Colector solar plano.

6.3.1 Synonym Based Transitive Equivalence

In order to provide sharing relations among multiple ontologies, we need to pro- vide an advanced ontology mapping schema. A frequent phenomenon across domains is the presence of homonyms and synonyms. In the ontology mapping process, a concept

Table 5: OBOs in Detail

ID Ontology Name Conc. Syn. Node Edge Type O1 Adult_mouse_anatomy 2703 0 2971 2820 IS-A O2 Arabidopsis_development 108 53 108 108 IS-A O3 Attribute_and_value 1228 0 1260 1248 IS-A O4 Brenda 2218 1179 2515 2353 IS-A O5 Cell 761 0 964 964 IS-A O6 Chebi 12734 23451 14666 14666 IS-A O7 Dictyostelium_discoideum_anatomy 38 13 73 58 IS-A O8 Disease 19136 0 19389 19383 IS-A O9 Emap 13731 0 13731 13731 Part-of O10 Event 2665 234 3499 3020 IS-A O11 Evidence_code 130 6 163 140 IS-A O12 Fly_anatomy 6130 0 13649 7273 IS-A O13 Flybase_vocab 660 65 664 664 IS-A O14 Fungal_anatomy 65 15 82 76 IS-A O15 GO 20733 17181 27574 27560 IS-A O16 Human_dev_anat_abstract 2314 0 2339 2324 Part-of O17 Human_dev_anat_staged 8340 0 8362 8339 Part-of

O18 Image 259 30 259 259 IS-A

O19 Loggerhead_nesting 308 2 322 317 IS-A O20 Mammalian_phenotype 4186 3010 6130 4630 IS-A

O21 Mao 164 45 164 164 IS-A

O22 Medaka_anatomy_development 4358 0 4404 4245 Part-of O23 MeSH 15337 33297 19525 19525 IS-A O24 Molecule_role 7255 23588 7641 7393 IS-A O25 Mosquito_anatomy 1804 3501 2290 2057 Part-of O26 Mouse_pathology 459 0 459 459 IS-A

O27 Pathway 486 62 554 554 IS-A

O28 Plant_environment 489 308 518 506 IS-A O29 Plant_trait 761 44 949 865 IS-A O30 Plasmodium_life_cycle 47 0 98 64 IS-A O31 Po_anatomy 763 218 785 785 IS-A O32 Po_temporal 274 996 274 274 IS-A

O33 Psi_mi 194 165 223 212 IS-A

O34 Rex 546 140 1099 671 IS-A

O35 Sequence 1034 251 1171 1094 IS-A O36 Temporal_gramene 235 168 235 235 IS-A O37 Worm_development 69 0 69 69 IS-A O38 Zea_mays_anatomy 179 30 181 141 Part-of O39 Zebrafish_anatomy 1558 0 2184 1553 Part-of O40 Fly_development 120 0 124 124 IS-A

in an OBO ontology can be associated with another concept in another OBO ontology if both concepts have a synonym relation. The synonym relation is reflexive, transitive, and symmetric. We propose three types of the synonym relation that can be identified in the ontology to ontology mapping of a concept.

There are many different meanings for the same word. For instance, “PGA” stands for “Polyglandular Autoimmune Syndrome” and the “Professional Golfers’ Association.” Synonyms are used to relate to each other. For instance, some refer to “stomach acid” with “Betaine HCl,” others use “Hydrochloric Acid”. Resolving these semantic problems present across multiple ontologies is a difficult task because it requires a comprehensive understanding of ontologies to be linked and implications of the mapping. These differ- ences occur because different ontology designers may bring different world views to the task, conceptualizing the world at different levels of granularity and abstraction. Such differences are commonly considered semantic problems.

To handle these semantic problems, we have identified three kinds of synonym relationships between ontologies. An ontology O1 can be related to another ontology O2 through synonyms of concepts. A concept X in O1 can be synonymously related

to another concept Y from O2 if 1) Y is included as a synonym of X in O1 or 2) if X is specified as a synonym of Y in O2. The confidence in the semantic equivalence

of X and Y is strengthened if they are mutually defined as synonyms of each other in

their ontologies. Another scenario that is indicative of semantic equivalence is when X

andY are linked through having a common synonym. Note that the case of exact matches

18 shows these relations, also formally defined below. C1 (e.g. scale) C2 (e.g. comb) S1 (e.g. comb) C1 (e.g. azacitidine) C2 (e.g. 5-azacytidine) S1 (e.g. 5-azacytidine)

Case 1

Case 2

S2 (e.g. azacitidine) C1 (e.g. scale) C2 (e.g. upper calypter) S1 (e.g. squama)

Case 3

S2 (e.g. squama)

O

_i

O

_j

O

_i

O

_i

O

_j

O

_j C1 (e.g. scale) C2 (e.g. comb) S1 (e.g. comb) C1 (e.g. azacitidine) C2 (e.g. 5-azacytidine) S1 (e.g. 5-azacytidine)

Case 1

Case 2

S2 (e.g. azacitidine) C1 (e.g. scale) C2 (e.g. upper calypter) S1 (e.g. squama)

Case 3

S2 (e.g. squama)

O

_i

O

_j

O

_i

O

_i

O

_j

O

_j Figure 18: Synonym Relations Between Ontologies

Let _{Ci ∈ Oi and Cj ∈ Oj, where Oi and Oj are ontologies, and Si ∈ S}′

and _{Sj ∈ S”, where S}′ and S” be a set of synonyms of Ci and Cj, respectively. The

following three cases might be considered for synonym based transitivity across different ontologies. The symbol_{≈ is used to represent a synonym relation between concepts.}

Case 1 If _{Si is a synonym of Ci (i.e., Si ≈ Ci) or Sj is a synonym of Cj (i.e.,}

Sj ≈ Cj) and either Ci = Sj or Cj = Si, but Ci 6= Cj, then Ci ≈ Cj can be

transitively retrieved from either _{Ci = Sj ≈ Cj or Cj = Si ≈ Ci. As an example,} Medicine is a concept in MeSH and Drug is a concept in CheBi and Medicine is defined as a synonym of Drug in CheBi. Therefore, Medicine in MeSH is synonymously related

to Drug in CheBi.

Case 2 _{Si is a synonym of Ci (i.e., Si ≈ Ci) and Sj is a synonym of Cj (i.e.,}

Sj ≈ Cj) and Ci = Sj and Cj = Si, but Ci 6= Cj, then Ci ≈ Cj can be transitively

retrieved from _{Ci = Sj ≈ Cj and Cj = Si ≈ Ci. As an example, Polysome is a} concept and Polyribosome is its synonym in GO while Polyribosome is a concept and Polysome is it synonym in MeSH. Therefore, Polysome in GO is synonymously related to Polyribosome in MeSH.

Case 3 If _{Si is a synonym of Ci (i.e., Si ≈ Ci) and Sj is a synonym of Cj} (i.e., _{Sj ≈ Cj) and Si = Sj, but Ci 6= Cj then Ci ≈ Cj can be transitively retrieved} from_{Ci ≈ Si = Sj ≈ Cj. As an example, Heterozygote is a concept and Carrier is its} synonym in MeSH and Transporter is a concept and Carrier is its synonym in Molecule role. Therefore, Heterozygote is synonymously related to Transporter.

6.3.2 Ontology Connecting Patterns

We are interested in relating distributed ontologies that share a common domain. In order to relate multiple ontologies, we use the notion of frequently recurring patterns in overlapping ontologies. The idea of patterns has been widely used in building soft- ware system. The motivation behind characterizing a pattern is to fully utilize known solutions for commonly recurring problems in a specific context. The focus of research on patterns has so far been mainly on ontology modeling and knowledge reuse such as ontology construction and management. Here we are introducing an initial method for exploiting ontology connecting patterns with the aim of further expanding ontology space

for query and inferencing. Two kinds of connecting patterns are discussed: quantitative connections and semantic connections. The first type of pattern is defined based on the quantity of overlapping while the latter is based on the connecting position of concepts in these ontologies.

Quantitatively connecting patterns The overall connectivity patterns between two ontologies can be identified from analyzing the extent to which concepts from one ontology are mapped to the other. Formally, the connectivity can be defined in terms of linguistic overlapping (concepts and synonyms) and structural overlapping aspects (links and paths). An ontology O can be defined as a set of constituent concepts, relations and properties, namely_{< O >. We now define the size of the concept set, (i.e., cs(O) = k <}

CO > k, where < CO > is the set of concepts in the ontology O) and the size of the

link set, (i.e.,_{ls(O) = k < LO > k, where < LO > is the set of the link type (such as} IS-A or Part-of) of the ontology hierarchy). We consider two types of the relationships: direct and indirect. The direct relationship defines a parent and child relationship of the given concepts in the hierarchy. The indirect relationship defines a predecessor/successor relationship of given concepts (path) in the hierarchy. The degree of concept overlap

cp(O1, O2) and the degree of link overlap lp(O1, O2) is computed by the formulas below:

cp1(O1, O2) = cs(O1) ∩ cs(O2)

cs(O1) ∪ cs(O2) − cs(O1) ∩ cs(O2)label(conceptOverlap1) (6.1)

cp2(O1, O2) = cs(O1) ∩ cs(O2)

cs(O1) ·

cs(O1) ∩ cs(O2)

cs(O2) label(conceptOverlap2) (6.2)

lp1(O1, O2) = ls(O1) ∩ ls(O2)

ls(O1) ∪ ls(O2) − ls(O1) ∩ ls(O2)label(linkOverlap1) (6.3)

The relationship between ontologiesO1 and O2 can be as follows:

• O1 is a subset of O2, i.e. O1 ⊆ O2, or O2 is a subset of O1, i.e. O1 ⊇ O2. • O1 partially overlaps O2, i.e. ∃x, y, (x ∈ O1 ∧ x ∈ O2) ∧ (y ∈ O1 ∧ y /∈ O2) • O1 is disjoint from O2, i.e. O1 ∪ O2 = φ

An ontology mapping from O1 = (cs1, ls1) to O2 = (cs2, ls2) is defined as follows:

There is a subset ontology mapping from O1 = (cs1, ls1) to O2 = (cs2, ls2) if there

exists_{cs1 ⊆ cs2 and ls1 ⊆ ls2. There is a partial overlapping from O1 = (cs1, ls1) to}

O2 = (cs2, ls2) if there exists ∃a, b, (a ∈ cs1 ∧ a ∈ cs2) ∧ (b ∈ cs1 ∧ b /∈ cs2) and ∃c, d, (c ∈ ls1 ∧ c ∈ ls2) ∧ (d ∈ ls1 ∧ d /∈ ls2)

Semantically Connecting Patterns This connecting pattern focuses on repre- senting inter-ontology relationships that might exist between multiple ontologies. For instance, an ontology can be a more specific ontology of another ontology (upper ontol- ogy). In this case, there is a super/subclass relationship between these two ontologies. Or there might be a sibling relationship between ontologies. Assume that the ontologyOi

and a concept x are given. In the following formulae, level(x@Oi) means the level of

the concept x at the ontology Oi and depth(Oi) means the depth of ontology Oi. The

Concept Connection Position (CCP) is computed as follows:

CCP (x, Oi) = level(x@Oi)

depth(Oi) (6.5)

The Ontology Connection Position (OCP) is computed based on the relative position of the concept in two ontologies, indicating the positions of the concept from these two ontology perspectives. Assuming that two ontologies Oi and Oj and a concept x are

OCP (x, Oi, Oj) = CCP (x, Oi)

CCP (x, Oj) (6.6)

There might be multiple connection patterns in multiple ontologies. Thus, it is necessary to accumulate the connecting patterns and normalize them into an accumulated connection score using a simple weight average formula which summarizes all weighted OCPs. The weight for each pattern can be defined by a domain expert based on the significance of the concept or simply as a uniform weight. The Accumulated Ontology Connection (AOC) score can be computed as follows:

AOC(Oi, Oj) =X

i

OCPi· Wi (6.7)

The connection pattern is a frequently recurring pattern observed during the ontology overlapping analysis used to connect an ontology to another. This pattern is mainly based on the location of the concept overlapping between ontologies.

1)Ontology O1 is quantitatively connected to Ontology O2. Let us assume that

a concept in ontology O1 is connected to a concept in another ontology O2 and count

means the number of the common concepts x. In this case, we map the class in O1 to

the class inO2, with the mapping being either equivalent or synonymously equivalent.

Given a threshold _{µ: O1 is quantitatively connected to O2 if ∃x, (x ∈ O1 ∧ x ∈ O2) ∧}

(count(x@O1) > µ) ∧ (count(c@O2) > µ)

2)Ontology O1 is semantically connected to ontology O2. This means that the

concepts in O1 can be semantically connected to the concepts in O2. In this case, a

a high level in ontologyO2. Note that the synonym patterns described in the synonym-

based transitive equivalence section have been incorporated into this semantic connection pattern. For instance, Table 42 in Chapter 7 shows the synonym pattern Cell death . Necrosis. Furthermore, if the number of connecting patterns between O1 and O2 is higher than a certain threshold defined by a domain expert, then the ontology O1 is a specialised ontology of the ontology O2. Then we can say the subconcepts of x in O2 are semantically related to the superconcepts of x in O1.

O1 is semantically connected to O2 if_{∃x, (x ∈ O1∧x ∈ O2)∧(OCP (x, O1, O2) >}

α ∨ OCP (x, O2, O1) > α)

Based on these pairwise similarity measures for concept and edge overlapping re- lationships, we have developed a simple ontology model for clustering overlap in multiple ontologies. This is discussed in the following section Ontology Clustering. These con- necting patterns can be essentially used for automatically connecting ontologies and ex- panding the query space of ontologies, and to retrieve information from available knowl- edge sources within the ontology space.

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