Ontoclean 2.0: a Framework for Rigidity
Total Page:16
File Type:pdf, Size:1020Kb
RC23754 (W0510-141) October 21, 2005 Computer Science IBM Research Report Towards OntoClean 2.0: A Framework for Rigidity Christopher Welty IBM Research Division Thomas J. Watson Research Center P.O. Box 704 Yorktown Heights, NY 10598 William Andersen Ontology Works, Inc. Research Division Almaden - Austin - Beijing - Haifa - India - T. J. Watson - Tokyo - Zurich LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. I thas been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g ,. payment of royalties). Copies may be requested from IBM T. J. Watson Research Center , P. O. Box 218, Yorktown Heights, NY 10598 USA (email: [email protected]). Some reports are available on the internet at http://domino.watson.ibm.com/library/CyberDig.nsf/home . Towards OntoClean 2.0: A framework for rigidity Christopher Welty IBM Watson Research Center 19 Skyline Dr., Hawthorne, NY 10532 [email protected] William Andersen Ontology Works, Inc. [email protected] Abstract A common criticism of OntoClean is that it relies on quanti- fied modal logic (S5) for its expression. While modal logic The OntoClean methodology was based on a set of is required for the expression of the rigidity axioms we pre- formal meta-properties whose semantics were sent here, many useful theorems derived from them may be specified in S5 modal logic. One of these used in non-modal settings. For this reason we give the be- metaproperties, Rigidity, has come under more fo- ginnings of a formal ontology of rigidity metaproperties cused scrutiny by the ontology community, and suitable for application with non-modal ontology authoring several problems with the formalization have been languages that permit quantification over relations. The discussed along with several solutions. In this pa- main point of this paper is to consolidate subsequent work per, we attempt to reconcile these results in a larger by many authors on the OntoClean meta-property called framework that exposes different kinds of rigidity, Rigidity, and establish a formal framework that exposes as well as two new metaproperties, actuality and differences between them. This work can be seen as a for- permanence, which deal more specifically with the mal ontology of rigid properties. behavior of properties with respect to time and ex- istence. 2 Background 1 Introduction One of the most often heard criticisms of the OntoClean methodology is that it requires modal logic. The truth is The notion of rigidity in the OntoClean methodology was that one does not need modal logic, nor modal logic reason- originally introduced to account for the conditions under ing, to use OntoClean in ontology-based systems. The for- which exemplification of properties by their instances is malizations of the OntoClean meta-properties were present necessary or essential1. Since then, many authors have fo- to clearly communicate their semantics, much like specify- cused on the analysis of rigidity in various settings, accom- ing a model theory for a language, and not with the intention panied by claims that the original definition failed to capture of being used in reasoning systems themselves. The formal- key elements such as time and actual existence. ization helped to maintain a level of rigor that can, in gen- The purpose of this paper is to consolidate work by these eral, make subtle distinctions clear. Continued analysis of authors on the notion of rigidity in OntoClean. We establish the formalizations themselves has shown that there were a unifying framework that elaborates the dimensions along more distinctions than originally realized, and will be the which the recent proposed accounts of rigidity differ. These subject of this paper. dimensions are alethic modality, time, and existence. We Modal logic was chosen for the formalization mainly due to apply this framework to develop a range of definitions that, the needs of specifying the semantics of rigidity, in particu- given basic intuitions of how time and existence influences lar anti-rigidity. We need to express the fact that some intuitions about rigidity, we claim cover the space of possi- class, e.g. HospitalPatient, is anti-rigid, that any instance of ble definitions. this class must possibly not be an instance. A purely tempo- ral axiomatization would require that every instance does 1 In this paper we uniformly use the term “property” to denote change, which is not true. A person who was a hospital unary relations in intension, as was the meaning of the term in the patient for his entire existence should not contradict the anti- original work on OntoClean done by Guarino and Welty and as is rigidity of the class – it was always possible for him to be- standard usage in philosophical literature. We acknowledge, how- come a non-patient, it just never happened. ever, that, in addition, the terms “class”, “kind”, and sometimes OntoClean was formalized in S5 modal logic with the Bar- “type” are commonly used. When talking about properties that can Formula, which gives us a constant domain (every ob- range over properties, we use the term “meta-property”. ject exists in every possible world) and universal accessibil- which amounts to saying the extension of a temporally rigid ity (every world is accessible from every other world). The property must be the same for all time points and all possi- domain of quantification is possibilia, which when com- ble worlds. bined with S5+BF introduces a need for an actual existence Andersen and Menzel [2004] pointed out that [A6] causes predicate (E), as opposed to logical existence, that indicates problems for non-exemplifiable properties, and does not some object actually exists in the possible world [Miller, accurately capture the intuition expressed as, “An instance 2002]. The unary existence predicate indicates timeless ex- of a rigid property cannot cease to be an instance of that istence, and the binary predicate indicates existence at a property, unless it ceases to exist,” [Welty & Guarino, 2001] particular time in the possible world. since [A6] requires an entity to have the property always Given the separate (i.e. non-modal) treatment of time within and in all possible worlds, e.g. if Person is a rigid class, possible worlds implied by the OntoClean formalizations, must Aristotle be a person even in a possible world in which we need to clarify the intuition that possible worlds have a he does not exist? To address this, they proposed: time line within them, which we also assume to be totally [A7] ±∀xt &(x,t) → ±∀t’(E(x,t’) → &(x,t’)) ordered wrt to a succession relation (<) [Artale & Lutz, (temporally existential rigidity) 2004]. Given the constant domain assumption, times across worlds are the same, and we further assume that, in order to and introduced the constraint (which we have adopted) that be the same, their ordering is maintained across worlds as & is restricted to only exemplifiable properties. Citing many of the same problems, Carrera et al [2004] pro- well: posed: [A1] ∀t t ¡ t < t → ± t < t 1 2 1 2 1 2 [A8] ±∀xt (E(x,t) . &(x,t)) → ±∀t’(E(x,t’) → &(x,t’)) We require a strong notion of subsumption in order to have which is similar to [A7], with a slightly stonger restriction modal consequences for the meta-properties [Kaplan, 2001]: on existence. [A2] subsumes(ψ,&) ↔ ± ∀x &(x) → ψ(x) Both Andersen&Menzel and Carrara et al point out that In order to prevent trivial satisfaction of the axioms, we their accounts of rigidity, by introducing actual existence in require that all properties be exemplifiable [Andersen & the antecedents, say nothing about what happens to entities Menzel, 2004], i.e. for any property &: when they do not exist, leaving open the possibility that an [A3] ¡∃x &(x) instance of a rigid property could change its membership when it does not exist. These assumptions may be somewhat controversial in a phi- losophical setting, however we believe for practical use in ontology engineering, these assumptions are widespread, 4 Kinds of Rigidity though often implicit. One of the original motivations for specifying the Onto- Clean meta-properties was to encourage more rigorous 3 History of Rigidity analysis of the properties in an ontology in order to make the meaning more clear. This clarity would also help to ex- Although not the central notion in OntoClean, Rigidity is pose differences in meaning between ontologies that shared the simplest and most intuitive, with more obvious immedi- terms, e.g. if two ontologies used a class named Person, but ate utility and applicability across the ontology, conceptual it was rigid in one ontology and non-rigid in another, then modeling, and domain modeling communities, and this has we would have some indication that the properties mean made it the most carefully studied of the OntoClean different things. metaproperties. The different accounts of rigidity above ([A5]-[A8]) were The general intuition of rigidity is that certain properties in all intended as corrections on the original formulation, in an an ontology are essential to their instances – an instance effort to come up with the one true formalization of the no- cannot change its membership, and was first axiomatized tion. In this paper, we take a slightly different stance: all of [Guarino & Welty, 2000a] as a property is rigid iff: & the accounts above are correct, and specify different kinds of [A4] ∀x &(x) → ±&(x) rigidity. This has encouraged us to clarify these distinctions Kaplan [2001] pointed out that [A4] is not a straightforward further, in order to establish a more general framework for extension of Kripke’s rigid designators [Kripke, 1982] to rigidity.