Table 1 Overview of patterns and their performance in representation of change of qualities

OWL property

A default OWL handling of qualities.

Very High - no additional classes or properties.

Very High - no reified instances.

High

Very low - no support for representing change of quality assignments.

T-indexed OWL property

The pattern is simple and works well for limited number of time indexes or for idiosyncratic time index.

Low for cell tracking experiments - the number of object properties is high and proportional to the number of t-indexes

Low for cell tracking due to high number of t-indexed property axioms.

Low for cell tracking - requires the adjustment of the T-box for each experiment. Complexity of T-box implies poor maintainability.

High - no reified modeling artifact must be introduced..

Reification

The pattern overcomes the limitations of patterns above - time-indexed quality value assignments are represented as reified instances only. Therefore,

even in situations where many time-indexed value assignments occur, the size of T-box is constant.

Moderate - the number of reified quality value assignment classes equals the number of qualities.

Moderate - the number of reified instances equals the product of objects, qualities and t-indexes. For temporally equal quality assignments it causes redundancy, i.e. for each quality observed at a given time point

a separate Quality Assignment instance has to be introduced.

Moderate - a new quality assignment requires a new instance of a reified class.

Moderate - reified quality assignments do not correspond to any tangible objects in a domain of cell tracking but are mere modeling constructs.

Reification w/ temporally ordered assignments

The pattern simplifies and restricts the expressivity of the reification pattern by no explicit representation of time entities but only a temporal order of quality value assignments.

High - same as above wrt quality assignment. Additionally, no classes for time entities are introduced.

Same as above wrt quality assignment. Additionally, no instances for time entities are introduced.

Moderate - same as above.

Moderate - same as above.

4d fluents (vertical) / states

The pattern, in contrast to the reification pattern, reifies not a temporally indexed relation but instead a temporal part of an object which can be interpreted as a state of an object.

High - number of reified classes is reduced to the number of object types

Very High for temporally equal qualities- instead of reifying each quality assignment at

a given time, all coinciding quality assignments are represented as a

a single instance.

Moderate for temporally overlapping qualities - the number of reified quality instances is a function of quality assignment changes and depends on the distribution of changes.

Very High for temporally equal qualities - no additional instance is needed when a time slice with the same time index already

exists in the model.

Low for temporally overlapping qualities - new quality assignment results in proliferation and reorganization of reified instances (slices) and multiplication of property axioms for non-changing qualities.

High for cell tracking experiments - presential cells represent the domain adequately - they are the cells represented in the acquired images or the temporally indexed states of cells.

4d fluents (horizontal)

The pattern, overcomes the limitations of the vertical 4d fluents pattern in representing the temporally overlapping qualities by the introduction of horizontal slicing such that a reified entity represents some quality assignment.

High - same as above.

Very High for temporally equal qualities - same as above.

High for temporally overlapping qualities - in contrast to the reification pattern, it enables the

bundling of temporally equal characteristics into a single entity, which limits the number of reified entities

Very High for temporally equal qualities - same as above.

High- for cell overlapping qualities solves the problem of the vertical 4d pattern. Additionally, in contrast to the reification pattern a new quality assignment requires a new instance only if a time slice for a given time does not exist yet in A-box.

Low - time slices do not reflect cells observed on time points but instead collections of temporally equal quality assignments. A non-obvious interpretation of the association entity limits the intuitiveness of the model.