A Time and Situation Dependent Semantics for Ontological Property Classification

This paper proposes a new semantics that characterizes the time and/or situation dependencies of properties, together with the ontological notion of existential rigidity. For this purpose, we present order-sorted tempo-situational logic (OSTSL) with rigid/anti-rigid sorts and an existential predicate. In this logic, rigid/anti-rigid sorted terms enable the expressions for sortal properties, and temporal and situational operators suitably represent the ontological axioms of existential rigidity and time and/or situation dependencies. A specific semantics of OSTSL adheres to the temporal and situational behaviors of properties based on existential rigidity. As a result, the semantics guarantees that the ontological axioms of properties expressed by sorted tempo-situational formulas are logically valid.

[1]  Nicola Guarino,et al.  An Ontology of Meta-Level Categories , 1994, KR.

[2]  Riichiro Mizoguchi,et al.  Ontological Knowledge Base Reasoning with Sort-Hierarchy and Rigidity , 2004, KR.

[3]  Christopher A. Welty,et al.  Towards OntoClean 2.0: A framework for rigidity , 2005, Appl. Ontology.

[4]  Anthony G. Cohn,et al.  Taxonomic reasoning with many-sorted logics , 1989, Artificial Intelligence Review.

[5]  Riichiro Mizoguchi,et al.  Distributed reasoning with ontologies and rules in order-sorted logic programming , 2009, J. Web Semant..

[6]  Claudio Gutiérrez,et al.  Introducing Time into RDF , 2007, IEEE Transactions on Knowledge and Data Engineering.

[7]  Alan M. Frisch.  The Substitutional Framework for Sorted Deduction: Fundamental Results on Hybrid Reasoning , 1991, Artif. Intell..

[8]  Gert Smolka.  Logic Programming over Polymorphically Order-Sorted Types , 1989 .

[9]  M. Schmidt-Schauβ.  Computational Aspects of an Order-Sorted Logic with Term Declarations , 1989 .

[10]  Trudy Weibel,et al.  An Order-Sorted Resolution in Theory and Practice , 1997, Theor. Comput. Sci..

[11]  Nicola Guarino,et al.  Ontological Analysis of Taxonomic Relationships , 2000, ER.

[12]  José Meseguer,et al.  Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations , 1992, Theor. Comput. Sci..

[13]  Nicola Guarino,et al.  Supporting ontological analysis of taxonomic relationships , 2001, Data Knowl. Eng..

[14]  Manfred Schmidt-Schauß,et al.  Computational Aspects of an Order-Sorted Logic with Term Declarations , 1989, Lecture Notes in Computer Science.

[15]  Ken Kaneiwa,et al.  Order-sorted logic programming with predicate hierarchy , 2004, Artif. Intell..

[16]  Riichiro Mizoguchi,et al.  An Order-Sorted Quantified Modal Logic for Meta-ontology , 2005, TABLEAUX.

[17]  Barry Smith,et al.  Basic Concepts of Formal Ontology , 1998 .

[18]  Christoph Walther.  A Mechanical Solution of Schubert's Steamroller by Many-Sorted Resolution , 1984, AAAI.