Task: Class Definition Understanding (ontology: Legal/LKIF_Core_Ontology)

Which of the following definitions best describes 'Abstract Entity'?

A. Metaphor of physical concepts, i.e. the things we mentally manipulate, either in thought or memory
B. An abstract concept is a concept which does not (necessarily) have a referent in either the physical or the mental world.   

Abstract entities are (proto)mathematical, formal entities, entities which have a purely formal, logical or mathematical meaning.

As all concepts are abstractions, one may argue that a separate abstract world is difficult to see. In common-sense, a circle has more properties and is less abstract than in mathematics. Even mathematicians marvel about the fact their pure abstractions enable us to predict very concrete things. However, we are not directly concerned with these mappings. The most important is that common-sense knows about a (small) number of proto-mathematical concepts, such as collections, sequences and count-numbers (positive integers). We know also about geometric simplifications such as line, circle, square, cube, etc. These common sense notions might even be the real roots of our mathematics. However, these kind of semi-formal abstractions do not play a very central role in law, and therefore LRI-Core is thinly populated with abstract classes.
C. We made the assumption that our views of the mental world have been developed in analogy with physical processes. Mental objects like thoughts are made of elementary parts: concepts. The contents (substance) of these objects are representations. The conceptual content of thoughts are intended by propositional attitudes, like belief, desire, norm etc. Mental objects are processed or stored in containers like a mind which has parts like various memories. Mental processes like thinking, memorizing, imaging, etc. are operations on mental objects. The energy equivalent of mental processing are emotions: the forces that make us focus our mental energies. 

There is an important difference between the mental world and the physical. Where physical processes occur causally, mental processes are controlled by an intentional stance. The outcome of mental processes can be the intention to act. The intention to act may consist of a structure of primary actions: a plan. The actions can be aimed at bringing about physical changes, but they may also be aimed at changing the mental state of another agent: these intended actions are communication actions. Like direct actions, communication actions have a physical appearance. They also need some physical medium to transfer the intended mental state. Speech act is the common term for these actions. 

Whether this notion of intended control over mental processes and actions is an illusion or not is besides the point in modeling common-sense. The intentional stance implies a kind of backward, teleological reasoning over causally related processes. A mental object like a  plan consists of a goal state (intention) and is produced by reasoning from goal to means (actions): this is what rational agency behavior is about. 

The mental world is not only a reflective one based in our minds eye. We may observe the stream of conscious mental processes, but the role of the mental conceptualizations is of even more important in understanding and communicating with other people. Mental processes and attitudes (sources of intention) are in the first place the building stones for modeling the minds of other people. The intentional stance means in the first place that we attribute to others and to some extent also to many animals intentions and intention directed mental processing and belief.
D. An occurrence in space-time

Answer: An abstract concept is a concept which does not (necessarily) have a referent in either the physical or the mental world.   

Abstract entities are (proto)mathematical, formal entities, entities which have a purely formal, logical or mathematical meaning.

As all concepts are abstractions, one may argue that a separate abstract world is difficult to see. In common-sense, a circle has more properties and is less abstract than in mathematics. Even mathematicians marvel about the fact their pure abstractions enable us to predict very concrete things. However, we are not directly concerned with these mappings. The most important is that common-sense knows about a (small) number of proto-mathematical concepts, such as collections, sequences and count-numbers (positive integers). We know also about geometric simplifications such as line, circle, square, cube, etc. These common sense notions might even be the real roots of our mathematics. However, these kind of semi-formal abstractions do not play a very central role in law, and therefore LRI-Core is thinly populated with abstract classes.