Get Started with NeuroLang

First Steps With NeuroLang

NeuroLang is a unifying formalism to perform complex queries and explorations using heterogeneous data sources like tabular data, volumetric images, and ontologies. To perform this in a sound manner, NeuroLang is a probabilistic logic programming language based on Datalog [abiteboul1995], [maier2018].

Note

If you are already familiar with logic programming, see NeuroLang for Logic Programmers for a more technical walkthrough.

The whole idea of logic programming is to be able to make assertions of the style:

region x is a left hemisphere gyrus if the label of x in Destrieux et al’s atlas starts with “L G”.

which can be formalised in first order logic as

\[(\forall x) \operatorname{left\_hemisphere\_gyrus}(x) \leftarrow (\exists l) \operatorname{region}(x) \wedge \operatorname{destrieux\_label}(l, x) \wedge \operatorname{startswith}('L\, G', l)\]

which, if we assume that \(x\) being on Destrieux et al’s atlas means that \(x\) is already a region, can be shortened as

\[(\forall x) \operatorname{left\_hemisphere\_gyrus}(x) \leftarrow (\exists l) \operatorname{destrieux\_atlas}(l, x) \wedge \operatorname{startswith}('L\,G', l)\]

Finally, for notation convenience, we will drop the quantifiers, assuming that all variables on the left of the arrow (such as \(x\)) are universally quantified, and all variables appearing only on the right of the arrow (such as \(l\)) will be existentially quantified [maier2018]. This leads to the expression

\[\operatorname{left\_hemisphere\_gyrus}(x) \leftarrow \operatorname{destrieux\_atlas}(l, x) \wedge \operatorname{startswith}('L\,G', l)\]

which we formalise in Python, where nl is a NeurolangDL instance, as:

with nl.scope as e:
    e.left_hemisphere_gyrus[e.x] = e.destrieux_atlas(e.l, e.x) & e.startswith('L G', e.l)

the full example is in our gallery in Loading and Querying the Destrieux Atlas’ Left Hemisphere Sulci.

Negation can also be used in NeuroLang, through the ~ operator. For instance, the regions of the atlas which are not left hemisphere gyri are

with nl.scope as e:
    e.not_left_hemisphere_gyrus[e.x] = (
        e.destrieux_atlas(e.l, e.x) & ~e.left_hemisphere_gyrus(e.x)
    )

Note that every variable of a negated atom must also appear in a positive atom of the same rule (here e.x is bound by destrieux_atlas).

Disjunctions in Logic Programming

Disjunctions in logic programming merit a specific discussion. For instance, let’s say that all the regions in the left hemisphere’s cortex are either a sulcus or gyrus, or more specifically

x is a left hemisphere region if x is left sulcus or x is left gyrus

which in first order logic can be formalised as

\[(\forall x)\operatorname{left\_hemisphere\_region}(x) \leftarrow \operatorname{left\_hemisphere\_sulcus}(x) \vee \operatorname{left\_hemisphere\_gyrus}(x)\]

alternatively, this can be written as a set of two propositions

\[\begin{split}\begin{cases} (\forall x)\operatorname{left\_hemisphere\_region}(x) \leftarrow \operatorname{left\_hemisphere\_sulcus}(x)\\ (\forall x)\operatorname{left\_hemisphere\_region}(x) \leftarrow \operatorname{left\_hemisphere\_gyrus}(x) \end{cases}\end{split}\]

which we formalise in NeuroLang in the classical logical programming syntax:

with nl.scope as e:
    e.left_hemisphere_region[e.x] = e.left_hemisphere_sulcus(e.x)
    e.left_hemisphere_region[e.x] = e.left_hemisphere_gyrus(e.x)

or in a less verbose manner:

with nl.scope as e:
    e.left_hemisphere_region[e.x] = e.left_hemisphere_sulcus(e.x) | e.left_hemisphere_gyrus(e.x)

Aggregations

Aggregations combine information from a set of tuples. A good example of an aggregation is the maximum. As a mathematical definition we could define an aggregation as

\[\begin{split}\begin{split} (\forall country)\operatorname{max\_population\_per\_country}\left(country, max(\{pop: (\exists province)\operatorname{population\_per\_country\_province}(country, province, pop)\})\right) \leftarrow \\ (\exists province)(\exists pop)\operatorname{population\_per\_country\_province}(country, province, pop) \end{split}\end{split}\]

which in NeuroLang is expressed as

with nl.scope as e:
    e.max_population_per_country[e.country, e.max(e.pop)] = e.population_per_country_province(e.country, e.province, e.pop)

[abiteboul1995]

Abiteboul, S., Hull, R. & Vianu, V. Foundations of databases. (Addison Wesley, 1995).

[maier2018] (1,2)

Maier, D., Tekle, K. T., Kifer, M. & Warren, D. S. Datalog: concepts, history, and outlook. in Declarative Logic Programming (eds. Kifer, M. & Liu, Y. A.) 3–100 (Association for Computing Machinery and Morgan & Claypool, 2018). doi:10.1145/3191315.3191317.