Development and Verification of , 2011 .

[10]  Furio Honsell,et al.  A framework for defining logics , 1993, JACM.

[11]  Huajun Chen,et al.  The Semantic Web , 2011, Lecture Notes in Computer Science.

[12]  Patrick J. Hayes,et al.  Common Logic and the Horatio problem , 2012, Appl. Ontology.

[13]  Yevgeny Kazakov,et al.  SRIQ and SROIQ are Harder than SHOIQ , 2008, Description Logics.

[14]  Torsten Hahmann,et al.  Ontology Verification with Repositories , 2010, FOIS.

[15]  Diego Calvanese,et al.  The Description Logic Handbook , 2007 .

[16]  Dieter Hutter,et al.  Development graphs - Proof management for structured specifications , 2006, J. Log. Algebraic Methods Program..

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

[18]  Grigore Rosu,et al.  Institution Morphisms , 2013, Formal Aspects of Computing.

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

[20]  Tomasz Borzyszkowski,et al.  Higher-Order Logic and Theorem Proving for Structured Specifications , 1999, WADT.

[21]  Till Mossakowski,et al.  The Onto-Logical Translation Graph , 2011, WoMO.

[22]  Adam Pease,et al.  Higher-order aspects and context in SUMO , 2012, J. Web Semant..

[23]  Till Mossakowski,et al.  Reasoning Support for Caslwith Automated Theorem Proving Systems , 2006, WADT.

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

[25]  Lawrence Charles Paulson,et al.  Isabelle/HOL: A Proof Assistant for Higher-Order Logic , 2002 .

[26]  Geoff Sutcliffe,et al.  THF0 - The Core of the TPTP Language for Higher-Order Logic , 2008, IJCAR.

[27]  Björn Pelzer,et al.  System Description: E-KRHyper , 2007, CADE.

[28]  Christoph Lange,et al.  Three Semantics for the Core of the Distributed Ontology Language , 2012, FOIS.

[29]  Geoff Sutcliffe,et al.  Evaluating general purpose automated theorem proving systems , 2001, Artif. Intell..

[30]  Peter Baumgartner,et al.  Implementing the Model Evolution Calculus , 2006, Int. J. Artif. Intell. Tools.

[31]  S. Wölfl,et al.  The Heterogeneous Tool Set , 2007 .

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

[33]  Till Mossakowski,et al.  Towards Logical Frameworks in the Heterogeneous Tool Set Hets , 2010, WADT.

[34]  Till Mossakowski.  Relating CASL with other specification languages: the institution level , 2002, Theor. Comput. Sci..

[35]  Ian Horrocks,et al.  The Even More Irresistible SROIQ , 2006, KR.

[36]  Alex Borgiday.  On the Relative Expressiveness of Description Logics and Predicate Logics , 1996 .

[37]  Yevgeny Kazakov,et al.  RIQ and SROIQ Are Harder than SHOIQ , 2008, KR.

[38]  Serge Autexier,et al.  The MathServe System for Semantic Web Reasoning Services , 2006, IJCAR.