Permanent Generic Relatedness and Silent Change Niels GREWE a,1 , Ludger JANSEN a , and Barry SMITH b a Institute of Philosophy, University of Rostock, Germany b University at Buffalo, NY, USA Abstract. Given the assertion of a relation between two types, like: “Epidermis has part some Keratinocyte”, we define silent change as any kind of change of the instance-relata of the relation in question that does not change the truth-value of the respective type-level assertion. Such assertions are notoriously difficult to model in OWL 2. To address this problem, we distinguish different modes of type-level relatedness giving rise to this problem and describe a conservative extension to the BFO top-level ontology that allows expressing these modes. Keywords. Description Logics, OWL 2, Basic Formal Ontology, Ontology Design Patterns, Processes, Change 1. Introduction Like many assertions about biological reality, [A] Human skin tissue contains keratinocytes appears if stated at the type level to be a representation of something static. Once translated to the instance level, however, it becomes clear that [A] may be true even in spite of constant changes in the entities it represents: a given portion of skin tissue is made up of different cells at different times. [A] is silent about such changes at the instance level. Assertions like [A] are notoriously difficult to model in OWL 2. Prima facie, the following expression seems to convey what is intended: SkinTissue SubclassOf has part some Keratinocyte (1) But given the first-order semantics of OWL 2, has part is just a set of tuples hx, yi. This means that two individuals, skin s1 and cell c1 , are all that is required to make (1) true, where nothing needs to be said about the respective lifetimes of s1 and c1 . Thus c1 might have been a part of s1 for the whole life of s1 or just for one brief interval. To counter this problem, the Graz release of the BFO [1] top-level ontology introduced the object property has continuant part at some time and its subrelation has continuant part at all times. Unfortunately, neither of these object properties can be used to represent silent change. The at-some-time version is too weak to convey the 1 Corresponding Author intended meaning because it asserts only that a cell is temporarily part of the skin (i.e. there could be a time where the skin has no cells). And the at-all-times version is too strong since it implies that there is a specific cell that is permanently part of the skin over its entire lifetime. What [A] requires is that cells of a certain type are part of portions of skin tissue generically – which means that different individual cells can perform this service provided only that, at all times, some cell of the appropriate type is present. Hence our talk of “silent change”. The objective of this paper is the presentation and discussion of a new OWL design pattern that allows silent change to be expressed in an OWL 2 compliant, BFO 2-based ontology, but could have much wider application. 2. Background 2.1. Basic Formal Ontology (BFO) The uppermost partition in the BFO hierarchy reflects two distinct modes of existence in time: Continuants are entities that (1) exist in full at any time that they exists at all, and (2) continue to exist self-identically for as long as they exist; occurrents are entities that unfold over a period of time and thus have temporal parts. For example, a cell is a continuant, while the process of cell division is an occurrent. Continuants may change while preserving their identity. BFO thus accepts both the 3D and a 4D view of the world as valid ontological perspectives. A crucial binding link between these two viewpoints is the history of relation, which establishes a one-to-one relationship between a material entity and a special process called its history, defined as “a process that is the sum of the totality of processes taking place in the spatiotemporal region occupied by a material entity or site”[2]. So while a cell, as a continuant, is a three-dimensional entity that cannot have temporal parts, its corresponding history can be broken up into distinct temporal parts such as prophase, metaphase, anaphase, and so on. 2.2. Representing temporal information in OWL One conventional strategy for representing time-sensitive relations is to use explicit timeindexes to specify the time interval over which a relational assertion is valid, and then quantify over the time interval. In first order logic, this could be expressed as: ∀x,t ((SkinTissue(x) ∧ exists at(x,t)) → ∃y (Keratinocyte(y) ∧ has part at(x, y,t))) (2) This approach is not available in OWL 2 due to the restriction to binary predicates, so to achieve something similar one needs to resort to reification, i.e. representing relational assertions as explicit individuals in the domain [3]. Examples of such approaches include the strictly four-dimensionalist approach of Welty and Fikes [4] or the approach Zamborlini and Guizzardi [5], who essentially duplicate the very same entities in both a 3D- and a 4D-view. Neither of these approaches is compatible with the stance taken by BFO. 3. Methods 3.1. Phases and Temporally Qualified Continuants (TQCs) To be able to model the cases of permanent generic relatedness and thus to allow for the phenomenon of silent change, we want to build on the BFO category of history. It is easy and useful to talk about specific temporal parts of a continuant’s history, for example, “Socrates’ youth”, or “the mosquito stage of this Plasmodium’s life-cycle”. These parts still share many traits of the whole history, because they are also comprised of sums of processes, taking place in a specific spatiotemporal region – a region that is determined by a single continuant entity – it is merely that the spatiotemporal region in question is truncated along the temporal dimension. We can call these restricted parts of histories phases of the corresponding history. Phases of histories are not themselves histories, since a history is defined in such a way that each history is the history of some single continuant. If, then, h is the history of the continuant c, and p is an occurrent part of h, it follows that p cannot also be a history since there is no continuant available to serve as that which it would be the history of, because continuants cannot have temporal parts. Given p, however, as a phase of history h, we can postulate what we call a temporally qualified continuant (TQC) of c [6], onto which p projects in the same way as the history h projects onto the continuant c. Two readings of the talk of TQCs are then available: on the one side we can see talk of TQCs as a mere façon de parler – a way of talking about (a practically useful model of) other things, which in and of itself has no ontological commitment; on the other side we can treat TQCs as full-fledged entities. In this paper we remain neutral as between these options. In analogy to the history of relation between histories and material entities, we introduce another relation, phase of, where history of becomes a subrelation of phase of. This means that there is a one-to-one relation that relates each TQC to some unique phase. Material Object TQC of has history TQC phase of History has occurent part Phase Figure 1. The TQ Entity Square The relationship between phases and TQCs thus matches that of histories and material objects. Additionally, all histories are a type of phase (of maximal extent) and all continuants are (or can be modelled as) TQCs of maximal extent. 3.2. TQC Modelling Patterns Our modelling pattern can be applied to relations that have material entities as their domain. We will always use the at-all-times version of the relation in question, adding the mechanism of phases and TQCs where necessary. The latter is not yet needed for permanent specific relatedness. E.g. each brain is always part of the same individual host: Brain SubclassOf continuant part of at all times some Human (3) Temporary relatedness will be achieved by asserting that the first continuant relatum has a sub-phase which maps onto a TQC that is at all times related to the second continuant relatum. For example, teeth may temporarily be part of some animal: Tooth SubclassOf has phase some has occurrent part some phase of some continuant part of at all times some Animal (4) Permanent generic relatedness is the case of [A], where different individuals are involved in the relation at different times. Here the TQC for every occurrent part of the history of the skin tissue portion can either be related to a specific cell using an atall-times relation, or the phase can exclusively be broken down further into sub-phases which fulfil this property. Since this requires a recursive definition that refers to itself, we need to define a helper class (HasKeratinocytePartPhase) in (5), and use it in the final axiom (6): HasKeratinocytePartPhase EquivalentTo((has proper occurrent part some HasKeratinocytePartPhase) and (has proper occurrent part only HasKeratinocytePartPhase)) or phase of some (has continuant part at all times some Keratinocyte) SkinTissue SubclassOf has phase some HasKeratinocytePartPhase (5) (6) These patterns correctly capture the BFO idea that continuant-continuant (or continuant-occurrent) relations have 3D entities as their subjects while capturing the different temporal strengths through an appeal to the different relation between temporal parts and wholes on the side of occurrents. Consequentially, the usual challenges and restrictions of implementing mereotopological relations correctly in OWL 2 still apply. For example, due to the restrictions on the set of mutually admissible axioms, has ocurrent part reflexive in the OWL 2 version of BFO 2, losing some expected inferences. 3.3. Usability Optimisation using Tawny OWL Since the pattern for the permanent generic case is quite complex, it seemed important to look at ways to improve usability. To this end, we used the Tawny OWL [7] which provides an internal domain specific language for describing OWL 2 ontologies based on a Lisp dialect. This allows the implementation of macros which capture the modeller’s intent and automatically generate the required helper classes and TQC-related sub-expressions, reformulating (5) and (6) as: (o/owl-class "Skin" :super (c/perm-gen "HasKeratinocytePartPhase" (o/owl-some b/has_continuant_part_at_all_times "Keratinocyte"))) 4. Results We implemented 13 test scenarios covering different cases from different categories in order to be able to pose competency questions challenging various aspects of the scheme. The test matrix combined material entities, processes and immaterial entities as the subjects of the assertions with all three temporal strengths. We found that apart from the phase/TQC classes and relations the OWL 2 axiomatisation of BFO 2 did not entail that all material entities have histories. Validation of the test cases was successful with one exception: Since BFO restricts histories to apply to material entities and sites, it was impossible to model, for example, an EHR that gets moved between different physical storage media. The competency questions are implemented as Clojure unit tests in the ontology source available from http://nie.gr/tqc/. 5. Conclusions With minimal interference to the set of axioms provided by BFO 2, we were able to provide modelling patterns that account for silent change through the lifetime of a continuant without forcing the user to adopt the sort of reductionistic four-dimensionalist approach, which is far removed from the everyday talk of life-scientists. But while these patterns succeed in enabling the required task, they introduce considerable complexity. Using Tawny OWL provides some degree of mitigation through expressive macros and at the same time enables a more agile write→test→refactor→deploy ontology development methodology. Acknowledgements The topic of this paper is part of a larger project within the BFO community. The paper benefited greatly from a multitude of fruitful discussions with Janna Hastings, Chris Mungal, Alan Ruttenberg, and Stefan Schulz. References [1] [2] [3] [4] [5] [6] [7] BFO 2 OWL Group. BFO 2 OWL Preview Release;. 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