# Orchestrating 28 logical theories of mereo(topo)logy

Parts and wholes, again. This time it’s about the logic-aspects of theories of parthood (cf. aligning different hierarchies of (part-whole) relations and make them compatible with foundational ontologies). I intended to write this post before the Ninth Conference on Knowledge Capture (K-CAP 2017), where the paper describing the new material would be presented by my co-author, Oliver Kutz. Now, afterwards, I can add that “Orchestrating a Network of Mereo(topo) logical Theories” [1] even won the Best Paper Award. The novelties, in broad strokes, are that we figured out and structured some hitherto messy and confusing state of affairs, showed that one can do more than generally assumed especially with a new logics orchestration framework, and we proposed first steps toward conflict resolution to sort out expressivity and logic limitations trade-offs. Constructing a tweet-size “tl;dr” version of the contents is not easy, and as I have as much space here on my blog as I like, it ended up to be three paragraphs here: scene-setting, solution, and a few examples to illustrate some of it.

Problems

As ontologists know, parthood is used widely in ontologies across most subject domains, such as biomedicine, geographic information systems, architecture, and so on. Ontology (the philosophers) offer a parthood relation that has a bunch of computationally unpleasant properties that are structured in a plethora of mereologicial and meretopological theories such that it has become hard to see the forest for the trees. This is then complicated in practice because there are multiple logics of varying expressivity (support more or less language features), with the result that only certain fragments of the mereo(topo)logical theories can be represented. However, it’s mostly not clear what can be used when, during the ontology authoring stage one may want to have all those features so as to check correctness, and it’s not easy to predict what will happen when one aligns ontologies with different fragments of mereo(topo)logy.

Solution

We solved these problems by specifying a structured network of theories formulated in multiple logics that are glued together by the various linking constructs of the Distributed Ontology, Model, and Specification Language (DOL). The ‘structured network of theories’-part concerns all the maximal expressible fragments of the KGEMT mereotopological theory and five of its most well-recognised sub-theories (like GEM and MT) in the seven Description Logics-based OWL species, first-order logic, and higher order logic. The ‘glued together’-part refers to relating the resultant 28 theories within DOL (in Ontohub), which is a non-trivial (understatement, unfortunately) metalanguage that has the constructors for the glue, such as enabling one to declare to merge two theories/modules represented in different logics, extending a theory (ontology) with axioms that go beyond that language without messing up the original (expressivity-restricted) ontology, and more. Further, because the annoying thing of merging two ontologies/modules can be that the merged ontology may be in a different language than the two original ones, which is very hard to predict, we have a cute proof-of-concept tool so that it assists with steps toward resolution of language feature conflicts by pinpointing profile violations.

Examples

The paper describes nine mechanisms with DOL and the mereotopological theories. Here I’ll start with a simple one: we have Minimal Topology (MT) partially represented in OWL 2 EL/QL in “theory8” where the connection relation (C) is just reflexive (among other axioms; see table in the paper for details). Now what if we add connection’s symmetry, which results in “theory4”? First, we do this by not harming theory8, in DOL syntax (see also the ESSLI’16 tutorial):

logic OWL2.QL
ontology theory4 =
theory8
then
ObjectProperty: C Characteristics: Symmetric %(t7)

What is the logic of theory4? Still in OWL, and if so, which species? The Owl classifier shows the result:

Another case is that OWL does not let one define an object property; at best, one can add domain and range axioms and the occasional ‘characteristic’ (like aforementioned symmetry), for allowing arbitrary full definitions pushes it out of the decidable fragment. One can add them, though, in a system that can handle first order logic, such as the Heterogeneous toolset (Hets); for instance, where in OWL one can add only “overlap” as a primitive relation (vocabulary element without definition), we can take such a theory and declare that definition:

logic CASL.FOL
ontology theory20 =
theory6_plus_antisym_and_WS
then %wdef
. forall x,y:Thing . O(x,y) <=> exists z:Thing (P(z,x) /\ P(z,y)) %(t21)
. forall x,y:Thing . EQ(x,y) <=> P(x,y) /\ P(y,x) %(t22)

As last example, let me illustrate the notion of the conflict resolution. Consider theory19—ground mereology, partially—that is within OWL 2 EL expressivity and theory18—also ground mereology, partially—that is within OWL 2 DL expressivity. So, they can’t be the same; the difference is that theory18 has parthood reflexive and transitive and proper parthood asymmetric and irreflexive, whereas theory19 has both parthood and proper parthood transitive. What happens if one aligns the ontologies that contain these theories, say, O1 (with theory18) and O2 (with theory19)? The Owl classifier provides easy pinpointing and tells you the profile: OWL 2 full (or: first order logic, or: beyond OWL 2 DL—top row) and why (bottom section):

Now, what can one do? The conflict resolution cannot be fully automated, because it depends on what the modeller wants or needs, but there’s enough data generated already and there are known trade-offs so that it is possible to describe the consequences:

• Choose the O1 axioms (with irreflexivity and asymmetry on proper part of), which will make the ontology interoperable with other ontologies in OWL 2 DL, FOL or HOL.
• Choose O2’s axioms (with transitivity on part of and proper part of), which will facilitate linking to ontologies in OWL 2 RL, 2 EL, 2 DL, FOL, and HOL.
• Choose to keep both sets will result in an OWL 2 Full ontology that is undecidable, and it is then compatible only with FOL and HOL ontologies.

As serious final note: there’s still fun to be had on the logic side of things with countermodels and sub-networks and such, and with refining the conflict resolution to assist ontology engineers better. (or: TBC)

As less serious final note: the working title of early drafts of the paper was “DOLifying mereo(topo)logy”, but at some point we chickened out and let go of that frivolity.

References

[1] Keet, C.M., Kutz, O. Orchestrating a Network of Mereo(topo)logical Theories. Ninth International Conference on Knowledge Capture (K-CAP’17), Austin, Texas, USA, December 4-6, 2017. ACM Proceedings.

# 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)

# Our ESWC17 demos: TDDonto2 and an OWL verbaliser for isiZulu

Besides the full paper on heterogeneous alignments for 14th Extended Semantic Web Conference (ESWC’17) that will take place next week in Portoroz, Slovenia, we also managed to squeeze out two demo papers. You may already know of TDDonto2 with Kieren Davies and Agnieszka Lawrynowicz, which was discussed in an earlier post that has been updated with a tutorial video. It now has a demo paper as well [1], which describes the rationale and a few scenarios. The other demo, with Musa Xakaza and Langa Khumalo, is new-new, but the regular reader might have seen it coming: we finally managed to link the verbalisation patterns for certain Description Logic axiom types [2,3] to those in OWL ontologies. The tool takes as input an ontology in isiZulu and the verbalisation algorithms, and out come the isiZulu sentences, be this in plain text for further processing or in a GUI for inspection by a domain expert [4]. There is a basic demo-screencast to show it’s all working.

The overall architecture may be of interest, for it deviates from most OWL verbalisers. It is shown in the following figure:

For instance, we use the Python-based OWL API Owlready, rather than a Java-based app, for Python is rather popular in NLP and the verbalisation algorithms may be used elsewhere as well. We made more such decisions with the aim to make whatever we did as multi-purpose usable as possible, like the list of nouns with noun classes (surprisingly, and annoyingly, there is no such readily available list yet, though isizulu.net probably will have it somewhere but inaccessible), verb roots, and exceptions in pluralisation. (Problems for integrating the verbaliser with, say, Protégé will be interesting to discuss during the demo session!)

The text-based output doesn’t look as nice as the GUI interface, so I will show here only the GUI interface, which is adorned with some annotations to illustrate that those verbalisation algorithms in the background are far from trivial templates:

For instance, while in English the universal quantification is always ‘Each’ or ‘All’ regardless the named class quantified over, in isiZulu it depends on the noun class of the noun that is the name of the OWL class. For instance, in the figure above, izingwe ‘leopards’ is in noun class 10, so the ‘Each/All’ is Zonke, amavazi ‘vases’ is in noun class 6, so ‘Each/All’ then becomes Onke, and abantu ‘people’/’humans’ is in noun class 2, making Bonke. There are 17 noun classes. They also determine the subject concords (SC, alike conjugation) for the verbs, with zi- for noun class 10, ­a- for noun class 6, and ba- for noun class 2, to name a few. How this all works is described in [2,3]. We’ve implemented all those algorithms and integrated the pluraliser [5] in it to make it work. The source files are available to check and play with already, you can do so and ask us during the ESWC17 demo session, and/or also have a look at the related outputs of the NRF-funded project Grammar Engine for Nguni natural language interfaces (GeNi).

References

[1] Davies, K. Keet, C.M., Lawrynowicz, A. TDDonto2: A Test-Driven Development Plugin for arbitrary TBox and ABox axioms. Extended Semantic Web Conference (ESWC’17), Springer LNCS. Portoroz, Slovenia, May 28 – June 2, 2017. (demo paper)

[2] Keet, C.M., Khumalo, L. Toward a knowledge-to-text controlled natural language of isiZulu. Language Resources and Evaluation, 2017, 51:131-157.

[3] Keet, C.M., Khumalo, L. On the verbalization patterns of part-whole relations in isiZulu. 9th International Natural Language Generation conference (INLG’16), 5-8 September, 2016, Edinburgh, UK. Association for Computational Linguistics, 174-183.

[4] Keet, C.M. Xakaza, M., Khumalo, L. Verbalising OWL ontologies in isiZulu with Python. 14th Extended Semantic Web Conference (ESWC’17). Springer LNCS. Portoroz, Slovenia, May 28 – June 2, 2017. (demo paper)

[5] Byamugisha, J., Keet, C.M., Khumalo, L. Pluralising Nouns in isiZulu and Related Languages. 17th International Conference on Intelligent Text Processing and Computational Linguistics (CICLing’16), Springer LNCS. April 3-9, 2016, Konya, Turkey.

# On heterogeneous mappings between ontologies

Representing information and knowledge often can be done in different ways even when the same representation language is used. In some cases, one way of representing it is always better than another—or: the other option is sub-optimal or plain wrong—but in other cases the distinction is not all that clear-cut. For instance, whether to represent ‘Employee’ as a subclass of ‘Person’ or that it inheres in ‘Person’. Now, if two ontologies (or conceptual models) represent it differently but they have to be aligned, then how to find such different modelling patterns and how to align them? And, taking a step back: which alternate modelling patterns are there, and why those? We sought to answer these questions, whose outcome will be presented (and appear in the proceedings of [1]) the 14th Extended Semantic Web Conference (ESWC’17) that will take place later this month in Portoroz, Slovenia.

Setting aside the formal stuff in this blog post, let’s first have a look at some of those different modelling patterns. At it’s core, there are 1) modelling practices in ontologies vs conceptual models and 2) foundational [or: top-level, or upper] ontology guidance vs being ‘compacter’ in representing the knowledge. The generalisations of the following handwaivy examples are described in more detail in the paper, but for this blog post, it hopefully will do as a teaser of the six formalised patterns. Take, e.g., the following examples that are all variations on the same theme: to-reify-or-not-to-reify, where the example in B is further dressed up with content from a foundational ontology:

Indeed, in the examples, what is shown on the left-hand side does not have the exact same information content as what is shown on the right-hand side, but the underlying conceptualization is pretty much the same. The models on the right-hand side are more precise, for one has the opportunity to specify those, like stating that a particular marriage is between two persons (so, no group marriages allowed). Whether one always needs such more precise constraints is a separate matter.

Then there’s the Employee example mentioned in this post’s introduction with two alternate ways of representing it:

That is, a modeller chooses between representing the role an object performs/has as a subclass of that object or in a separate hierarchy of roles. Foundational ontologies take the latter option, domain ontologies the former.

These examples are instantiations of small modelling patterns (of which there may be more than the six formalised in the paper). To devise mappings between them, one ends up with alignments in such a way that they are between two patterns, rather than 1:1 mappings. To get there, we had to take some preliminary steps on how to represent it all formally, such as specifying the language for a pattern and a defining an ontology pattern alignment. This allowed us to formalise the patterns and devise that formal specification of the heterogeneous alignments.

That outcome, in turn, feeds into the alignment pattern search and checking algorithms. The algorithms show that it is feasible to find those patterns automatically, which then can propose possible alignments to the modeller, and that, upon aligning, one can check whether that’s done correctly. For instance, take the following two ontologies graphically represented in an (extended, enhanced) ICOM tool:

Two inter-ontology assertions have been made, pointed out with the two yellow arrows; i.e., ‘Tennis’ is a subclass of ‘Tournament’ and ‘TennisPlayer’ is a subclass of ‘Athlete’. The pattern search algorithm then will try to find instantiations for the small modelling patterns for alignment. Once something is found—in this case, pattern A fits—it will check whether all conditions for the alignment can be satisfied, and if so, it will propose a possible alignment, which is shown in the following illustrative figure:

Of interest here is, perhaps, the ‘new’ object property being proposed, indicated with the yellow arrow, that amounts to an equivalence to the partOf+Match+played. (That threesome can’t be mapped as equivalent to ‘participated’ due to differences in domain and range axioms, and drawing three subsumption lines from ‘participated’ to ‘part of’, ‘Match’, and ‘played’ is awkward.). The algorithms’ output then thus reduces the alignment into a final question to the modeller along the line of “are you ok with the alignment between the purple elements in the two diagrams?”, and accept or reject it. Please refer to the paper for further details.

The principles presented could possibly be used also for refactoring of an ontology, like in TDD [2] or when ‘preparing’ an ontology to align to a foundational ontology. More results on this topic are in the pipeline, and if you want to know now already, we can have a chat at ESWC.

References

[1] Fillottrani, P.R., Keet, C.M. Patterns for Heterogeneous TBox Mappings to Bridge Different Modelling Decisions. 14th Extended Semantic Web Conference (ESWC’17). Springer LNCS. Portoroz, Slovenia, May 28 – June 2, 2017. (in print)

[2] Keet, C.M., Lawrynowicz, A. Test-Driven Development of Ontologies. In: Proceedings of the 13th Extended Semantic Web Conference (ESWC’16). Springer LNCS 9678, 642-657. 29 May – 2 June, 2016, Crete, Greece.

# Relations with roles / verbalising object properties in isiZulu

The narratives can be very different for the paper “A model for verbalising relations with roles in multiple languages” that was recently accepted paper at the 20th International Conference on Knowledge Engineering and Knowledge management (EKAW’16), for the paper makes a nice smoothie of the three ingredients of language, logic, and ontology. The natural language part zooms in on isiZulu as use case (possibly losing some ontologist or logician readers), then there are the logics about mapping the Description Logic DLR’s role components with OWL (lose possible interest of the natural language researchers), and a bit of philosophy (and lose most people…). It solves some thorny issues when trying to verbalise complicated verbs that we need for knowledge-to-text natural language generation in isiZulu and some other languages (e.g., German). And it solves the matching of logic-based representations popularised in mainly UML and ORM (that typically uses a logic in the DLR family of Description Logic languages) with the more commonly used OWL. The latter is even implemented as a Protégé plugin.

Let me start with some use-cases that cause problems that need to be solved. It is well-known that natural language renderings of ontologies facilitate communication with domain experts who are expected to model and validate the represented knowledge. This is doable for English, with ACE in the lead, but it isn’t for grammatically richer languages. There, there are complications, such as conjugation of verbs, an article that may be dependent on the preposition, or a preposition may modify the noun. For instance, works for, made by, located in, and is part of are quite common names for object properties in ontologies. They all do have a dependent preposition, however, there are different verb tenses, and the latter has a copulative and noun rather than just a verb. All that goes into the object properties name in an ‘English-based ontology’ and does not really have to be processed further in ontology verbalisation other than beautification. Not so in multiple other languages. For instance, the ‘in’ of located in ends up as affixes to the noun representing the object that the other object is located in. Like, imvilophu ‘envelope’ and emvilophini ‘in the envelope’ (locative underlined). Even something straightforward like a property eats can end up having to be conjugated differently depending on who’s eating: when a human eats, it is udla in isiZulu, but for, say, a dog, it is idla (modification underlined), which is driven by the system of noun classes, of which there are 17 in isiZulu. Many more examples illustrating different issues are described in the paper. To make a long story short, there are gradations in complicating effects, from no effect where a preposition can be squeezed in with the verb in naming an OP, to phonological conditioning, to modifying the article of the noun to modifying the noun. A ‘3rd pers. sg.’ may thus be context-dependent, and notions of prepositions may modify the verb or the noun or the article of the noun, or both. For a setting other than English ontologies (e.g., Greek, German, Lithuanian), a preposition may belong neither to the verb nor to the noun, but instead to the role that the object plays in the relation described by the verb in the sentence. For instance, one obtains yomuntu, rather than the basic noun umuntu, if it plays the role of the whole in a part-whole relation like in ‘heart is part of a human’ (inhliziyo iyingxenye yomuntu).

The question then becomes how to handle such a representation that also has to include roles? This is quite common in conceptual data modelling languages and in the DLR family of DL languages, which is known in ontology as positionalism [2]. Bumping up the role to an element in the representation language—thus, in addition to the relationship—enables one to attach information to it, like whether there is a (deep) preposition associated with it, the tense, or the case. Such role-based annotations can then be used to generate the right element, like einen Betrieb ‘some company’ to adjust the article for the case it goes with in German, or ya+umuntu=yomuntu ‘of a human’, modifying the noun in the object position in the sentence.

To get this working properly, with a solid theoretical foundation, we reused a part of the conceptual modelling languages’ metamodel [3] to create a language model for such annotations, in particular regarding the attributes of the classes in the metamodel. On its own, however, it is rather isolated and not immediately useful for ontologies that we set out to be in need of verbalising. To this end, it links to the ‘OWL way of representing relations’ (ontologically: the so-called standard view), and we separate out the logic-based representation from the readings that one can generate with the structured representation of the knowledge. All in all, the simplified high-level model looks like the picture below.

Simplified diagram in UML Class Diagram notation of the main components (see paper for attributes), linking a section of the metamodel (orange; positionalist commitment) to predicates (green; standard view) and their verbalisation (yellow). (Source: [1])

That much for the conceptual part; more details are described in the paper.

Just a fluffy colourful diagram isn’t enough for a solid implementation, however. To this end, we mapped one of the logics that adhere to positionalism to one of the standard view, being DLR [4] and OWL, respectively. It equally well could have been done for other pairs of languages (e.g., with Common Logic), but these two are more popular in terms of theory and tools.

Having the conceptual and logical foundations in place, we did implement it to see whether it actually can be done and to check whether the theory was sufficient. The Protégé plugin is called iMPALA—it could be an abbreviation for ‘Model for Positionalism And Language Annotation’—that both writes all the non-OWL annotations in a separate XML file and takes care of the renderings in Protégé. It works; yay. Specifically, it handles the interaction between the OWL file, the positionalist elements, and the annotations/attributes, plus the additional feature that one can add new linguistic annotation properties, so as to cater for extensibility. Here are a few screenshots:

OWL’s arbeitetFuer ‘works for’ is linked to the relationship arbeiten.

The prey role in the axiom of the impala being eaten by the ibhubesi.

Annotations of the prey role itself, which is a role in the relationship ukudla.

We did test it a bit, from just the regular feature testing to the African Wildlife ontology that was translated into isiZulu (spoken in South Africa) and a people and pets ontology in ciShona (spoken in Zimbabwe). These details are available in the online supplementary material.

The next step is to tie it all together, being the verbalisation patterns for isiZulu [5,6] and the OWL ontologies to generate full sentences, correctly. This is set to happen soon (provided all the protests don’t mess up the planning too much). If you want to know more details that are not, or not clearly, in the paper, then please have a look at the project page of A Grammar engine for Nguni natural language interfaces (GeNi), or come visit EKAW16 that will be held from 21-23 November in Bologna, Italy, where I will present the paper.

References

[1] Keet, C.M., Chirema, T. A model for verbalising relations with roles in multiple languages. 20th International Conference on Knowledge Engineering and Knowledge Management EKAW’16). Springer LNAI, 19-23 November 2016, Bologna, Italy. (in print)

[2] Leo, J. Modeling relations. Journal of Philosophical Logic, 2008, 37:353-385.

[3] Keet, C.M., Fillottrani, P.R. An ontology-driven unifying metamodel of UML Class Diagrams, EER, and ORM2. Data & Knowledge Engineering, 2015, 98:30-53.

[4] Calvanese, D., De Giacomo, G. The Description Logics Handbook: Theory, Implementation and Applications, chap. Expressive description logics, pp. 178-218. Cambridge University Press (2003).

[5] Keet, C.M., Khumalo, L. Toward a knowledge-to-text controlled natural language of isiZulu. Language Resources and Evaluation, 2016, in print.

[6] Keet, C.M., Khumalo, L. On the verbalization patterns of part-whole relations in isiZulu. Proceedings of the 9th International Natural Language Generation conference 2016 (INLG’16), Edinburgh, Scotland, Sept 2016. ACL, 174-183.

# Surprising similarities and differences in orthography across several African languages

It is well-known that natural language interfaces and tools in one’s own language are known to be useful in ICT-mediated communication. For instance, tools like spellcheckers and Web search engines, machine translation, or even just straight-forward natural language processing to at least ‘understand’ documents and find the right one with a keyword search. Most languages in Southern Africa, and those in the (linguistically called) Bantu language family, are still under-resourced, however, so this is not a trivial task due to the limited data and researched and documented grammar. Any possibility to ‘bootstrap’ theory, techniques, and tools developed for one language and to fiddle just a bit to make it work for a similar one will save many resources compared to starting from scratch time and again. Likewise, it would be very useful if both the generic and the few language-specific NLP tools for the well-resourced languages could be reused or easily adapted across languages. The question is: does that work? We know very little about whether it does. Taking one step back, then: for that bootstrapping to work well, we need to have insight into how similar the languages are. And we may be able to find that out if only we knew how to measure similarity of languages.

The most well-know qualitative way for determining some notion of similarity started with Meinhof’s noun class system [1] and the Guthrie zones. That’s interesting, but not nearly enough for computational tools. An experiment has been done for morphological analysers [2], with promising results, yet it also had more of a qualitative flavour to it.

I’m adding here another proverbial “2 cents” to it, by taking a mostly quantitative approach to it, and focusing on orthography (how things are written down) in text documents and corpora. This was a two-step process. First, 12 versions of the Universal Declaration of Human Rights were examined on tokens and their word length; second, because the UDHR is a quite small document, isiZulu corpora were examined to see whether the UDHR was a representative sample, i.e., whether extrapolation from its results may be justified. The methods, results, and discussion are described in “An assessment of orthographic similarity measures for several African languages” [3].

The really cool thing of the language comparison is that it shows clusters of languages, indicating where bootstrapping may have more or less success, and they do not quite match with Guthrie zones. The cumulative frequency distributions of the words in the UDHR of several languages spoken in Sub-Saharan Africa is shown in the figure below, where the names of the languages are those of the file names of the NLTK data kit that contains the quality translations of the UDHR.

Cumulative frequency distributions of the words in the UDHR of several languages spoken in Sub-Saharan Africa (Source: [3]).

The paper contains some statistical tests, showing that the bottom cluster are not statistically significantly different form each other, but they are from the ‘middle’ cluster. So, the word length distribution of Kiswahili is substantially different from that of, among others, isiZulu, in that it has more shorter words and isiZulu more longer words, but Kiswahili’s pattern is similar to that of Afrikaans and English. This is important for NLP, for isiZulu is known to be highly agglutinating, but English (and thus also Kiswahili) is disjunctive. How important is such a difference? The simple answer is that grammatical elements of a sentences get ‘glued’ together in isiZulu, whereas at least some of them are written as separate words in Kiswahili. This is not to be conflated with, say, German, Dutch, and Afrikaans, where nouns can be concatenated to form new words, but, e.g., a preposition is glued onto a noun. For instance, ‘of clay’ is ngobumba, contracting nga+ubumba with a vowel coalescence rule (-a + u- = -o-), which thus happens much less often in a language with disjunctive orthography. This, in turn, affects the algorithms needed to computationally process the languages, hence, the prospects for bootstrapping.

Note that middle cluster looks deceptively isolating, but it isn’t. Sesotho and Setswana are statistically significantly different from the others, in that they are even more disjunctive than English. Sepedi (top-most line) even more so. While I don’t know that language, a hypothetical example suffice to illustrate this notion. There is conjugation of verbs, like ‘works’ or trabajas or usebenza (inflection underlined), but some orthographer a while ago could have decided to write that separate from the verb stem (e.g., trabaj as and u sebenza instead), hence, generating more tokens with fewer characters.

There are other aspects of language and orthography one can ‘play’ with to analyse quantitatively, like whether words mainly end in a vowel or not, and which vowel mostly, and whether two successive vowels are acceptable for a language (for some, it isn’t). This is further described in the paper [3].

Yet, the UDHR is just one document. To examine the generalisability of these observations, we need to know whether the UDHR text is a ‘typical’ one. This was assessed in more detail by zooming in on isiZulu both quantitatively and qualitatively with four other corpora and texts in different genres. The results show that the UHDR is a typical text document orthographically, at least for the cumulative frequency distribution of the word length.

There were some other differences across the other corpora, which have to do with genre and datedness, which was observed elsewhere for whole words [4]. For instance, news items of isiZulu newspapers nowadays include words like iFacebook and EFF, which surely don’t occur in a century-old bible translation. They do violate the ‘no two successive vowels’ rule and the ‘final vowel’ rule, though.

On the qualitative side of the matter, and which will have an effect on searching for information in texts, text summarization, and error correction of spellcheckers, is, again, that agglutination. For instance, searching on imali ‘money’ alone would be woefully inadequate to find all relevant texts; e.g., those news items also include kwemali, yimali, onemali, osozimali, kwezimali, and ngezimali, which are, respectively of -, and -, that/which/who has -, of – (pl.), about/by/with/per – (pl.) money. Searching on the stem or root only is not going to help you much either, however. Take, for instance -fund-, of which the results of just two days of Isolezwe news articles is shown in the table below (articles from 2015, when there were protests, too). Depending on what comes before fund and what comes after it, it can have a different meaning, such as abafundi ‘students’ and azifundi ‘they do not learn’.

Placing this is the broader NLP scope, it also affects the widely-used notion of lexical diversity, which, in its basic form, is a type-to-token ratio. Lexical diversity is used as a proxy measure for ‘difficulty’ or level of a text (the higher the more difficult), language development in humans as they grow up, second-language learning, and related topics. Letting that loose on isiZulu text, it will count abafundi, bafundi, and nabafundi as three different tokens, so wheehee, high lexical diversity, yet in English, it amounts to ‘students’, ‘students’ and ‘and the students’. Put differently, somehow we have to come up with a more meaningful notion of lexical diversity for agglutinating languages. A first attempt is made in the paper in its section 4 [3].

Thus, the last word has not been said yet about orthographic similarity, yet we now do have more insight into it. The surprising similarity of isiZulu (South Africa) with Runyankore (Uganda) was exploited in another research activity, and shown to be very amenable to bootstrapping [5], so, in its own way providing supporting evidence for bootstrapping potential that the figure above also indicated as promising.

As a final comment on the tooling side of things, I did use NLTK (Python). It worked well for basic analyses of text, but it (and similar NLP tools) will need considerable customization for the agglutinating languages.

References

[1] C. Meinhof. 1932. Introduction to the phonology of the Bantu languages . Dietrich Reiner/Ernst Vohsen, Johannesburg. Translated, revised and enlarged in collaboration with the author and Dr. Alice Werner by N.J. Van Warmelo.

[2] L. Pretorius and S. Bosch. Exploiting cross-linguistic similarities in Zulu and Xhosa computational morphology: Facing the challenge of a disjunctive orthography. In Proceedings of the EACL 2009 Workshop on Language Technologies for African Languages – AfLaT 2009, pages 96–103, 2009.

[3] C.M. Keet. An assessment of orthographic similarity measures for several African languages. Technical report, arxiv 1608.03065. August 2016.

[4] Ndaba, B., Suleman, H., Keet, C.M., Khumalo, L. The Effects of a Corpus on isiZulu Spellcheckers based on N-grams. IST-Africa 2016. May 11-13, 2016, Durban, South Africa.

[5] J. Byamugisha, C. M. Keet, and B. DeRenzi. Bootstrapping a Runyankore CNL from an isiZulu CNL. In B. Davis et al., editors, 5th Workshop on Controlled Natural Language (CNL’16), volume 9767 of LNAI, pages 25–36. Springer, 2016. 25-27 July 2016, Aberdeen, UK.

# On generating isiZulu sentences with part-whole relations

It all sounded so easy… We have a pretty good and stable idea about part-whole relations and their properties (see, e.g., [1]), we know how to ‘verbalise’/generate a natural language sentence from basic description logic axioms with object properties that use simple verbs [2], like $Professor \sqsubseteq \exists teaches.Course$ ‘each professor teaches at least one course’, and SNOMED CT is full of logically ‘simple’ axioms (it’s in OWL 2 EL, after all) and has lots of part-whole relations. So why not combine that? We did, but it took some more time than initially anticipated. The outcomes are described in the paper “On the verbalization patterns of part-whole relations in isiZulu”, which was recently accepted at the 9th International Natural Language Generation Conference (INLG’16) that will be held 6-8 September in Edinburgh, Scotland.

What it ended up to be, is that notions of ‘part’ in isiZulu are at times less precise and other times more precise compared to the taxonomy of part-whole relations. This interfered with devising the sentence generation patterns, it pushed the number of ‘elements’ to deal with in the language up to 13 constituents, and there was no way to avoid proper phonological conditioning. We already could handle quantitative, relative, and subject concords, the copulative, and conjunction, but what had to be added were, in particular, the possessive concord, locative affixes, a preposition (just the nga in this context), epenthetic, and the passive tense (with modified final vowel). As practically every element has to be ‘completed’ based on the context (notably the noun class), one can’t really speak of a template-based approach anymore, but a bunch of patterns and partial grammar engine instead. For instance, plain parthood, structural parthood, involvement, membership all have:

• (‘each whole has some part’) $QCall_{nc_{x,pl}}$ $W_{nc_{x,pl}}$ $SC_{nc_{x,pl}}-CONJ-P_{nc_y}$ $RC_{nc_y}-QC_{nc_y}-$dwa
• (‘each part is part of some whole’) $QCall_{nc_{x,pl}}$ $P_{nc_{x,pl}}$ $SC_{nc_{x,pl}}-COP-$ingxenye $PC_{\mbox{\em ingxenye}}-W_{nc_y}$ $RC_{nc_y}-QC _{nc_y}-$dwa

There are a couple of noteworthy things here. First, the whole-part relation does not have one single string, like a ‘has part’ in English, but it is composed of the subject concord (SC) for the noun class (nc) of the noun that play the role of the whole ( W ) together with the phonologically conditioned conjunction na- ‘and’ (the “SC-CONJ”, above) and glued onto the noun of the entity that play the role of the part (P). Thus, the surface realisation of what is conceptually ‘has part’ is dependent on both the noun class of the whole (as the SC is) and on the first letter of the name of the part (e.g., na-+i-=ne-). The ‘is part of’ reading direction is made up of ingxenye ‘part’, which is a noun that is preceded with the copula (COP) y– and together then amounts to ‘is part’. The ‘of’ of the ‘is part of’ is handled by the possessive concord (PC) of ingxenye, and with ingxenye being in noun class 9, the PC is ya-. This ya- is then made into one word together with the noun for the object that plays the role of the whole, taking into account vowel coalescence (e.g., ya-+u-=yo-). Let’s illustrate this with heart (inhliziyo, nc9) standing in a part-whole relation to human (umuntu, NC1), with the ‘has part’ and ‘is part of’ underlined:

• bonke abantu banenhliziyo eyodwa ‘All humans have as part at least one heart’
• The algorithm, in short, to get this sentence from, say $Human \sqsubseteq \exists hasPart.Heart$: 1) it looks up the noun class of umuntu (nc1); 2) it pluralises umuntu into abantu (nc2); 3) it looks up the quantitative concord for universal quantification (QCall) for nc2 (bonke); 4) it looks up the SC for nc2 (ba); 5) then it uses the phonological conditioning rules to add na- to the part inhliziyo, resulting in nenhliziyo and strings it together with the subject concord to banenhliziyo; 6) and finally it looks up the noun class of inhliziyo, which is nc9, and from that it looks up the relative concord (RC) for nc9 (e-) and the quantitative concord for existential quantification (QC) for nc9 (being yo-), and strings it together with –dwa to eyodwa.
• zonke izinhliziyo ziyingxenye yomuntu oyedwa ‘All hearts are part of at least one human’
• The algorithm, in short, to get this sentence from $Heart \sqsubseteq \exists isPartOf.Human$: 1) it looks up the noun class of inhliziyo (nc9); 2) it pluralises inhliziyo to izinhliziyo (nc10); 3) it looks up the QCall for nc10 (zonke); 4) it looks up the SC for nc10 (zi-), takes y- (the COP) and adds them to ingxenye to form ziyingxenye; 5) then it uses the phonological conditioning rules to add ya- to the whole umuntu, resulting in yomuntu; 6) and finally it looks up the noun class of umuntu, which is nc1, and from that the RC for nc10 (o-) and the QC for nc10 (being ye-), and strings it together with –dwa to oyedwa.

For subquantities, we end up with three variants: one for stuff-parts (as in ‘urine has part water’, still with ingxenye for ‘part’), one for portions of solid objects (as in ‘tissue sample is a subquantity of tissue’ or a slice of the cake) that uses umunxa instead of ingxenye, and one ‘spatial’ notion of portion, like that an operating theatre is a portion of a hospital, or the area of the kitchen where the kitchen utensils are is a portion of the kitchen, which uses isiqephu instead of ingxenye. Umunxa is in nc3, so the PC is wa- so that with, e.g., isbhedlela ‘hospital’ it becomes wesibhedlela ‘of the hospital’, and the COP is ng- instead of y-, because umunxa starts with an u. And yet again part-whole relations use locatives (like the containment type of part-whole relation). The paper has all those sentence generation patterns, examples for each, and explanations for them.

The meronymic part-whole relations participation and constitution have added aspects for the verb, such as generating the passive for ‘constituted of’: –akha is ‘to build’ for objects that are made/constituted of some matter in some structural sense, else –enza is used. They are both ‘irregular’ in the sense that it is uncommon that a verb stem starts with a vowel, so this means additional vowel processing (called hiatus resolution in this case) to put the SC together with the verb stem. Then, for instance za+akhiwe=zakhiwe but u+akhiwe=yakhiwe (see rules in paper).

Finally, this was not just a theoretical exercise, but it also has been implemented. I’ll readily admit that the Python code isn’t beautiful and can do with some refactoring, but it does the job. We gave it 42 test cases, of which 38 were answered correctly; the remaining errors were due to an ‘incomplete’ (and unresolvable case for any?) pluraliser and that we don’t know how to systematically encode when to pick akha and when enza, for that requires some more semantics of the nouns. Here is a screenshot with some examples:

The ‘wp’ ones are that a whole has some part, and the ‘pw’ ones that the part is part of the whole and, in terms of the type of axiom that each function verbalises, they are of the so-called ‘all some’ pattern.

The source code, additional files, and the (slightly annotated) test sentences are available from the GENI project’s website. If you want to test it with other nouns, please check whether the noun is already in nncPairs.txt; if not, you can add it, and then invoke the function again. (This remains this ‘clumsily’ until we make a softcopy of all isiZulu nouns with their noun classes. Without the noun class explicitly given, the automatic detection of the noun class is not, and cannot be, more than about 50%, but with noun class information, we can get it up to 90-100% correct in the pluralisation step of the sentence generation [4].)

References

[1] Keet, C.M., Artale, A. Representing and Reasoning over a Taxonomy of Part-Whole Relations. Applied Ontology, 2008, 3(1-2):91-110.

[2] Keet, C.M., Khumalo, L. Basics for a grammar engine to verbalize logical theories in isiZulu. 8th International Web Rule Symposium (RuleML’14), A. Bikakis et al. (Eds.). Springer LNCS vol. 8620, 216-225. August 18-20, 2014, Prague, Czech Republic.

[3] Keet, C.M., Khumalo, L. On the verbalization patterns of part-whole relations in isiZulu. 9th International Natural Language Generation conference (INLG’16), September 5-8, 2016, Edinburgh, UK. (in print)

[4] Byamugisha, J., Keet, C.M., Khumalo, L. Pluralising Nouns in isiZulu and Related Languages. 17th International Conference on Intelligent Text Processing and Computational Linguistics (CICLing’16), Springer LNCS. April 3-9, 2016, Konya, Turkey. (in print)