A Top-down Approach to Combining Logics

The mechanization and automation of combination of logics, expressive ontologies and notions of context are prominent current challenge problems. I propose to approach these challenge topics from the perspective of classical higher-order logic. From this perspective these topics are closely related and a common, uniform solution appears in reach.

[1]  Luciano Serafini,et al.  Comparing formal theories of context in AI , 2004, Artif. Intell..

[2]  Peter B. Andrews.  An introduction to mathematical logic and type theory - to truth through proof , 1986, Computer science and applied mathematics.

[3]  Gérard P. Huet,et al.  A Unification Algorithm for Typed lambda-Calculus , 1975, Theor. Comput. Sci..

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

[5]  Andrei Voronkov,et al.  Sine Qua Non for Large Theory Reasoning , 2011, CADE.

[6]  Lawrence C. Paulson,et al.  Quantified Multimodal Logics in Simple Type Theory , 2009, Logica Universalis.

[7]  Peter B. Andrews.  General models and extensionality , 1972, Journal of Symbolic Logic.

[8]  Geoff Sutcliffe,et al.  Large theory reasoning with SUMO at CASC , 2010, AI Commun..

[9]  Geoff Sutcliffe,et al.  THF 0 – The Core TPTP Language for Classical Higher-Order Logic , 2007 .

[10]  Dov M. Gabbay,et al.  Embedding and automating conditional logics in classical higher-order logic , 2012, Annals of Mathematics and Artificial Intelligence.

[11]  Peter B. Andrews.  Resolution in type theory , 1971, Journal of Symbolic Logic.

[12]  Valeria de Paiva.  Natural Deduction and Context as (Constructive) Modality , 2003, CONTEXT.

[13]  Christoph Benzmüller,et al.  Higher-order semantics and extensionality , 2004, Journal of Symbolic Logic.

[14]  Christoph Benzmüller,et al.  Quantified Conditional Logics are Fragments of HOL , 2012, ArXiv.

[15]  Christoph Benzmüller.  Automating Access Control Logics in Simple Type Theory with LEO-II (Techreport) , 2009, SEC.

[16]  C. E. Brown.  Automated Reasoning in Higher-Order Logic: Set Comprehension and Extensionality in Church's Type Theory , 2007 .

[17]  John McCarthy,et al.  Notes on Formalizing Context , 1993, IJCAI.

[18]  R. Guha.  Contexts: a formalization and some applications , 1992 .

[19]  Hans Jürgen.  Semantics-Based Translation Methods for Modal Logics , 1991 .

[20]  Alan Bundy,et al.  Reasoning with Context in the Semantic Web , 2012, J. Web Semant..

[21]  Geoff Sutcliffe,et al.  TPTP, TSTP, CASC, etc , 2007, CSR.

[22]  Alonzo Church,et al.  A formulation of the simple theory of types , 1940, Journal of Symbolic Logic.

[23]  T. Pietrzykowski,et al.  A complete mechanization of (ω) -order type theory , 1972, ACM Annual Conference.

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

[25]  Krister Segerberg,et al.  Two-dimensional modal logic , 1973, J. Philos. Log..

[26]  Lawrence C. Paulson,et al.  Lightweight relevance filtering for machine-generated resolution problems , 2009, J. Appl. Log..

[27]  John McCarthy,et al.  Generality in artificial intelligence , 1987, Resonance.

[28]  Dov M. Gabbay,et al.  Handbook of the history of logic , 2004 .

[29]  Leon Henkin,et al.  Completeness in the theory of types , 1950, Journal of Symbolic Logic.

[30]  Fausto Giunchiglia,et al.  Contextual Reasoning , 1998, ECAI.

[31]  Deepak Ramachandran,et al.  First-Orderized ResearchCyc : Expressivity and Efficiency in a Common-Sense Ontology , 2005 .

[32]  Fausto Giunchiglia,et al.  Multilanguage hierarchical logics (or: how we can do without modal logics) , 1994, CNKBS.

[33]  Lawrence C. Paulson,et al.  Multimodal and intuitionistic logics in simple type theory , 2010, Log. J. IGPL.

[34]  Ian A. Mason,et al.  Metamathematics of Contexts , 1995, Fundam. Informaticae.

[35]  Gérard P. Huet,et al.  A Mechanization of Type Theory , 1973, IJCAI.

[36]  Christoph Benzmüller,et al.  Extensional Higher-Order Paramodulation and RUE-Resolution , 1999, CADE.

[37]  M. Baldoni.  Normal Multimodal Logics: Automatic Deduction and Logic Programming Extension , 1998 .

[38]  R. Thomason.  Combinations of Tense and Modality , 2002 .

[39]  Varol Akman,et al.  Steps Toward Formalizing Context , 1996, AI Mag..

[40]  Lawrence C. Paulson,et al.  Exploring Properties of Normal Multimodal Logics in Simple Type Theory with LEO-II , 2008 .

[41]  Robert Stalnaker.  A Theory of Conditionals , 2019, Knowledge and Conditionals.

[42]  Christoph Benzmüller,et al.  Comparing Approaches To Resolution Based Higher-Order Theorem Proving , 2002, Synthese.

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

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

[45]  Christoph Benzmüller,et al.  Combining and automating classical and non-classical logics in classical higher-order logics , 2011, Annals of Mathematics and Artificial Intelligence.