Critical debate as well as uncertain or subjective claims are pivotal elements in arts scholarly analysis. Asserting such statements in RDF is hindered by the correct representation of uncertain or evolving aspects. In this article we examine and discuss the need and usefulness of expressing without asserting (EWA) arbitrary claims as RDF named graphs. We examine efectiveness of prior approaches to EWA and we propose a solution, called conjectures, to express and retrieve statements whose truth value is not specified.
attributed over time to Rembrandt, Hooch, and finally to Vermeer (currently, the accepted attribution). Simply presenting the attribution statements (list. 1) has obvious drawbacks: : painting −pr crm : P14_carried_out_by ulan : 5 0 0 0 1 1 0 5 1 . # Rembrandt : painting −pr crm : P14_carried_out_by ulan : 5 0 0 0 2 0 2 2 9 . # Hooch : painting −pr crm : P14_carried_out_by ulan : 5 0 0 0 3 2 9 2 7 . # Vermeer
Given this dataset, any automatic inference engine would be prompted to allow that either the three artists collaborated to the painting or even that they were actually the same individual. A human would therefore be needed to clarify that these options are not all acceptable at the same time, that only one of these artists can be assumed, and that other claims are available for completeness but they should not be considered true. To this extent, superseded claims would rather need to be expressed without asserting (EWA), so that they can be contemplated without contributing to the truth value of the dataset. However, the lack of expressivity of datasets in conveying uncertainty leads to a great loss of information, and to an additional increase of complexity in the critical analysis that must be performed by humans. We believe these situations are the norm in the Humanities and need to be properly addressed, especially when integrating data sources which may carry a diferent (both informal and formal) interpretation of uncertainty.
We expect that any reasonable methodology for EWA is able to express disputed, undisputed
and settled claims, and to distinguish between them with minimal complexity. Over time, several
approaches have been proposed to address EWA [
The purpose of our work is therefore to be able to examine and retrieve statements whose truth is not available. We survey existing methods and we address their benefits and limitations with respect to a common scenario in the Arts, i.e. representing competing attributions. Finally, we propose another approach for expressing without asserting statements, called "conjectures". We compare our solution to prior ones and we discuss the benefits of our contribution.
Expressing uncertainty is considered a key issue in knowledge representation, especially when
dealing with data whose truth-value is not declared [
Ontology-dependent solutions include OWL ontologies for describing provenance,
uncertainty, and trust-related aspects. Generally N-ary Relations [
ontologies do not prevent limitations derived from the actual assertion of claims, e.g. in settled disagreements, where superseded statements remain asserted despite having been rejected.
To prevent the adoption of multiple vocabularies and to cope with the problem of EWA,
ontology-independent solutions have been proposed. These span from the usage of reification
[
In this section we present a survey of existing technologies aimed to represent uncertainty and we classify them with respect to their efectiveness. Since a shared definition of efectiveness in EWA does not exist, we intuitively define it as the overall accuracy and thoroughness of the achieved representation. We base our analysis over the following criteria:
(1) EWA: does the approach allow one to express without asserting arbitrary content? (2) Graph: can non-assertion be associated also to graphs when appropriate? (3) Mapping: is it possible to map data to plain semantics of RDF? (4) Increment: if compatible with RDF, how many triples must be added to map individual statements to plain RDF? (5) Independence: is the approach independent from bespoke technologies, such as parsers, serializations, query languages? (6) Semantics: does it extend RDF semantics?
We selected criteria that allow us to address minimum requirements to EWA contents of named graphs (1 and 2), and focus on those approaches that can be reused from day one (3, 5 and 6) eficiently (4).
In table 1 we present methods that have been evaluated at least twice in the most recent
literature on provenance or meta-knowledge research [
Reification (list. 2) is part of RDF 1.1 semantics. A reified triple is not entailed, therefore complying with our minimum requirement. However, since it requires an expensive addition of triples (4+) and it does not allow inference on reified triples, it has been disregarded as a solution to describe provenance and it has been proposed for deprecation3 [23].
N-ary relations (list. 3) are adopted in CIDOC-CRM. To represent concurring statements, instances of the class crm:E13_Attribute_Assignment are annotated with context information. This method shows some verbosity and redundancy of triples to add context to statements. Additionally, all statements are considered asserted, and therefore, in our example, the three attributions are equally asserted, despite the debate is settled toward only one. : aa1 r d f : type r d f : S t a t e m e n t ; r d f : s u b j e c t : p a i n t i n g − pr ; r d f : p r e d i c a t e crm : P 1 4 _ c a r r i e d _ o u t _ b y ; r d f : o b j e c t ulan : 5 0 0 0 1 1 0 5 1 ; # Rembrandt crm : P4_has_time −span : X V I I I _ c e n t . : aa2 r d f : type r d f : S t a t e m e n t ; r d f : s u b j e c t : p a i n t i n g − pr ; r d f : p r e d i c a t e crm : P 1 4 _ c a r r i e d _ o u t _ b y ; r d f : o b j e c t ulan : 5 0 0 0 2 0 2 2 9 ; # Hooch crm : P4_has_time −span : 1 8 2 1 . : aa3 r d f : type r d f : S t a t e m e n t ; r d f : s u b j e c t : p a i n t i n g − pr ; r d f : p r e d i c a t e crm : P 1 4 _ c a r r i e d _ o u t _ b y ; r d f : o b j e c t ulan : 5 0 0 0 3 2 9 2 7 ; # Vermeer crm : P4_has_time −span : 1 8 6 0 ; crm : P 1 4 _ c a r r i e d _ o u t _ b y ulan : 5 0 0 3 2 6 9 4 8 . # Thore Listing 2: Competing
attributions with Reification : aa1 a crm : E 1 3 _ A t t r i b u t e _ A s s i g n m e n t ; crm : P 1 7 7 _ a s s i g n e d _ p r o p e r t y _ o f _ t y p e crm : P 1 4 _ c a r r i e d _ o u t _ b y ; crm : P 1 4 1 _ a s s i g n e d ulan : 5 0 0 0 1 1 0 5 1 ; # Rembrandt crm : P 1 4 0 _ a s s i g n e d _ a t t r i b u t e _ t o : p a i n t i n g − pr ; crm : P4_has_time −span : X V I I I _ c e n t . : aa2 a crm : E 1 3 _ A t t r i b u t e _ A s s i g n m e n t ; crm : P 1 7 7 _ a s s i g n e d _ p r o p e r t y _ o f _ t y p e crm : P 1 4 _ c a r r i e d _ o u t _ b y ; crm : P 1 4 1 _ a s s i g n e d ulan : 5 0 0 0 2 0 2 2 9 ; # Hooch crm : P 1 4 0 _ a s s i g n e d _ a t t r i b u t e _ t o : p a i n t i n g − pr ; crm : P4_has_time −span : 1 8 2 1 .
A singleton (list. 4) is a unique predicate that is used only once to represent a triple, instead of the original predicate. As such, it can be subject of additional triples. The property :singletonPropertyOf maps new predicates to the original ones. However, it is a subproperty of rdf:type, therefore the new statements must be considered asserted as well. : p a i n t i n g − pr : P 1 4 _ c a r r i e d _ o u t _ b y #1 ulan : 5 0 0 0 1 1 0 5 1 ; # Rembrandt : P 1 4 _ c a r r i e d _ o u t _ b y #1 r d f : s i n g l e t o n P r o p e r t y O f crm : P 1 4 _ c a r r i e d _ o u t _ b y ;
crm : P4_has_time −span : X V I I I _ c e n t . : p a i n t i n g − pr : P 1 4 _ c a r r i e d _ o u t _ b y #2 ulan : 5 0 0 0 2 0 2 2 9 ; # Hooch : P 1 4 _ c a r r i e d _ o u t _ b y #2 r d f : s i n g l e t o n P r o p e r t y O f crm : P 1 4 _ c a r r i e d _ o u t _ b y ;
crm : P4_has_time −span : 1 8 2 1 . : p a i n t i n g − pr : P 1 4 _ c a r r i e d _ o u t _ b y #3 ulan : 5 0 0 0 3 2 9 2 7 ; # Vermeer : P 1 4 _ c a r r i e d _ o u t _ b y #3 r d f : s i n g l e t o n P r o p e r t y O f crm : P 1 4 _ c a r r i e d _ o u t _ b y ; crm : P4_has_time −span : 1 8 6 0 ; crm : P 1 4 _ c a r r i e d _ o u t _ b y ulan : 5 0 0 3 2 6 9 4 8 . # Thore
Named graphs (list. 5) present a peculiar situation. It has been argued that graphs do not
contribute in determining the truth of a dataset [
GRAPH : aa1 { : p a i n t i n g − pr c o n j 0 0 0 1 : P 1 4 _ c a r r i e d _ o u t _ b y ulan : 5 0 0 0 1 1 0 5 1 . # Rembrandt } : aa1 crm : P4_has_time −span : X V I I I _ c e n t .
GRAPH : aa2 { : p a i n t i n g − pr c o n j 0 0 0 2 : P 1 4 _ c a r r i e d _ o u t _ b y ulan : 5 0 0 0 2 0 2 2 9 . # Hooch } : aa2 crm : P4_has_time −span : 1 8 2 1 .
GRAPH : aa3 { : p a i n t i n g − pr c o n j 0 0 0 3 : P 1 4 _ c a r r i e d _ o u t _ b y ulan : 5 0 0 0 3 2 9 2 7 . # Vermeer }
In N3, graphs can be quoted by other formulas, which do not assert the contents of the
RDF graph (list. 6). N3 syntax is compact. Since graphs in N3 do not have an identifier, the
annotation must be performed in place. Yet, N3 graphs can nest at arbitrary depth levels, while
RDF 1.1 graphs cannot contain other graphs. Recent works [
RDF* is a recent extension of RDF that allows a concise representation of statement-level metadata (list. 7). However, multiple statements, encapsulated in graphs, cannot be quoted. It is backward-compatible to RDF, requiring the specification of 6 to 9 additional triples for every quoted statement. In order to leverage all the potentialities of this proposal, bespoke languages (RDF* and SPARQL*) and technologies (RDF* graph stores) must be used. << : painting −pr crm : P14_carried_out_by ulan :5 00 01 1 05 1 >> crm : P4_has_time −span : X VI II_ ce nt . << : painting −pr crm : P14_carried_out_by ulan :5 00 02 0 22 9 >> crm : P4_has_time −span : 1 8 2 1 . << : painting −pr crm : P14_carried_out_by ulan :5 00 03 2 92 7 >> crm : P4_has_time −span : 1 8 6 0 ; crm : P14_carried_out_by ulan : 50 03 26 9 48 .
In summary, it is currently possible to achieve EWA respectively, with reification, N3 and RDF*. However, it comes with the cost of adding triples (between 4 and 9), the impossibility to annotate graphs (RDF*), and the complexity of tracking the re-assertion of triples (N3). Nonetheless, we believe it is possible to build on previous work to define a strategy that is fully compliant with RDF1.1., without dramatically increasing the number of triples.
The motivation driving this work is to have the possibility to make claims that must not be interpreted as facts (i.e., as asserted statements). In addition, even if in our examples we simplified claims to individual triples, real-world scenarios often include claims that cannot be reduced to a binary relation expressible as a single RDF statement. Therefore we aim at a solution that allows us to express content of named graphs without asserting them.
Conjectures are used for this purpose. A conjectural graph is a named graphs where all triples (, , ) are represented with two triples, (, , ) and (, : , ), where is a unique newly minted predicate created specifically for the triple to conjecture.
Listing 8 shows the aforementioned example with conjectures. Conjectures adopt newly minted predicates used exactly once4, that are mapped to their original predicate via the property conj:isAConjecturalFormOf. Similarly to :singletonPropertyOf, the property allows to easily retrieve original predicates. However, the conjectural property is not a subproperty of rdf:type, meaning that the original statements are not asserted. Conjectural graphs can now be annotated with statements to express their provenance, their temporal validity, and any other constraint that may be necessary to specify the conditions under which the conjecture can be considered true.
Indeed, the use of minted predicates has a few advantages. First, the original triples (i.e. those not using conjectural predicates) are not stated, thus fulfilling the basic requirement of expressing without asserting. Second, contradictory statements, each adopting a conjectural predicate derived from the same original predicate, are explicitly mapped to the original one through the conj:isAConjecturalFormOf predicate, which ensures clear identification and facilitates querying for unsettled disputes. Moreover, conjectural predicates comply with RDF semantics and only require a minimal increase of triples (one new RDF triple is added for every conjectured triple).
In the introduction we identified (at least) three classes of statements that are of interest to scholars, namely undisputed, disputed and settled statements. Accordingly, we employ plain named graphs for undisputed claims (to be interpreted as asserted until a disagreement is recorded), and conjectural graphs for disputed claims (to be interpreted as expressed without positive assertion). Finally, a settled dispute is a statement that has been put in doubt by someone (and therefore disputed), but for which eventually a consensus was reached and the relevant community (and the dataset that expresses its point of view) record both the fact that the claim was disputed, as well as its subsequent assertion. To handle settled disputes we define collapse graphs.
A collapse graph 1 consists of two graphs: the first is the conjecture 1 expressed as in list. 8, and the second is a new graph 1 including all the triples in 1 but with their original predicates, excluding : , and adding the triple (1, : , 1).
In our running example, the community has now agreed on Vermeer being the author of the painting (graph :aa3), which can be represented as a settled conjecture in listing 9.
4We mint new predicates by creating URIs with a diferent prefix for every named graph (in these examples, conj0001, conj0002, etc.) and the same local part as the original predicate (e.g., crm:P14_carried_out_by) to map newly created predicates to the original ones
Conjectures can be expressed as a variant of singleton properties (that we call the weak form) or as RDF 1.1 named graphs extension, which we call strong form. Strong and weak forms aim to provide two (non alternative) solutions to EWA, preventing technological barriers in their adoption. The full semantics and interpretation of Conjectures is separately documented [25], along with a longer dissertation on the structure of conjectures, and an online parser5.
In this article we examined solutions for EWA. We showcased benefit and limitations of recent
works on uncertainty, provenance, and meta-knowledge with RDF technologies [