What is Context?
Context is the property of an object and a non object that enables an agent to identify an object as a unique entity or something separate from the non object. Notice that words come in pairs, it is contrast that perception is based on, and a dual nature of concepts rules the mind. That enables comparison, the building block of learning, acquiring practical knowledge and abstract thinking. I interpret the world in terms of a lean upper ontology, the first three concepts of which must be familiar from upper ontology.
Context is an abstract noun. As an abstract noun it is either an object, or a property or a relation.
Definition 1. Context is the property of objects
There are many (physical) objects around. They have many-to-many relationship, which is another name for chaos. What you want is a one-to-one relation in place. In order to be able to do that you need pick two items and see them being in one-to-one relationship in your mind and/or in reality. This is done by bringing them in your focus (perception, mental operation No0). Depending on your distance to the two objects you will have one that you can touch, feel, see, hear or otherwise experience as existing, hence also defined by its boundaries that are the boundaries of another object called the context or the environment.
Comments: Note that you normally cannot have two objects focused in your sight, and sometimes in your mind either. So you need to isolate (isolation, mental operation No1) the object both in reality and in your mind. What you need is a shift (your attention, glance) away from an object to another one. But time and memory available, you are still capable of comparing the two. You want to make a comparison (mental operation No2) in order to be able to see their relation (how they are related). In all likelihood one object will be larger than the other one. Perceiving the difference will enable you to abstract the property of size (abstraction, mental operation No3). That object is then interpreted as being in a contain(ment) relation with the smaller one. (Interpretation, mental operation No4). This relation offers you the chance to sort all the objects that there are by size which corresponds to the option of using a numeric system of identifiers as well as labels given ad hoc over time and across space that are another tool for identifying objects in a sorted manner. The purpose of any sorted arrangement of objects is to help identification and location (orientation). The only suitable property to sort on is size, i.e. a serial number, because of the containment relation (the same as part of and father of, if you take age on the time dimension).
Definition 2. Context is a relation between objects
Based on the property of differences in size and subject to the object in your focus and the relation containment prevailing between them the larger object shall be conceived as a necessary complement of the smaller one, or context. Examples: one word. Makes no sense, has no meaning without a reference: Triangle of Meaning also suggests that context is larger, wider than the object. Note that even syllogisms are built on terms sorted by size (quantity of reference).
Comments: Abstract words always have “larger” references than the names for physical objects. Physical objects in plural or in undefined forms (e.g. a school) behave similarly to abstract words that are not countable and not tangible. This means spatial relation exists between objects, and which abstract spatial relation must be converted into concrete, specific terms (units of measurement) for us to be able to act. Such concrete identification may come from numbers (thesauri) or parts lists (Bills of Materials) used in the manufacturing industries. If you are after engineering or building an ontology, you should forget about library science and rethink what the difference between a thesauri and a BoM is. One important difference is that you can apply top-down design, i.e. start off from the categories of an upper ontology and by improving it with the adaptation of mental operations, you can produce a dynamic denotation that is suitable for writing algorithms to process your data.
Definition 3. Context is an object
Surely, context is an object as it is embodying various concepts and ideas describing the world using a number of approaches and methodologies. As for an embodiment (another mental operation) you should look for any medium of information, since information is transformation, by agents leaving marks on some media capable of recording the products of non tangible processes of mental operations. We have seen how space, one of the pair of abstract words space and time (properties) is used for a further breakdown and decomposition, now we have some more properties to choose from. They are form and content, quality and quantity. (If form and content are seen as objects, then form is larger than content). Quantity and quality (properties) are the two sides of the same object, similarly to the two faces of a number (serial and cardinal numbers).
Now the form of a context is determined by the framing or the scope of focus in the minds of the stakeholders. If they believe that the purpose/the use of an ontological structure is to harmonize the working and the elements of thinking in human beings, then it is not just the vocabulary/glossary/taxonomy/nomenclature/repertory used to describe objects that must be shared and be common, but the interpretation of the world through mental operations made explicit. And why operations? Because, although we are not trained to be aware of them (the operations), yet post festam, we are able to pinpoint and compare them to see the differences, good matches and lucky encounters and fallacies alike.
So currently we have structured word lists in ontologies where the place of an individual word is determined by the assumed relationship between the word and other words of similar or associated meaning. But those joint neighborhood occurrences are rarely met in everyday parlance, thus they are out of context as far as usage is concerned. Neither are they suitable for making propositions or other utterances for the very reason that they would not present any verb, an essential component of a statement or a message that you either want to create or want to analyze the meaning to understand. The assumption is that smaller units you decompose things into, a better understanding you get. What is true, however, that you will be more capable to synthesize things.
In contrast contexts are indicated by dictionaries as word senses. Individual senses are explained by sentences that are a random example of usage, not really indicating explicit grammar, syntactical, semantic and pragmatic constraints. Constraints represent form, and their form are explicit rules of usage which implies selecting from the options. In this respect none of the book-form dictionaries can be regarded as exhaustive, But several dictionaries are available to indicate such restrictions, a dictionary of collocations is one of them. The reason why you may want them is to follow some rules as concordance, compliance, etc. in the use of terminology and PoS', but there are no rules laid down on the needs for making generalizations, specifications, concretization, reification, etc. (further mental operations) that emerge from a dialogue, real or imaginary. Clearly, it is no longer sufficient to have just one word in your focus; you must work with linguistic/semantic data crossing sentence boundaries. And you make comparisons of items from subsequent clauses too. In the meantime you need to be able to make constant comparisons as to what you already know and what you do not.
The content of contexts is the real-world references themselves. With respect to verbal contexts (texts) it is the physical objects, etc. that the forms (constraints) name or identify. The content of non-verbal contexts also needs to be interpreted in verbal terms to come to the common language used in the representational system. An important point: natural languages are context-sensitive or context-dependent languages, which is a part of the headache that people using context-free languages may feel and want to get rid of. Context as an object with quality and quantity is likely to call for taking an inventory of the contexts for each object that there is.
The description of any such context may vary but should better be standardized as long as the nature of the objects allows. It may well be that the usual context provided for this purpose is not the best possible. The fact that you have 49 nyms based on similarity of some kind and the usual hierarchical setup show that it is still a long way from establishing one-to-one relations the ideal condition to get out of a mess of context-sensitive languages. But it is also a device that has enabled humankind to escape from reality and create myths, religions, arts, poetry, lies, laws and science, a further level of existence that should be differentiated in any ontology that worth its name, i.e. a directory of what exists.
Talking about verbal (text) contexts only, the solution that I am suggesting in response to the call for a research proposal may sound peculiar. I believe the first big step to sort out the problems around ontologies is to attempt to convert the vocabulary of the English language, a context-sensitive language into a context-free language. The resources and the technology are available. You need to create a list of all the English words without the usual grammar notations. It is estimated that there is more than one million English words now. But compare that to the number of car parts, 30 thousand, the components of the wing of an airbus 380, half a million, or the whole airplane, 4 millions. We could use the entry words in the WordNet files and apply data-mining algorithms to produce something similar to a word frequency list.
Second, we should follow the usual principles or notations from computer science and provide context to each word occurrence. Every word in the list shall be defined by the rest of the collection and each use shall be noted. But no word would be duplicated and each should have numeric identifier, instead, it would have a pointer to tell where used. Then content words shall be separated into groups of nouns, adjectives and verbs, following the usual content word classification. Verbs shall be separated into those of denotation and those of connotation. The list of verbs shall be made complete by supplying all their theta roles/valences, and phrasal verbs, verbs with dependencies shall also be made complete. I am not going into more details and should stop her in a wait for any comments.
The point is that different routes are to be followed if you pursue a text generation approach or a semantic parsing exercise of existing texts. My point is that the end result of such decomposition shall not be propositions with true or false values but a list of final constituents, namely objects, properties and relations. And as a final notice. Verbs represent relations any other verbal form may be converted into verbs. But of course not all verbs indicate meaningful relations.
How is context generated?
The repertory to be produced is about the knowledge we collectively have and recorded, but probably not completed or updated to keep up with the changes in the world of things and the people, not to mention the oceans of publications. Book form written text is alternatively used with screen pages where the rules of reading and writing from left to right no longer apply. Yet we have an aim in mind, to hit a target, to create a match, which is the double pleasure of meeting form and content, quality and quantity, by touching and connecting to generate a bidirectional flow. Such a flow is only possible if the resulting structure includes the operational dimension, i.e. it makes clear how you interpret a clause or a proposition built from semantic primitives after applying constraints inherent in text generation. In time, we get more and more accustomed to using the concept of mental operations that are garbled up by our language as in algebraic operations too. You do not keep count of the number of “tagging” on enumerating involving the connection between two objects, the very minimum of all measurements. And you do not indicate a multiplication operation in the phrase ab either. Nevertheless, we are limited to representing every idea in a 2D plane, where it is a problem to indicate the multi faceted relations that are suggested by our verbs, usually introduced on the basis of analogy. We should remember that language itself is metaphysics, a system that is used not just to reflect what there is in the physical world tested by a practical, constructive manner to produce artifacts, but what there is in a figurative manner, using heavily and mistakenly metaphors.
You will be able to generate contexts as soon as you accept that there is a rotation feature to thinking, so it is not impossible to synchronize as long as the direction, speed and sign of the rotation of the items in your mind can be harmonized. Harmonization requires practice as in playing music, the sports and the military, so we need to take small steps at a time and repeat them until mastery.
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 Why is context interpreted in terms of three concepts?
1. Context is an object, because it is a noun, meaning a name. Nevertheless it has two references or senses: https://en.oxforddictionaries.com/definition/context 1. The circumstances or setting for an event, statement or idea 2. The parts of something written or spoken that immediately precede and follow a word or passage, etc. In both cases the purpose of providing context is to clarify meaning and understanding. This suggests that neither an event, nor a word (clause) is complete or clear without knowing the context. Consequently, if you specify context in sense 1, you need to specify or describe an event complete with the description/identification of its wider environs that the event belongs to as a smaller entity. In sense 2, your description will be similar, because you identify the elements that include the word or clause needing specification. Notice that anything may call for an explanation or the provision of context and may be provided at other times as context itself. This is what I called the Matryoshka variables metaphore. Once you are a container, once you are containment. If you accept that, then clearly context is an object, although not necessarily easy to identify in physical terms. With texts, it is easy though. Also with pictures, but with ideas, it is hell.
2. Context is a property, because it is used to explain, describe and identify an object that context is the context of. Here your ambition is to discover as many elements constituting context as possible or necessary. The effort is a function of purpose, the aim in your mind. Understanding better? Clarification? Implicatures? Establishing the frontiers of the universe of discourse or framing? Separate or isolate your point from possible misinterpretations (finding excuses)? To place your item in a sorted system of classification of items? Notice two phrases: in context and out of context. They identify a location and a location is an abstract object. That abstract object is characterized by the attributes of some other (physical or non physical) object being inside or outside the item making it either more, or less understandable.
3. Context is a relation, because you have two items between which context is contemplated, usually by visual check. This spatial relation is then transitively used to concoct ideas, words in the mind, and then in turn it is represented by lines in 2D planes. We have no idea of how anything is related in the mind, apart from the neurobiological terminology that provides form to what we have here, i.e. concepts, words, etc. as content. We have one word, verb association, connecting, or (two) being connected. Apart from the fact that such a connection, in theory, allows a flow to pass in and to both directions, displaying the property of commutativity, we cannot break it down any further. But it is probably not true; it is not likely that flow in both directions results in the same output. What is more likely, however, is that one direction indicates a move to a larger or wider context and may be this is why we want to arrange (sort by size) things in a linear order and a hierarchy. But apart from such spatial and hierarchical relation that are used in ontologies the analysis of clauses, the dependents of verbs or the theta roles offer configurations with a verb in the center. Of course, verbs are different and so are the configurations. We differentiate between verbs of denotation and verbs of connotation, as obviously they have different configurations and plausibility. Besides, verbs represent the components of models that our thinking devises and which are available in abstract word pairs such as cause and effect, space and time, form and content, quality and quantity. They should be used at the next level following objects, relations and properties for the description of the entities that exist in the world. Making sure, however that the entities that exist in poetry and fiction only and not in the real world shall be separated.
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