# Figuring out the verbalisation of temporal constraints in ontologies and conceptual models

Temporal conceptual models, ontologies, and their logics are nothing new, but that sort of information and knowledge representation still doesn’t gain a lot of traction (cf. say, formal methods for verification). This is in no small part because modelling temporal information is not easy. Several conceptual modelling languages do have various temporal extensions, but most modellers don’t even use all of the default language features yet [1]. How could one at least reduce the barrier to adoption of temporal logics and modelling languages? The two principle approaches are visualisation with a diagrammatic language and rendering it in a (pseudo-)natural language. One of my postgraduate students looked at the former, trying to figure out what would be the best icons and such, which showed there was still a steep learning curve [2]. Before examining whether that could be optimised, I wondered whether the natural language option might be promising. The problem was, that no-one had yet tried to determine what the natural language counterpart of the temporal constraints were supposed to be, let alone whether they be ‘adequate’ or the ‘best’ way of rendering the temporal constraints in tolerable natural language sentences. I wanted to know that badly enough that I tried to find out.

Given that using templates is a tried-and-tested relatively successful approach for atemporal conceptual models and ontologies (e.g., for ORM, the ACE system), it makes sense to do something similar, but then for some temporal extension. As temporal conceptual modelling language I used one that has a Description Logics foundation (DLRUS [3,4]) for that easily links to ontologies as well, added a few known temporal constraints (like for relationships/DL roles, mandatory) and removing others (some didn’t seem all that interesting), which resulted in 34 constraints, still. For each one, I tried to devise more and less reasonable templates, resulting in 101 templates overall. Those templates were evaluated on semantics and preference by three temporal logic experts and five ‘mixed experts’ (experts in natural language generation, logic, or modelling). This resulted in a final set of preferred templates to verbalise the temporal constraints. The remainder of this post first describes a bit about the templates and then the results of which I think they are most interesting.

Templates

The basic idea of a template—in the context of the verbalisation of conceptual models and ontologies—is to have some natural language for the constraint where then the vocabulary gets slotted in at runtime. Take, for instance, simple named class subsumption in an ontology, $C \sqsubseteq D$, for which one could define a template “Each [C] is a(n) [D]”, so that with some axiom $Manager \sqsubseteq Employee$, it would generate the sentence “Each Manager is an Employee”. One also could have devised the template “All [C] are [D]” and then it would have generated “All Managers are Employees”. The choice between the two templates in this case is just taste, for in both cases, the semantics is the same. More complex axioms are not always that straightforward. For instance, for the axiom type $C \sqsubseteq \exists R.D$, would “Each [C] [R] some [D]” be good enough, or would perhaps “Each [C] must [R] at least one [D]” be better? E.g., “Each Professor teaches some Course” vs “Each Professor must teach at least one Course”.

The same can be done for the temporal constraints. To get there, I did a bit of a linguistic detour that informed the template design (described in the paper [5]). Let us take as first example for templates temporal class that has a semantics of $o \in C^{\mathcal{I}(t)} \rightarrow \exists t' \neq t. o \notin C^{\mathcal{I}(t')}$; for instance, UndergraduateStudent (assuming they graduate and end up as alumni or as drop outs, and weren’t undergrads from birth):

1. If an object is an instance of entity type [C], then there is some time where it is not a(n) [C].
2. [C] is an entity type whose objects are, for some time in their existence, not instances of [C].
3. [C] is an entity type of which each object is not a(n) [C] for some time during its existence.
4. All instances of entity type [C] are not a(n) [C] for some time.
5. Each [C] is not a(n) [C] for some time.
6. Each [C] is for some time not a(n) [C].

Which one(s) do you think captures the semantics, and which one(s) do you prefer?

A more elaborate constraint for relationships is ‘dynamic extension for relationships, past, mandatory], which is formalised as $\langle o , o' \rangle \in \mbox{{\sc RDexM}-}_{R_1,R_2}^{\mathcal{I}(t)} \rightarrow (\langle o , o' \rangle \in{\tt R_1}^{\mathcal{I}(t)} \rightarrow \exists t' where $\langle o , o' \rangle \in \mbox{{\sc RDex}}_{R_1,R_2}^{\mathcal{I}(t)} \rightarrow ( \langle o , o' \rangle \in{\tt R_1}^{\mathcal{I}(t)} \rightarrow \exists t'>t. \langle o , o' \rangle \in {\tt R_2}^{\mathcal{I}(t')})$.; e.g., every passenger who boards a flight must have checked in for that flight. Two options could be:

1. Each ..C_1.. ..R_1.. ..C_2.. was preceded by ..C_1.. ..R_2.. ..C_2.. some time earlier.
2. Each ..C_1.. ..R_1.. ..C_2.. must be preceded by ..C_1.. ..R_2.. ..C_2.. .

I’m not saying they are all correct; they were some of the options given, which the participants could choose from and comment on. The full list of constraints and template options are available in the supplementary material, which also contains a file where you can fill in your own answers, see what the (anonymised) participants said, and it has the final list of ‘best’ constraints.

Results

The main aggregate quantitative results are shown in the following table.

Many observations can be made from the data (see the paper for details). Some of the salient aspects are that there was low inter-annotator agreement among the experts, despite that they know each other (temporal logics is a small community) and that the ‘mixed group’ deemed many sentences correct that the experts deemed wrong in the sense of not properly capturing the semantics of the constraint. Put differently, it looks like the mixed experts, as a group, did not fully grasp some subtle distinction in the temporal constraints.

With respect to the templates, the preferred ones don’t follow the structure of the logic, but are, in a way, a separate rendering, or: there’s no neat 1:1 mapping between axiom type and template structure. That said, that doesn’t mean that they always chose the shortest template: the experts definitely did not, while the mixed experts leaned a bit toward preferring templates with fewer words even though they were surely not always the semantically correct option.

It may not look good that the experts preferred different templates, but in a follow-up interview with one of the experts, the expert noted that it was not really a problem “for there is the logic that does have the precise meaning anyway” and thus “resolves any confusion that may arise from using slightly different terminology”. The temporal logic expert does have a point from the expert’s view, fair enough, but that pretty much defeats my aim with the experiment. Asking more non-experts may not be a good strategy either, for they are, on average, too lenient.

So, for now, we do have a set of, relatively, ‘best’ templates to verbalise temporal constraints in temporal conceptual models and ontologies. The next step is to compare that with the diagrammatic representation. This we did [6], and I’ll describe those results informally in a next post.

I’ll present more details at the upcoming CREOL: Contextual Representation of Events and Objects in Language Workshop that is part of the Joint Ontology Workshops 2017, which will be held next week (21-23 September) in Bolzano, Italy. As the KRDB group at FUB in Bolzano has a few temporal logic experts, I’m looking forward to the discussions! Also, I’d be happy if you would be willing to fill in the spreadsheet with your preferences (before looking at the answers given by the participants!), and send them to me.

References

[1] Keet, C.M., Fillottrani, P.R. An analysis and characterisation of publicly available conceptual models. 34th International Conference on Conceptual Modeling (ER’15). Johannesson, P., Lee, M.L. Liddle, S.W., Opdahl, A.L., Pastor López, O. (Eds.). Springer LNCS vol 9381, 585-593. 19-22 Oct, Stockholm, Sweden.

[2] T. Shunmugam. Adoption of a visual model for temporal database representation. M. IT thesis, Department of Computer Science, University of Cape Town, South Africa, 2016.

[3] A. Artale, E. Franconi, F. Wolter, and M. Zakharyaschev. A temporal description logic for reasoning about conceptual schemas and queries. In S. Flesca, S. Greco, N. Leone, and G. Ianni, editors, Proceedings of the 8th Joint European Conference on Logics in Artificial Intelligence (JELIA-02), volume 2424 of LNAI, pages 98-110. Springer Verlag, 2002.

[4] A. Artale, C. Parent, and S. Spaccapietra. Evolving objects in temporal information systems. Annals of Mathematics and Artificial Intelligence, 50(1-2):5-38, 2007.

[5] Keet, C.M. Natural language template selection for temporal constraints. CREOL: Contextual Representation of Events and Objects in Language, Joint Ontology Workshops 2017, 21-23 September 2017, Bolzano, Italy. CEUR-WS Vol. (in print).

[6] Keet, C.M., Berman, S. Determining the preferred representation of temporal constraints in conceptual models. 36th International Conference on Conceptual Modeling (ER’17). Springer LNCS. 6-9 Nov 2017, Valencia, Spain. (in print)

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