Representing temporal knowledge and information in temporal logics for ontologies and conceptual data models has faced issues due to inaccessibility of the underlying logic and limited intuitiveness of diagrammatic extensions to the modelling languages. We aim to address this by designing controlled natural language templates for generating sentences that verbalise in English the temporal constraints de ned in a temporal logic. We devised 101 templates, which were evaluated by experts in temporal logics and by novice temporal modellers on semantic adequacy and preference. There was only 12% unanimity among the experts, and 89% by majority voting. The novice temporal modellers were much more lenient in judgment on whether the templates captured the semantics adequately. Instead of a direct 1:1 mapping between an axiom's components and the natural language rendering, the more natural-sounding sentences were preferred, therewith linking an axiom type as a whole to a template.
Time is pervasive in communication and relevant for almost any subject domain
of interest. For instance, a business rule that states that any manager of a
company must already be an employee of that company, biological knowledge that
each butter y used to be a caterpillar, and census information stating that a
divorce can only occur if there was a marriage before. Several options are at one's
disposal to represent such temporal information, be this for ontology development
or information system design. For ontology, the focus has been on fundamental
representation choices such as 3-dimensional objects with time vs 4-dimensional
entities. For representation languages, the emphasis is on features to represent
more or less temporal constraints and automated reasoning over it, which can
be grouped into ontology languages [
A. Sample temporal model in TREND notation
Board Member
EmpID
DEXDEV
Employee Manager
Office (0,n) DEX (1,n) work manage
(1,n) DEX
Project (1,1)
B. Partial logic-based reconstruction in DLRus notation
C. What we aim for: natural language rendering of temporal constraints
The natural language option means to verbalise structured input or use
Natural Language Generation (NLG). Atemporal verbalisation has been successful
for both conceptual data models [
The aim is thus to nd out what is the best way of verbalising the temporal constraints and answer 1) Does each proposed natural language sentence template capture the semantics of the temporal constraint adequately? and 2) Which sentence among the options is preferred? We used the semantics of the Description logic (DL) DLRUS as structured information and knowledge representation, as it currently has the most comprehensive set of temporal constraints and it easily can be mapped to one's preferred logic or modelling language. We discuss the template development to verbalise the 34 temporal constraints. One or more templates were devised for each temporal constraint. The templates were evaluated by three temporal logic experts and ve `mixed experts' (experts in modelling, logic, or NLG, but not temporal). There was little unanimous agreement on template preferences among the experts. The `mixed experts' judged many more sentences to be correct than the experts, yet there was even less agreement among the participants. Overall, 26 of the 34 constraints did result in preferred sentences, and the remaining 8 sentences were updated by taking into account the written feedback. These nal templates map an axiom type as a whole to the template as a whole, rather than by consituent.
In the remainder of the paper, we rst describe preliminaries in Section 2. Possible templates with word choices are discussed in Section 3. The evaluation is presented in Section 4. We discuss and conclude in Sections 5 and 6.
Linguistically, there are two principal ways to refer to temporal points and intervals in a sentence: using verb tenses, such as `have eaten' and `will eat', or prepositions and adjuncts, such as `before' and `some time later', or both to stress the time dimension and relation between events at points or during intervals, like `have eaten before [some other event]'. The major languages in the world have between zero (e.g., Chinese) and three (e.g., Romance languages) tenses, with variations using compound forms with auxiliary verbs.
Within commonly used information and knowledge representation that we restrict ourselves to here, not all verb tenses and adjuncts will be needed, because it is a restricted application domain concerning tracking the evolution of objects, relations, and, possibly, attributes over time, not, say, events that did not happen in the past (`could/would have done'). The core relevant temporal aspects are depicted in Figure 2. First, we have \snapshot (rigid)", which is essentially atemporal, or `at all times' for the duration of the entity's existence. The \temporal options (antirigid)" denotes that an entity is an instance of a type at some time, but not at all times, which is indicated with a non-solid line. There are four core transition constraints: \extension" means that at some time an entity also instantiates another type and \evolution" means that the entity instantiates one type after another. These constraints may be quantitative (a xed amount of time), and are either optional (universally quanti ed) or mandatory (existentially now
flow of time snapshot (rigid) } temporal options (antirigid) extension in the future evolution in the future extension in the past evolution in the past quanti ed). As they can be declared for entity types, relationships, and attributes, this amounts to 48 possible temporal constraints. These changes can be covered by just a few verb tenses. Mainly, they constitute choices on the future single vs future continuous (respectively, the past).
Some of the temporal constraints are computationally more interesting than others. In particular, constraints on the future are trivially satis ed and thus cannot be checked, whereas constraints about the past|which must be present in a prior state of the data or knowledge base|and quantitative constraints can be checked. Also, it was di cult to devise good examples for some of the attribute constraints, and they are not used often in ontologies anyway. Taking this into account, we reduced it to 34 axiom types out of the 48. Further, it makes sense to include domain and range when verbalising a relationship of a conceptual model. This context is necessary because a conceptual model may reuse the name of an attribute or relationship, but never with the same entity types. This is in contrast with relations in ontologies that do not require a domain and range restriction, and as also re ected in DLRUS . We have made templates for both scenarios, but it appeared that the templates for the relations (OWL object properties, DL roles) in ontologies always resulted in a subset of those of conceptual models such that it required one conversion rule (illustrated below). Therefore, we opt here for the more comprehensive ones with domain and range.
We created 1-7 candidate templates for each constraint, which would verbalise
the constraints more or less precisely or colloquially. For each list of options for a
constraint, the rst one is most literal with respect to the formal semantics, and
the other ones are more or less precise rewordings that sound less `clunky' and
arti cial. Regarding the formal counterpart, we rely on the formal foundations of
TREND, being the semantics of DLRUS [
IC IC to each relation R 2 R and a set AI(t) of tuples over IC ID to each attribute A 2 A. While DLRUS permits n-ary relations, we present just the case for binaries. The formalisation of all constraints is available in the supplementary material at http://www.meteck.org/files/CREOL17suppl.zip.
The entity types, relationships, and attributes can be divided into atemporal (`snapshot') and temporal entities, where the former has no explicit speci cation of time|or: holds globally at all times|and the latter do. A temporal entity type is formalised as o 2 CI(t) ! 9t0 6= t:o 2= CI(t0). A template option with a closer 1:1 match between the axiom type with its structure and the natural sentence and, say, the entity type Student would generate If an object is an instance of entity type Student, then there is some time where it is not a Student or one could paraphrase it as Each Student is not a Student for some time, among the possible options.
For temporal relationships, with the semantics r 2 RI(t) ! 9t0 6= t:r 2= RI(t0), we devised two options that amounted to largely just shu ing around the constituents of the template, with Ci an entity type and Ri a relationship: (a) The objects in the facts in ..C1.. ..R1.. ..C2.. do, at some time, not relate through ..R1.. (b) The objects participating in a fact in ..C1.. ..R1.. ..C2.. do not relate through ..R1.. at some time.
Note that for an ontology setting, one can simply drop the C1 and C2 variables for the entity types: The objects in ..R1.. do, at some time, not relate through ..R1.. .
The semantics of a basic temporal attribute is o 2 CI(t) ^ ho; di 2 AI(t) ! 9t0 6= t:ho; di 2= AI(t0), where the templates assume that any `has' from the attribute's name is dropped if it is already in the name (e.g., hasColour), or it is substituted with the verb in the attribute's name. For instance, its option (e) with an example about bonus payments would generate a sentence alike An Employee receives a Bonus, but not always.
The two basic types of dynamic constraints are extension and evolution (recall Figure 2), where extension has the element remain a member of the source class and in an evolution it stops being member of the source class once it evolves to the target class. This may be at `some' time or at a metric (quantitative) time, and it may persist or not. They can be optional or mandatory, i.e., whether some object, relation, or attribute may evolve or all objects/relations that instantiate the class/relationship must evolve. This can be verbalised more or less harshly, just like with atemporal constraints2. That is, for future tense one can use the auxiliary verb `will' versus the stronger-sounding `has to' or `must'. Likewise, for the past there is a similar type of di erence between `was already/before/earlier, but not now' vs. `must have been'. For instance, mandatory dynamic evolution in the past (DevM ), i.e., o 2 DevM IC(1t;)C2 ! (o 2 C1I(t) ! 9t0 < t:o 2 DevIC(1t;0C)2 ) where the semantics of Dev is o 2 DevIC(1t;)C2 ! (o 2 C1I(t) ^ o 2= C2I(t) ^ o 2 C2I(t+1) ^ o 2= C1I(t+1)), with, e.g., Butter y (to be lled in for C2 in the template) and the Caterpillar (C1) it used to be, with the following possible templates: (a) Each ..C1.. must have been a(n) ..C2.. , but is not a(n) ..C2.. anymore. (b) Each ..C1.. was a(n) ..C2.. before, but is not a(n) ..C2.. now. (c) If ..C1.. , then ..C1.. was a(n) ..C2.. before, but is not a(n) ..C2.. anymore.
Persistence (PDex/PDev) has the change holding at all times in the future, which is built from whatever will be chosen from the possible templates and appended by a phrase like , and this remains so. or , and this remains so inde nitely..
For quantitative extension and evolution, we need a speci c number for counting and, implicitly, some time unit to be able to construct, e.g., `after 2e.g., `each Prof teaches at least one course' vs. `each Prof must teach at least one course'. at least 3 years'. The number is denoted with the variable D1 in the template. For instance, mandatory quantitative extension in future (QexM), i.e., o 2 QexIC(1t;)C2 ! (o 2 C1I(t) ! 9(t + n) > t:o 2 QexIC(1t;+Cn2)), e.g., all Students (to be slotted in at C1) have to Volunteer (C2) in the second year (D1) of their study, with template options: (a) Each ..C1.. will also become a(n) ..C2.. after [at least/at most/exactly] ..D1.. . (b) If ..C1.. for [at least/at most/exactly] ..D1.. , then ..C1.. becomes a(n) ..C2.. as well.
Regarding word choice in template design for relationships, the transition concerns overlapping or successive processes; thus verbs such as `precede' and `follows' are applicable. On their own, they do not distinguish between the two cases of whether the relations may co-exist or if one occurs after the other. This can be addressed by disambiguating both cases, or one of the two with the other left implicit. We chose the latter option, and add it to the evolution cases rather than the extension cases, as they are stricter constraints. Likewise, `sequentially' and `successively' are roughly synonyms and imply that earlier state has ended, so the only core di erence to test is whether that should be made explicit, e.g., with inclusion of terms such as `ending' or `terminating', or not. For instance, for mandatory dynamic extension for relationships in the past (RDexM ), i.e., ho; o0i 2 RDexMR1;R2 I(t) ! (ho; o0i 2 R2I(t) ! 9t0 < t:ho; o0i 2 RDexR1;R2 I(t0)), where the semantics of `just' RDex is ho; o0i 2 RDexR1;R2 I(t) ! (ho; o0i 2 R1I(t) ! 9t0 > t:ho; o0i 2 R2I(t0)), option (a) was Each ..C1.. ..R1.. ..C2.. is preceded by ..C1.. ..R2.. ..C2... For instance, every passenger who boards a ight must have had a check-in process before with its template option (a) then results in a somewhat clunky Each Passenger boards Flight is preceded by Passenger checksIn Flight. Note that also here it is easy to see how this template can be adapted for ontologies by dropping the C1 and C2 variables.
These time markers are more challenging with the more complex constraints. For instance, mandatory dynamic evolution for relationships in the past (RDevM ), with the typical example that any pair of humans who are divorced were married before that. The full set of template options to choose from was: (a) Each ..C1.. ..R1.. ..C2.. is strictly preceded by ..C1.. ..R2.. ..C2.. . (b) Each ..C1.. ..R1.. ..C2.. is preceded by ..C1.. ..R2.. ..C2.. and they are not in that ..C1..
..R2.. ..C2.. relation anymore. (c) If ..C1.. ..R1.. ..C2.. , then it was preceded by ..C1.. ..R2.. ..C2.. and they are not in that ..C1.. ..R2.. ..C2.. relation now. (d) Each ..C1.. ..R1.. ..C2.. must have been preceded by ..C1.. ..R2.. ..C2.. and they are then not in that ..R2.. relation anymore. (e) If ..C1.. ..R1.. ..C2.. , then it must have been preceded by ...C1.. ..R2.. ..C2.. , but ..C1..
not ..R2.. ..C2.. anymore.
Two dynamic attribute constraints were included in the evaluation, which were uncontentious, and therefore they are omitted here due to space limitations.
The templates designed for the temporal elements and constraints are evaluated aiming to answer: 1. Does each proposed template for a natural language sentence capture the semantics of the temporal constraint adequately? 2. Which sentence among the options is preferred? The principal approach is to use a two-pronged survey: a small group of experts in temporal logic, and a `mixed' group of experts in related relevant elds that is not temporal logic, which includes modellers, NLG experts, and logicians.
A survey was designed with the temporal constraints and elements, and 1-7 templates for each. The participants were given a brief written explanation of the logic and how to read a template, an example for each constraint, and the scope of the evaluation. They were instructed to evaluate each template on whether it would capture the meaning adequately, which could be answered with either \yes", \sort of" denoting borderline, or \no", and which of the templates they preferred, if any, among the set of templates for that constraint. They also were allowed to comment on each template option.
The three temporal logic experts are remote colleagues and were recruited by email through purposive sampling. The mixed group also was recruited through purposive sampling, with as prerequisite that they have a good to excellent understanding of modelling, logic, or NLG. No personal information was recorded other than whether they have English as their mother tongue language. The answers were collected in a pre-formatted spreadsheet. A follow-up interview with one expert was also conducted to obtain further qualitative feedback on the choices.
All materials and results are available at http://www.meteck.org/files/ CREOL17suppl.zip.
We present rst the results of the experts and then those of the mixed group.
An overview of the quantitative results is included in Table 1. 41% of the templates were deemed to properly represent the semantics of the temporal constraint, though only 12 templates received the same score (either all \yes", \sort of", or \no") with most (78) receiving two the same verdicts, reaching 89% then. Four templates of constraints were unanimously preferred: those for Mandatory Quantitative Extension and for Evolution (QexM and QevM) and the two attribute constraints (Freez `frozen attribute' and AQev `Quantitative evolution, attribute'). With majority voting, this increased to 13 constraints. This is remarkable, because the experts know each other well and have collaborated. Even the simple constraint of `temporary class' (Tc) had three di erent verdicts for its option (b) ..C1.. is an entity type whose objects are, for some time in their existence, not instances of ..C1.., as did option (b) of dynamic evolution in the past (Dev ).
Quantitative extension and evolution used the grammatically correct `for' in the sentence, but this was deemed wrong. Instead, the experts preferred `since'. This may be due to either the Since operator in the logic, or it has a stronger sense of time and fewer senses than the multiple-use `for', or that neither of the experts has English as mother tongue. A follow-up interview on this matter with one of the experts (e3 in the data) revealed that at least for e3 it was not so much about `for' vs `since' but the ne-grained distinction between \for an x amount of time since x" (or: holding between x ago and now) vs. \x chronons ago" but it may not hold some time between x and now. On closer inspection, the logic stated the latter, while the former was intended, which is what caused the confusion.
Regarding `preceded by' and `followed by' in the templates (recall Section 3.2), there were a few comments such as \I don't like \followed" that can be understood as \at the next time point"". Thus, only using strictly/immediately to indicate the next/previous time point and therewith leaving implicit when this may not be the case when it is not stated explicitly was found to be ambiguous. Put di erently: an explicit time marker was perceived to be needed also for the `some time'. We updated the templates accordingly (see online supplementary material).
An important result to note for the preferred templates, is that they do not
follow the structure of the axiom, regardless whether it would be rendered in the
formal semantics or DLRUS syntax. That is, the preferred templates amount to a
mapping between an axiom type rather than the axiom's structure. To illustrate:
{ Formal Semantics: o 2 DevM IC(1t;)C2 ! (o 2 C1I(t) ! 9t0 < t:o 2
DevIC(1t;0C)2 ): \For objects involved in a mandatory dynamic evolution in the
past, if o is an instance of C1, then there exists a time t0 earlier than time
t such that at that earlier time t0 it evolved from C1 to C2."
{ DLRUS shorthand notation: C1 v 3 DevC1;C2 : \Each C1 is a subclass of
some time in the past dynamically evolved from C1 to C2"
{ DLRUS full notation: C1 v C1 u :C2 u (:C1 u C2): \Each C1 is a subclass
of C1 and not C2 and at the next moment (not C1 and C2)"
versus the preferred rendering Each C1 was a C2 before, but is not a C2 now. Not
linking each axiom component to a fragment of the natural language sentence
deviates from common practices of verbalising ontologies and conceptual models
(e.g., [
The follow-up interview with expert e3 included a clari cation on the aforementioned for/since issue. Expert e3 also noted that if neither expert has English as rst language, this may have contributed to the low amount of unanimity. It may seem disconcerting that experts each use their own terminology, but e3 did not see that as a real issue, \for there is the logic that does have the precise meaning anyway" and thus \resolves any confusion that may arise from using slightly di erent terminology" (paraphrased). In this light, it is not likely that asking many more temporal logic experts will make the results converge. Lastly, e3 suggested that the relative large di erence in \yes" between e3 and e1 (29 vs 62 `yes') may be due to attitude toward judging, in that e3 aimed for one and at most two \yes" per constraint. However, this does not explain why e2 had only 34 \yes", but where no such criterion could have been used.
The aggregate result for the mixed experts are included in Table 1. The main interesting outcome is the large di erences with the temporal logic experts on whether the templates capture the semantics adequately. The mixed experts deemed many more sentences to be fully or borderline acceptable. This is in large part explainable in that the experts have a better grasp of the subtleties of the temporal constraints. A clear illustration of this is RDevM `Dynamic evolution for relationships, past, mandatory' option (a), where e1 had commented \Absolutely false!" with 2 \no" and 1 \sort of" from the experts, yet it had 3 \yes" and 2 \sort of" from the mixed group, and Sr `Snapshot relationship' option (a) received 3 \no" from the experts, yet 2 \yes" and 3 \sort of" from the mixed group.
Further, the aggregate evens out the more strict grading by the single mixed expert who has English as rst language (p1 in the data), which may also contribute to assessing precision of verbalising the constraints, and one of the two logicians who is well-versed in modal logics and thus may grasp the nesses of temporal logics better. The aforementioned for/since issue of Qex `Quantitative extension, past, optional' and QexM `Quantitative extension, past, mandatory' was absent from the mixed group, who deemed it mostly acceptable.
Regarding preferences for a particular template, there was no unanimous preference on any template, 4 where 4 out of 5 agreed on a preference, and 17 by majority voting (3 out of 5). As to unanimity of verdicts, the mixed group answered the same on 6 templates. There is a slight preference for shorter sentences: 13 preferences were sole or shared shortest template, 5 were sole or shared longest template, and 4 were neither.
Few comments were made by the mixed participants. Recurring ones include NLG expert (p2)'s option that several templates were either vague (e.g., option (a) of Tc `Temporal class'), repetitive (PDex/PDev `Persistent extension/evolution'), or that it \does not sound natural enough" (e.g., Dev `Dynamic evolution, past, optional'). Participant p1 provided most feedback on word choices and preferences; e.g., instead of ..., but is not now in Qev `Quantitative evolution, past, optional' and QevM `Quantitative evolution, past, mandatory', rather ..., but is not a C2 now, a dislike for the use of sequentially in dynamic evolution templates (which the experts marked down as well), and on ceasing in the template suggesting instantaneous change \rather than stating so explicitly".
The outcome with the preferred templates is, to the best of our knowledge, the rst proposal for linking temporal knowledge or information to natural language. The number of participants is relatively small, but a larger group will neither resolve the low inter-annotator agreement of the temporal logic experts, nor the comparatively high `yay-saying' among the mixed expert group whose di erence would likely be exacerbated with, say, a group of 4th year student participants that are less conversant in temporal constraints. It is nigh on impossible to examine whether a non-expert group would really have understood the logic, because it would require participants to communicate the meaning in a di erent mode than the natural language, and those alternative modes were precisely a problem that the natural language approach aimed to address. rendering it di cult to discern whether a lack of understanding may be due to the other representation, Simplicity or potential di culty of the templates, as measured by number of words, did not show unequivocal preference for shorter templates (hence, sentences), especially among the experts. The data collected cannot explain this, and it thus merits further investigation whether some temporal constraints indeed cannot be simpli ed further without losing their meaning.
Looking back at Figure 1, the temporal entities and constraints are now
verbalised as shown in Figure 1-C. One might pose that once implemented, it may
end up in too many sentences for a modeller to check. However, one could 1)
further prioritise constraints and 2) rely on an automated reasoner. Regarding
prioritisation, the mandatory, past, and quantitative constraints are more interesting
from an information systems point of view, for they can be easily implemented
in a database as integrity constraints. Optional past and future constraints may
be interesting for querying and database updates only. Regarding the latter: with
the logic foundation, one could specify just a few important temporal constraints
and let the rest be inferred by the reasoner thanks to the logical implications
[
Template selection of temporal constrains in temporal logics and logic-based temporal conceptual modelling languages showed low expert inter-annotator unanimous agreement, although 89% with majority voting. The experts were more strict (41%) on whether a template captured the semantic than the mixed group (64%), noting that there were few unanimous preferences. Taking into account judgement of semantics, indicated preferences, and comments, all 34 axiom types now have a template for verbalisation. The templates map as a whole to an axiom type rather than their constituents.
We have recently completed a modelling experiment showing that, on the
whole, the template-based natural language was preferred over other notations
(semantics, DL, diagram, coding-style) especially for the more complex
constraints [
Acknowledgments The author would like to thank the participants for their valuable feedback and the reviewers for their suggestions.