Logic and Reasoning Challenges

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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 all_exhibit can be used in the top-down reasoning as shown below. The new rule is shown in (Rule-4)

Rule-4: <math>\forall</math>A, B, x: is_a(A, B) <math>\and </math>exhibit(B, x) <math>\and</math> ¬rank(B, "species") <math>\Rightarrow</math> all_exhibit(A, x)

Assertion (A-6) is a phenotype assertion to a taxon of a higher rank, let us say a Genus Gen1. Now, let's assume Gen1 has 2 species Sp1 and Sp2. Inferences to Sp1 and Sp2 from the assertion (A-6) may use the new relation all_exhibit as shown in (I-14) and (I-15).

<javascript> Gen1 PHENOSCAPE:exhibit Phen1 -- (A-6) Sp1 OBO_REL:is_a Gen1 -- (A-7) Sp2 OBO_REL:is_a Gen1 -- (A-8)

Sp1 PHENOSCAPE:all_exhibit Phen1 -- (I-14) Sp2 PHENOSCAPE:all_exhibit Phen1 -- (I-15) </javascript>

The inferences with the all_exhibit relation cannot be associated with the higher taxa.

Similarly, for any taxon to which a phenotype assertion has been made, the phenotype can be inferred on the higher taxa using the some_exhibit relation as shown in (Rule-5)

Rule-5: <math>\forall</math>A, B, x: is_a(A, B) <math>\and </math>exhibit(A, x) <math>\Rightarrow</math> some_exhibit(B, x)

Given assertion (A-6) to a genus and assuming it belongs to a family Fam1, the inference (I-16) can be made about the family Fam1. <javascript> Gen1 PHENOSCAPE:exhibit Phen1 -- (A-6) Gen1 OBO_REL:is_a Fam1 -- (A-9)

Fam1 PHENOSCAPE:some_exhibit Phen1 -- (I-16) </javascript>

The relation some_exhibit cannot be used to infer down the taxonomy. Therefore, we can see that this new methodology can use the existing assertions that use the exhibits relation, but can distinguish the inferences that are made in both top-down and bottom-up reasoning. The relations all-exhibit and some-exhibit are only inferred, never asserted. Moreover, they can never be used to create new inferences. This distinction averts the extraction of incorrect inferences.

In this solution, no changes are necessary to the NeXML format or to Phenex. The changes need to be made to the OBD reasoner to use these two new relations and the data query module needs to be changed to deal with the two new relations as well. The REST services would not need to be modified for this purpose.

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 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 FMA and the 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 Ceusters et al and Hoehndorf et al. Both these publications propose solutions to integrate these aberrant observations with canonical definitions, without causing inconsistencies in reasoning procedures.


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 existing semantics and 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 here.