View source for Logic and Reasoning Challenges

This page discusses issues to be resolved in the near future. These issues pertain to relation semantics as well as inference procedures.

==Inferring in both directions on the taxonomy==

It is desired that annotations to higher taxa in the taxonomy be propagated to the lower taxa that are subsumed by the higher taxon; i.e. classical top down inferences. Given that the reasoner already reasons bottom upward, associating phenotype annotations from the lower level taxa to the higher level taxa, adding top-down inferencing may cause widespread inconsistencies in the data if unchecked.

The OBD reasoner can reason from annotations at the lower levels of the taxonomy to the higher levels. Given that ''Danio rerio'' exhibits a phenotype P, the OBD reasoner infers that ''Danio'' exhibits the same phenotype P. This is reasoning up the taxonomy, using the subsumption relationship between ''Danio rerio'' and ''Danio''. This is possible because the annotations to each taxon are (implicitly) existentially quantified. The annotation "''Danio rerio'' exhibits increased length of maxillary barbel towards orbit" is shown in (1). The semantics are in (2).

<javascript>
TTO:1001979            PHENOSCAPE:exhibits         PATO:0000573^OBO_REL:inheres_in(TAO:0001938)^OBO_REL:towards(TAO:0001967)             -- (1)
</javascript>


<math>\exists</math> X : ''instance_of''(X, TTO:1001979) <math>\and</math> ''PHENOSCAPE:exhibits''(X, PATO:0000573^OBO_REL:inheres_in(TAO:0001938)^OBO_REL:towards(TAO:0001967))                                                               -- (2)


Given that ''Danio rerio'' (TTO:1001979) is subsumed by the genus ''Danio'' (TTO:101040) in the Teleost Taxonomy as shown in (3), it is possible to infer that "''Danio'' exhibits increased length of maxillary barbel towards orbit" (4).

<javascript>
TTO:1001979           OBO_REL:is_a                 TTO:101040                                                                            -- (3)
TTO:101040            PHENOSCAPE:exhibits          PATO:0000573^OBO_REL:inheres_in(TAO:0001938)^OBO_REL:towards(TAO:0001967)             -- (4)
</javascript>

Inferring down the taxonomy, that is using assertions at higher levels to extract inferences at lower levels, requires universal quantification. For example, the assertion that all "Siluriformes exhibit decreased width of mesethmoid bone" can be captured using OBD semantics as shown in (5). The universal semantics of this assertion is shown in (6). Siluriformes directly subsumes Ictaluridae as shown in (7). From (5) and (7), it is straightforward to infer that "Ictaluridae exhibit decreased width of mesethmoid bone" as shown in (8).

<javascript>
TTO:1380            PHENOSCAPE:exhibits          PATO:0000599^OBO_REL:inheres_in(TAO:0000323)                                            -- (5)
</javascript>


<math>\forall</math> X : ''instance_of''(X, TTO:1380) <math>\and</math> ''PHENOSCAPE:exhibits''(X, PATO:0000599^OBO_REL:inheres_in(TAO:0000323))    -- (6)


<javascript>
TTO:10930           OBO_REL:is_a                 TTO:1380                                                                    -- (7)
TTO:10930           PHENOSCAPE:exhibits          PATO:0000599^OBO_REL:inheres_in(TAO:0000323)                                -- (8)
</javascript>

The problem with using top-down inferences using universally quantified statements is that currently there is no way to distinguish these from existentially quantified statements. We use the ''PHENOSCAPE:exhibits'' relation for existentially quantified statements. Using the same relation for universally quantified statements would make it possible to extract incorrect inferences given the current configuration. Consider the subsumption relationship between ''Danio'' and ''Danio choprai'' shown in (9). If there is no distinction between existentially and universally quantified statements, it is possible to infer from (9) and (4) the erroneous conclusion that "''Danio choprai'' exhibits increased length of maxillary barbel towards orbit" (10). At present, there are no annotations to ''Danio choprai''.

<javascript>
TTO:1052801           OBO_REL:is_a                 TTO:101040                                                                   -- (9)
TTO:1052801           PHENOSCAPE:exhibits          PATO:0000573^OBO_REL:inheres_in(TAO:0001938)^OBO_REL:towards(TAO:0001967)    -- (10)
</javascript>

Recall that the reasoner works in sweeps. It extracts one set of inferences (Inf-1) from the assertions (A) in its first sweep. In the next sweep, the reasoner pulls out a different set of inferences (Inf-2) from the assertions A '''AS WELL AS''' the inferences Inf-1 from the previous sweep. The reasoner repeats these sweeps until no new inferences are added. This is why the reasoner will likely infer all taxa exhibit all phenotypes if it is used to reason both up and down the taxonomy without checking for universal and existential semantics.

===Possible solutions===

In this section, we discuss possible approaches to resolving this issue with reasoning both up and down the taxonomy.

====Different relations for different purposes====

In classical first-order logic (FOL), all relations and properties asserted upon concepts (or taxa in the case of Phenoscape) are inherited by the subsumed concepts. This is because by default, all assertions about the concepts are universally quantified, i.e. hold true for ALL instances of the concept. If all cars have four wheels, and if all SUVs are cars, then all SUVs have four wheels. This is the way of top-down, classical FOL inferencing.

In Phenoscape, we have adopted the OBD schema of modeling concepts, wherein all assertions to the concepts are existentially quantified, i.e. the assertion is true with at least one instance of the concept. This is very convenient for the life sciences, where exceptions are so prevalent. As a ready example, consider how the duck-billed platypus easily overrules the "all mammals are viviparous" rule. Further, existential quantification allows us to reason up the taxonomy. If some Teleostei exhibit round fins, and all Teleostei are Ostariophysi, then some Ostariophysi exhibit round fins.

By default, we use the ''PHENOSCAPE:exhibits'' relation to link taxa to phenotypes using existential semantics. Using the same relation to model universally quantified relationships between taxa and phenotypes, would cause incorrect inferencing and loss of data integrity. The easiest way to address this issue is to use different relations; one for universally quantified relations and the other for existentially quantified relations. Let us call these relations ''PHENOSCAPE:all_exhibit'' and ''PHENOSCAPE:some_exhibit'' respectively.

Now the OBD reasoner uses the following rule to extract inferences up the taxonomy using the ''PHENOSCAPE:exhibits'' relation (1).

'''Rule-1:''' <math>\forall</math>A, B, x: ''is_a''(A, B)  <math>\and </math>''exhibits''(A, x)  <math>\Rightarrow</math> ''exhibits''(B, x)

This can be replaced with the following two rules, which use the two new relations, ''PHENOSCAPE:all_exhibit'' and ''PHENOSCAPE:some_exhibit''. (Please suggest better names for these if you can think of them).

'''Rule-2:''' <math>\forall</math>A, B, x: ''is_a''(A, B)  <math>\and </math>''some_exhibit''(A, x)  <math>\Rightarrow</math> ''some_exhibit''(B, x)

'''Rule-3:''' <math>\forall</math>A, B, x: ''is_a''(A, B)  <math>\and </math>''all_exhibit''(B, x)  <math>\Rightarrow</math> ''all_exhibit''(A, x)

This will keep the inferences from getting mixed up. Let us consider the scenario where species Sp1 and Sp2 (from genus Gen1) are asserted to exhibit phenotype Phen1. These assertions are shown in (A-1) and (A-2). The subsumption relations are shown in (A-3) and (A-4)

<javascript>
Sp1           PHENOSCAPE:some_exhibit          Phen1                               -- (A-1)
Sp2           PHENOSCAPE:some_exhibit          Phen1                               -- (A-2)
Sp1           OBO_REL:is_a                     Gen1                                -- (A-3)
Sp2           OBO_REL:is_a                     Gen1                                -- (A-4)
</javascript>

The reasoner makes the inference (I-1) from the assertions (A-1) ~ (A-4) and the inference rule Rule-2.

<javascript>
Gen1           PHENOSCAPE:some_exhibit          Phen1                              -- (I-1)
</javascript>

Now. given this new inference (I-1), the reasoner cannot infer that all the species Sp1, Sp2, and let us say 10 other species Sp3 ~ Sp12 also exhibit Phen1, because the inference rule for some_exhibit cannot be used to infer down the taxonomy. Again, consider the assertion that ALL instances of genus Gen1 exhibit a phenotype Phen2 as shown in (A-5)

<javascript>
Gen1           PHENOSCAPE:all_exhibit          Phen2                              -- (A-5)
</javascript>

Given (A-5) and all the subsumption relations between Gen1 and the hypothetical twelve species under Gen1 (including A-3 and A-4), the reasoner uses inference rule Rule-3 to infer (I-2) ~ (I-13)

<javascript>
Sp1           PHENOSCAPE:all_exhibit          Phen2                              -- (I-2)
Sp2           PHENOSCAPE:all_exhibit          Phen2                              -- (I-3)
..
..
Sp12          PHENOSCAPE:all_exhibit          Phen2                              -- (I-13)
</javascript>

Again, cyclical inferences are ruled out because there are no inference rules to infer up the taxonomy using the ''all-exhibit'' relation.

=====What has to change?=====

To implement this strategy, two new relations can be defined in the Phenoscape Vocab ontology, where the current definition of the ''PHENOSCAPE:exhibits'' relation is found. At the curation level, curators have to qualify their assertions as being either existentially or universally quantified. Specifically, the Phenex UI could tap the curator's shoulder and ask, "Ahem, does this annotation hold true for all specimens belonging to this taxa or just some specimens?" This needs some changes (no less!) to the Phenex interface and also to the character matrix format in which the data is exported. The data loader module of Phenoscape has to know this information so that the appropriate relation is used in creating the taxon-phenotype statement to be loaded into the knowledgebase. The query module will have to be modified to retrieve both inferred and asserted taxon-phenotype statements using the two different relations. The JSON format in which the data is exported needs to be modified to accommodate the two different kinds of relation statements, and lastly the UI will have to explicitly distinguish between the two.

======A possible simpler solution (Update: Feb 22, 2010)======

It is possible to check the rank of the taxon to which the phenotype assertion is made. If the rank of the taxon is not "species", then the new relation can be used in the top-down reasoning as shown below. Assertion (A-6) is a phenotype assertion to a taxon of a higher rank, let us say a Genus G1. Now, G1 has 6 species S1 ~ S6. Inferences to S1 ~ S6 from the assertion (A-6) may use the new relation ''all_exhibit'' as shown.

====Probabilistic assertions====

Uncertainties are everywhere in the life sciences. The taxon-phenotype assertions can be augmented with uncertainty factors to address this issue. Inferences could use uncertainty calculi such as the [http://en.wikipedia.org/wiki/Dempster%E2%80%93Shafer_theory Dempster-Schafer method] or Bayes conditional probability rule to derive uncertainty factors of the inferences given the uncertainty factors of the assertions.

The advantage of this strategy will be that we can continue to use the ''PHENOSCAPE:exhibits'' relation for taxon-phenotype statements, and at the same time display the uncertainty values associated with every assertion displayed at the UI; far more intuitive than "Taxon T exhibits increased size of E AND decreased size of E."

=====What needs to change?=====

Curators will have to manually enter uncertainty factors (UFs) of the assertions in the Phenex UI, which needs modification to handle these. The character matrix format needs to be modified to accommodate UFs. The data loader module needs to use reified statements around assertions to store UFs. The OBD reasoner will have to be augmented with an implementation of uncertainty calculus. The query module needs to retrieve the UF associated with every assertion, and export this in a modified JSON format. Lastly, the UI will have to add a provision to display uncertainty factors.

== The problem with absence of features==

Descriptions of phenotypes as used in the Phenoscape project (and a plethora of phenomena in the real world) are replete with exceptions, or aberrations from what is considered to be "normal." While canonical ontologies like the [http://sig.biostr.washington.edu/projects/fm/ FMA] and the [http://www.berkeleybop.org/ontologies/obo-all/teleost_anatomy/teleost_anatomy.obo TAO] contain ontological definitions of ideal specimens, observations in the life sciences are full of aberrations to these general rules.

Phenoscape has some typical issues dealing with absence of anatomical features in certain species of Ostariophysian fishes. For example, the basihyal cartilage is found in all species of Ostariophysian fishes, except the Siluriformes. At present, this information is captured in Phenoscape using the combination of the PATO term for "absent in organism" (PATO:0000462), the "inheres_in" relation from the OBO Relations Ontology, the TAO term for "basihyal cartilage" (TAO:0001510), the "exhibits" relation from the PHENOSCAPE ontology, and the TTO term for Siluriformes (TTO:1380). This is shown below.

<javascript>
TTO:1380              PHENOSCAPE:exhibits                  PATO:0000462^OBO_REL:inheres_in(TAO:0001510)
</javascript>

In plain English, this translates to "Siluriformes exhibit absence in organism which inheres in basihyal cartilage." The semantics of this sentence are vague to say the least. Going by this methodology, it is impossible to state that basihyal cartilage is absent in Siluriformes without referring to ''at least one'' instance of basihyal cartilage. Combining a quality ''absent'' with a ''feature'' through the ''inheres_in''  property is very misleading in itself (ex: absence inheres in cartilage), contorting the intrinsic semantics of the ''inheres_in'' relation. These problems have been discussed in [http://www.ncbi.nlm.nih.gov/pubmed/17369081 Ceusters et al] and [http://www.biomedcentral.com/1471-2105/8/377 Hoehndorf et al]. Both these publications propose solutions to integrate these aberrant observations with canonical definitions, without causing inconsistencies in reasoning procedures.

[[Media:PhenotypesInPhenoscape.ppt]]

[[Discussion about the Absence of Phenotypes issue]]

Another issue specific to the Phenoscape project was raised by Paula at the SICB workshop. Given that basihyal cartilage is absent in Siluriformes, basihyal bone should be absent in Siluriformes as well. This is because basihyal bone develops from basihyal cartilage. This may be inferred by adding a new relation chaining rule shown below to the OBD reasoner

'''Rule:'''<math>\forall</math>F1, F2, S: ''absent_in''(F1, S) <math>\and</math> ''develops_from''(F2, F1) <math>\Rightarrow</math> ''absent_in''(F2, S)

This relation chain corresponds to the observation GIVEN THAT Basihyal_Cartilage ''absent_in'' Siluriformes AND Basihyal_Bone ''develops_from'' Basihyal_cartilage, THEN Basihyal_Bone ''absent_in'' Siluriformes. This and other similar relation chains (as per identified requirements) are to be implemented for the Phenoscape project in the future. Strategies to deal with absent features in general are also to be implemented in the near future.

Differences between the [[The exhibits relation conundrum|existing semantics]] and [[Relating taxa to phenotypes|desired semantics]] of the ''exhibits'' relation need to be resolved to address this issue. Potential strategies to implement the absence of features problem are discussed [[Novel reasoning strategies|here]].

[[Category:EQ Annotation]]
[[Category:Informatics]]
[[Category:Ontology]]
[[Category:Queries]]
[[Category:Reasoning]]
[[Category:Data]]
[[Category:Curation]]
[[Category:Taxonomy]]
[[Category:OBD]]