On the semantic engineering of scienti c hypotheses as linked data

Abstract

The term `hypothesis' is part of the Linked Science Core Vocabulary (LSC) as one of the core elements for making scienti c assets explicit and linked in the web of data. Hypotheses are generally understood as propositions for explaining observed phenomena, but eliciting and linking hypotheses can be a challenge. In this paper, we elaborate on a semantic view on hypotheses and their linkage, by striving for minimal ontological commitments. We address the engineering of hypotheses as linked data, and build upon LSC by extending it in order to accommodate terms necessary in model-based sciences such as Computational Science. Then we instantiate the extended LSC by eliciting and linking hypotheses from a published research in Computational Hemodynamics.

Keywords

• Linked Science Core Vocabulary (LSC)
• Scienti c Hypothesis
• Semantic Engineering
• Hypothesis Linkage
• Computational Science

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Data-intensive science has large-scale data management as a key technology for enabling the scienti c practice. Nevertheless, there is still signi cant challenges w.r.t. real-world semantics (meaning) for humans as cognitive agents to be able to browse the data deluge [ 4 ]. In this sense, Linked Science emerges as a promising program [ 11 ]. It has the potential to enable a semantic-sensitive linkage between scienti c assets, providing support to both humans and machines.

Scientists need to access data still in order to formulate and evaluate hypotheses [ 4 ]. The term `hypothesis' is part of the Linked Science Core Vocabulary (LSC) as one of the core elements for linking science [ 11 ]. Nevertheless, eliciting and linking hypotheses can be a challenge. Scienti c hypotheses are falsi able statements [ 19 ], which are proposed to explain a phenomenon.1 Let us consider a well-known Einstein's hypothesis to refer as an example. It is identi ed in Wikipedia as (i) the mass-energy equivalence, and presented together with (ii) the famous mathematical equation E = mc2. There can be variations in the formulation of this mathematical expression, yet referring to the same hypothesis. Wikipedia's article2 is introduced with the sentence \In physics, mass-energy

1 http://en.wikipedia.org/wiki/Hypothesis. 2 http://en.wikipedia.org/wiki/Mass-energy_equivalence. Access on 7/31/2012.

equivalence is the concept that the mass of a body is a measure of its energy content." This hypothesis is strongly supported by experiments, and explains the transfer of energy and mass as a general phenomenon (cf. Wikipedia's article).

That example illustrates a semantic view on scienti c hypotheses that draws on their existence apart from a particular statement formulation in some mathematical framework. The mathematical equation is not enough to identify the hypothesis, rst because it must be physically interpreted, second because there can be many ways to formulate the same hypothesis. The link to a mathematical expression, however, brings to the rei ed hypothesis concept (Wikipedia's entry) higher semantic precision. Another link, in addition, to an explicit description of the explained phenomenon (emphasizing its \physical interpretation") can then (reasonably) succeed in bringing forth the intended meaning.

In this paper, we elaborate on a semantic view on scienti c hypotheses and their linkage, by striving for minimal ontological commitments [ 7 ]. We address the engineering of hypotheses as linked data, and build upon LSC [ 11 ] by extending it in order to accommodate terms necessary in model-based sciences such as Computational Science. We focus on this powerful new scienti c discipline [ 21 ], where scienti c hypotheses are assumptions that constrain the interpretation of observed phenomena for computer simulation. Then we instantiate the extended LSC by eliciting and linking hypotheses in a published research in Computational Hemodynamics [ 1 ]. This paper points out the important role hypotheses are to play as conceptual entities in Linked Science [ 11 ] and theory-driven eScience [ 2 ].

The paper is organized as follows. In Section 2 we comment on a related work background, and in Section 3 we introduce hypotheses in Computational Hemodynamics. In Section 4 we present our semantic view on hypotheses and its engineering in Linked Science by extending LSC. This section is fully illustrated with examples from Computational Hemodynamics. In Section 5 we instantiate the extended LSC in a published research on the modeling and simulation of the human cardiovascular system. Finally, in Section 6 we conclude the paper.

2 Related Work

The HyBrow (Hypothesis Browser) conceptual framework [ 20 ] addresses hypothesis modeling in Bioinformatics. It aims at providing biologists with a uni ed eScience infrastructure for hypothesis formulation and evaluation against observed data. HyBrow is based on an OWL ontology and application-level rules to contradict or validate hypothetical statements. As an upgrade of HyBrow, the HyQue [ 3 ] framework adopts linked data technologies and employs Bio2RDF to add to HyBrow semantic interoperability capabilities. HyBrow/HyQue's hypotheses are domain-speci c statements that correlate biological processes (seen as events) in First-Order Logic (FOL) with free quanti ers. Hypothesis formulation in HyBrow/HyQue is constrained to a FOL-based model-theoretic semantics in favor of hypothesis evaluation. Our point, nevertheless, is that such requirement could also be met without hardwiring hypothesis modeling and encoding (cf. [ 13 ]). In our work, we strive for eliciting and linking hypotheses as conceptual entities and capitalize on the co-existance of di erent formulations (possibly in di erent languages) of the same hypothesis on the web.

LSC provides core terms for making scienti c assets explicit and linked in the web of data.3 In [11, p. 12], Kauppinen et al. instantiate LSC to a research in Environmental Conservation that investigates \the notion that hazards to Amazonian forests have declined over the last decade" [ 16 ] (the emphasis is ours). In fact, by dealing with that hypothesis as a conceptual entity, the scientists make it possible to change its statement formulation or even to assert a semantic mapping to another incarnation of the hypothesis in case someone else reformulates it. The preservation of the hypothesis conceptual identity is particularly interesting in that case, since it can then be tracked in public a airs.

Brodaric et al.'s Science Knowledge Infrastructure ontology (SKIo) [ 2 ] is a foundational work to leverage data-driven eScience to a theory-driven paradigm. SKIo extends the top-level ontology DOLCE [ 17 ], following a top-down approach to characterize concepts of the scienti c method. SKIo aims at providing ontological distinctions of terms like `theory', `law', `problem', which can appear in different contexts with subtle di erent meanings. This quali es SKIo as a reference ontology (in the sense of Guarino [8, p. 5], also called foundational [17, p. 3]) for scienti c knowledge representation. On the one hand, a well-founded, negrained ontology such as SKIo can be used to support meaning negotiation in science, enabling the semantic interoperability of scienti c assets. On the other hand, SKIo's top-down ontology engineering approach requires from scientists (as independent knowledge engineers) to subscribe to abstract ontological commitments [ 10 ]. This justi es the need for a lightweight ontology [17, p. 2], a second kind of ontology, like LSC, to serve as a shareable, minimally laden vocabulary that ts the needs of a community (cf. [ 7 ]). One can take bene ts of both artifacts by instantiating the lightweight ontology, yet by referring to the reference one as an interlingua. This is sought for in our work, which considers SKIo as a reference ontology and LSC as a lightweight ontology for Linked Science. In this paper we concentrate on extending and instantiating LSC for realizing Linked Science in a research. An alignment of the extended LSC to SKIo can be addressed in future work for the semantic interoperability of scienti c assets in di erent researches. Then the technique for hypothesis linkage introduced here (see Section 4.3) shall be extended to map hypotheses in di erent researches, in support of the (decentralized) growth of scienti c knowledge on the web.

Next section introduces hypotheses in Computational Hemodynamics. In Computational Science, state-of-the-art models are the vehicle of several entangled hypotheses about a studied phenomenon [ 21 ]. The terms `hypothesis' and (modeling) `assumption' are used interchangeably in that eld. We then stick to LSC's minimal commitment in the de nition of lsc:Hypothesis as \any kind of hypothesis" [ 11 ], and do not distinguish assumptions from (say) laws, empirical regularities, (under-)theories|for such distinctions, refer to SKIo [ 2 ]. 3

Hypotheses in Computational Hemodynamics

Among plenty of natural phenomena that are addressed by research groups from our institution, we have chosen to work in this paper with Hemodynamics. The 3 Version 11/29/2011. Available at http://linkedscience.org/lsc/ns-20111129. reason is that the sheer complexity of the human cardiovascular system (CVS) stresses the nature and role of hypotheses in the formulation of a complex mathematical model. The computational modeling of blood ow in vascular vessels can support investigations about the development of pathologies [ 5 ]. A model used to simulate such a phenomenon has to be simple enough to allow for a numerical treatment at reasonable computational costs. Yet, it has to provide all the information that is essential for their comprehension. A relevant feature of the phenomena of in CVS is their \multiscale" nature both with respect to time and space variables. Blood vessels in di erent regions of CVS vary signi cantly in terms of their diameter, wall thickness, elasticity, etc. As of time scales, the long-term formation of atherosclerotic plaques can be a response of the vascular tissue to speci c stresses induced by the blood during heart beats ( 0:8 s). A plaque developed, e.g., in the carotid artery, could a ect the blood ow rate to the brain and change the overall circulation in CVS.

The challenge of CVS modeling with multiscale techniques is addressed in the literature by several groups, one of which leading the HemoLab project at our institution.4 In their published research papers, an implicit complex hypothesis is typically formulated as a sophisticated mathematical model, with the implicit meaning that the model is t in simulating the phenomenon of interest. That nal, synthesized hypothesis formulated as an e ective model can be used to make predictions. For this reason we shall refer to it henceforth as a hypotheticodeductive (H{D) system [ 9 ] whenever is relevant to distinguish it as such.

Nonetheless, it is worth highlighting that a H{D system is only the scientist's nished work [ 9 ] and can hardly be grasped (neither is it described) at once. Instead, it is worked out in modeling steps as the scientist goes back and forth by assuming and revising simpler hypotheses and assembling them together. This is something important to be considered for the sake of reproducibility. We shall refer from now on to hypotheses in Computational Hemodynamics throughout this paper to illustrate our semantic engineering of hypotheses as linked data. 4

Semantic Engineering of Scienti c Hypotheses

A scienti c hypothesis is a falsi able statement [ 19 ]. That is, it must be prone to be either supported or refuted by observation and experimentation. Another point to note is that in model-based sciences, a formal language with some notation constitutes the technical manner to express hypotheses as models, while non-formal expressions like image sketches or natural language itself are used as more exible alternatives to convey meaning in papers, books, conversations.

4.1 A Semantic View on Hypotheses

In a careful examination on what a scienti c hypothesis is, we note that (i) its falsi ability grounds it in the observable world, while (ii) its statement formulation allows to be assigned for it truth values. An additional feature we should add still is that (iii) it comprises the scientist's interpretation of the observed phenomenon [ 9 ], and this third feature brings forth the hypothesis' conceptual

4 http://macc.lncc.br.

nature which is important for semantic interoperability. This hypothesis threefold notion can be compared to Ogden and Richards' meaning (or semiotic) triangle (see Fig. 1) [ 18 ], if we consider the hypothesis conceptual identity (thought or reference), its statement formulation as a model that can be evaluated (symbol), and its reference to a phenomenon that can be observed or measured (referent).

Ogden and Richards' meaning triangle has been adopted by Kuhn in his characterization of concept for the purpose of semantic engineering [ 12 ], which ts well to this semantic view on scienti c hypotheses. In Linked Science, as we commented on the Einstein's hypothesis example, all of those three corners of the triangle are relevant to be made explicit. In next section we elaborate on the design of this semantic view on hypotheses in the framework of Linked Data.

4.2 Hypotheses as Linked Data

We design our semantic view on scienti c hypotheses as a Model{Hypothesis{ Phenomenon triad and call it the hypothesis triangle (see Fig. 2). Data and phenomenon-related entities (viz., Region, Time, and Observable) ground the hypothesis triangle in the observable world. All of those entities are RDF resources by design.

With the hypothesis triangle, scientists are able to express themselves in multiple co-existing forms on each of its three corners. This is captured by assigning to them RDF properties. For a prompt example, let us consider a hypothesis in Computational Hemodynamics (see Fig. 3). In the current state-of-the-art [ 1, 5 ], the blood ow in the microvascularity (say) of the hands is assumed to behave analogously to an electrical circuit: a resistor-capacitor connection in parallel (standing for the ow in the arterioles), in series with another resistor (standing for the ow in the capillaries). The rationale is that the blood ows like an electrical current. The arterioles' wall tissue absorbs (\dissipates") it, while still stretching itself (locally accumulating blood) in response to a blood pressure gradient (\voltage"). The capillaries in turn have a very small diameter, for which deformation is neglectable w.r.t. the resistance to the ow. In this illustration (Fig. 3), we are using known terms such as rdfs:label, rdf:value, dc:description and foaf:depiction as RDF properties. These, once arranged together, can all be worth as expressions of hypotheses, models, and phenomena. The convention of proper RDF properties for the RDF resource Model can bene t further from ontologies for representing mathematics on the semantic web [ 15 ].

The conceptualization shown in Fig. 2 extends LSC by striving for minimal ontological commitments.5 Three terms are new, namely, Phenomenon, Observable and Model. They come with ve additional relational terms: explains, formulates, represents, hasAspect and realizes; all of them are potentially n n. The hypothesis triangle relations explains, formulates, represents turn out to be functional in the scientist's nal decision in adopting a particular model m1 to formulate a hypothesis h1, which is meant to explain phenomenon p1. To anticipate next section, all that lies within the scope of a research, where such instances are to be made semantically explicit. The represents link is dashed to point out that its instances do not have to be asserted, since they can be inferred by a rule, namely, for all hm; h; pi 2 M H P , if formulates(m, h) and explains(h, p), then represents(m, p); where M , H and P are sets of models, hypotheses and phenomena, respectively. In model-based sciences, it is such a triple hm; h; pi that can a ord to convey a scienti c hypothesis unambiguously.

A Phenomenon, as originally de ned by Kant, is \any observable occurrence," which is distinguished from `noumenon' (thing-in-itself, not directly accessible to observation).6 A Phenomenon isAboutRegion and isAboutTime, and it hasAspect Observable. We adopt the term Observable, di ering to (say) `physical quantity', in order to refer to the quanti able observable world but still cover non-quantities such as genes and astronomical objects.7 The term Data appears as a core element in LSC. We then add the link realizes to Observable in order to tie up the 5 In particular, we have strived to make it possible for computational scientists to promptly recognize and instantiate this extended LSC in their research. 6 http://en.wikipedia.org/wiki/Phenomenon. 7 Although in this paper we focus on Computational Science, we have strived not to restrict this conceptualization to that discipline. hypothesis triangle according to its grounding in the measurements of observables. Refutation can be considered a function : H ! [0; 1], as a measure of the distance between data produced (model output, or, conceptually, hypothesis predictions) and data used (model input, or, conceptually, phenomenon observations). This metrics can be designed as an RDF datatype property refutation to be assigned by the scientist users in order to explicitly assess the quality of their hypotheses (models) in explaining (representing) their observed phenomena. 4.3

Linking Hypotheses in a Local Research

To make only a nal hypothesis (a H{D system [ 9 ]) explicit may not provide much conceptual traceability about a research (ibid.). This issue can be addressed, however, by eliciting simpler hypotheses and linking them properly in the derivation of more complex ones. While complex hypotheses are formed by combining two or more hypotheses already assumed, atomic hypotheses constitute for the scientist a single unit of thought either because it has been borrowed from another research or because it has been assumed at once from scratch.

Nevertheless, hypotheses (e.g., in Mathematical Modeling) are entangled in such a way that the primitive can no longer be identi ed in the resulting one. Therefore, we do not attempt to prescribe any logical structure for hypothesis combination. Rather, we borrow prov:wasDerivedFrom8 as a semantically lightweight relation under a notion of provenance and consider that a complex hypothesis is a blend of others. We use prov:wasDerivedFrom as an ordering relation to make up a data structure for hypothesis linkage as follows. 8 From the PROV Ontology, available at http://www.w3.org/TR/prov-o/. Def. 1 Let H be the set of hypotheses in a local research, and < be a strict order (asymmetric and transitive). For all h1; h2 2 H, we write h1 < h2 if h1 was derived from h2. More speci cally, if h1 < h2 and for no h 2 H, h1 < h < h2, then we write h1 h2 and say that h1 was directly derived from h2. Def. 2 We call h 2 H an atomic hypothesis if there exists exactly one h1 2 H such that h h1. Otherwise, we call h 2 H a complex hypothesis if there exists at least two hypotheses h1; h2 2 H such that h h1 and h h2. Def. 3 There is a special hypothesis h0 2 H, such that for all h 2 H n fh0g, h < h0. We call h0 H's top hypothesis. (trivially, h0 assumes nothing).

Our design approach for hypothesis linkage turns out to form a lattice data structure [ 22 ], but both its formalization and the semantics of hypothesis blending fall outside the scope of this paper. Fig. 4 shows the hypothesis lattice which comprises the H{D system (h17) of our application case in Computational Hemodynamics (cf. Section 5). Symbol `>' is used as a label for the top hypothesis h0. The hypothesis shown in Fig. 3 is h14 in this hypothesis lattice.

4.4 Links of the Hypothesis Triangle as Morphisms

From the design solutions presented in the two previous sections, we obtain an interesting framework for linking scienti c assets in a research. For example, Fig. 5 shows a complex hypothesis h8 for explaining a general phenomenon of uid behavior (p8) which is present in our application case (where the uid is human blood). This hypothesis, as a H{D system for explaining p8, is the bottom element of the hypothesis lattice shown on the top center in Fig. 5. The hypothesis lattice is unfolded into model and phenomena isomorphic lattices according to the hypothesis triangle (Fig. 2).9 The lattices are isomorphic if one takes subsets of M , H and P such that formulates, explains and represents are both one-to-one and onto mappings (i.e., bijections), seen as structure-preserving mappings (morphisms). This turns out to be the case in published research papers where scientists propose exactly one hypothesis to explain exactly one phenomenon of interest, and formulate the former in exactly one way.

We are eliciting in Fig. 5, for example, the hypotheses underlying the socalled continuity equation (m1) and the Navier-Stokes equations (m7). These are standard models in the study of uid mechanics [ 14 ] and they are applied in our case in Computational Hemodynamics. The hypothesis lattice shown in Fig. 5 (on the top center) is a sublattice of the hypothesis lattice shown in Fig. 4. Deductions from h8 as a H{D system can be too coarse for predicting conditions of blood ow in vascular vessels, for which predictions from h17 can be adequate. 5

Instantiation of the Extended LSC

In this section we present a published research in Computational Hemodynamics as an instantiation of the extended LSC proposed here. The research we instantiate is reported in the article \On the potentialities of 3D-1D coupled models in hemodynamics simulations " by Blanco et al. [ 1 ] from our institution. The article elaborates on the potential of such coupled models (introduced preliminarily by Formaggia et al. [ 5 ]) for predicting two hemodynamics conditions: (i) the sensitivity of local blood ow in the carotid artery to the heart in ow condition, and (ii) the sensitivity of the cardiac pulse to the presence of an aneurysm. A 9 We are using symbol `>' to denote a top hypothesis, and abusing this notation slightly to mean the same (isomorphically) for the model and phenomenon lattices. representative account of the extended LSC instantiation on that research is described in Table 1. The scienti c assets presented in Table 1 are linked according to the conceptualization shown in Fig. 2.

In particular, Table 1 includes the nal complex hypothesis h17 which is Blanco et al.'s H{D system as shown in Fig. 4. With the extended LSC, we can provide scientists with interesting querying functionalities on the web. SPARQL queries can select, e.g., all the atomic hypotheses built into h17, or all the modelhypothesis-phenomenon triples in a research. We present below a SPARQL query Q1 selecting a particular triple hm; h; pi 2 M H P , namely, the one shown in Fig. 3. It exempli es a scientist interested in Blanco et al.'s research. Q1. Find in Blanco et al.'s research a hypothesis (if any) explaining phenomena of blood ow in microvascular vessels and show which model formulates it. PREFIX rdfs: <http://www.w3.org/2000/01/rdf-schema#> PREFIX dc: <http://purl.org/dc/elements/1.1/> PREFIX lsc: <http://linkedscience.org/lsc/ns#> SELECT ?hypothesis_name ?model_name WHERE { ?h rdfs:label ?hypothesis_name . ?m rdfs:label ?model_name . ?h a lsc:Hypothesis . ?p a lsc:Phenomenon . ?m a lsc:Model . ?h lsc:explains ?p . ?m lsc:formulates ?h . ?p dc:description ?d .

FILTER regex(?d, "blood flow", "i") . FILTER regex(?d, "microvascular", "i") } ---------------------------------------------------------------------------------------| hypothesis_name | model_name | ======================================================================================== | "Electrical circuit terminal analog" | "Lumped windkessel terminal" |----------------It is worth now to draw attention to our initial motivation w.r.t. the semantic engineering of hypotheses in the context of data-intensive science. The datasets in Table 1 are linked to model m17, which is in turn linked to hypothesis h17. The latter can be an interpretation key to the research, and to those datasets in particular. This can be an interesting line of thought to be investigated further by developing querying patterns that bind hypotheses to data.

Recall that hypothesis evaluation is not addressed in this paper. But as we discuss elsewhere [ 6 ], state-of-the-art scienti c work ow systems can be extended to manage hypotheses and models. The numerical methods which are necessary for computing model m17 nd their place under the term lsc:Method. To cope with them, however, is another challenge and it falls out the scope of this paper. The Linked Science program provides a proper framework for overcoming such a limitation under the partial knowledge view of Linked Data. It allows the level of detail of a published research to be improved in a stepwise manner.

6 Conclusions

In this paper we have elaborated on a semantic view on scienti c hypotheses and their linkage, by striving for minimal ontological commitments. We have addressed the engineering of hypotheses as linked data by extending LSC and instantiating it in a research in Computational Hemodynamics.10 10 This extension has been proposed to LSC's authors and is under consideration to be incorporated into a next version of it (the current one dates to 11/29/2011) to be available at http://linkedscience.org/lsc/ns/.

In our work we have taken a direction tailored not to reduce hypotheses to a rigid logical structure, but to seek for them proper forms of expression as linked data. In this way, our approach allows for the co-existance of hypotheses and their formulations over multiple scienti c domains and formalisms. The very problem of hemodynamics multiscale modeling is an astonishing example of hypotheses co-existance across multiple scales and the boundaries of disciplines.

We have shown that an e ort in eliciting and linking of hypotheses can be rewarded with interesting functionalities in terms of conceptual traceability. The hypothesis lattice (see Fig. 4) is a data structure meant for the management of hypothesis evolution, as the scientist user operates over it by re ecting her cognitive operations on the scienti c problem at hand. We aim at providing scientists with such a tool. We are developing an algebraic speci cation of abstract data types such as model, hypothesis and phenomenon for scientists to operate over on the web|e.g., by assuming, borrowing and revising hypotheses.

Signi cant e ort still has to be carried on until we have sophisticated computational models reproducible online. This work is a step towards conceptual traceability, which might open some seaways for sailing on the big data [ 4 ].

Acknowledgments.

We thank three anonymous reviewers for providing valuable comments on a previous version of this manuscript, and LSC's authors Tomi Kauppinen, Alkyoni Baglatzi and Carsten Kessler for their openness and feedback w.r.t. our extension proposal to LSC. The rst author would like to express his gratitude to Jose Karam Filho for delivering insightful lectures on the principles of mathematical modeling that contributed to ideas of this paper. This research received nancial support from the National Research Council (CNPq) under grants no. 141838/2011-6, 309502/2009-8 and 382489/2009-8.

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