A Whiteheadian approach to data and knowledge Sebastian Siemoleit1,2,* and Heinrich Herre1 1 Institute of Medical Informatics, Statistics and Epidemiology, University of Leipzig, Germany 2 In Mind Cloud Pte Ltd, Munich, Germany ABSTRACT We hold that this view is questionable and unsettled. One may ask Motivation: We live in the age of Big Data. Data are collected whether it is possible to extract Einstein’s General Theory of Rela- about everything which has a mode of existence; this can be ob- tivity out of petabytes of physical data by methods of knowledge jects, processes, pictures, verbal reports, and many other types mining and statistics. Another example is expressed by the follow- of things. The final purpose of data is not to collect more data but ing quote of the statistician E. P. Box: “Essentially, all models are to transform data into relevant applications. For this purpose, wrong, but some are useful” (Box 1987). We disagree, and believe that Box misunderstood the role of models and underestimates the there is a need to transform data into knowledge which is the ba- importance of theory formation. Our detailed analysis of this topic sis for a manifold of applications. The current situation of data will be published elsewhere. overload is caused by a lack of methods for abstraction and inter- Members of other communities, notably from psychology, are pretation of data, but also by an insufficient understanding of the more aware of problems pertaining to the relation between data and relation between data and knowledge. The overall goal of our knowledge. In (Mausfeld 2011) the author addresses the fundamen- work, intended to be realized within a longstanding project, is to tal problem of perception theory. Mausfeld notes that in the standard establish an ontological framework which may serve as a unifying model of perceptual psychology, which is basically used in com- theory of data and knowledge. We explore various philosophical puter vision, occurs an explanatory gap because this model borrows sources, and ascertain whether they may contribute to the reali- concepts, such as surfaces, shadows, boundaries or illuminations, zation of this project. In the present paper we consider White- implicitly from the output of the perceptual system. In the spirit of head’s philosophy. Whitehead, these concepts are localized in the realm of eternal ob- jects and not directly in the raw data. The remaining problem is un- Approach: We explore the philosophy of Whitehead, expounded solved, namely to understand how the perceptual system integrates in Process and Reality, with respect to its relation to a recently the sensory input with the eternal objects to create a perceptual ob- developed ontology of data called GFO-Data. Whitehead’s Pro- ject. cess and Reality provides a non-formal approach to the creation In (Albertazzi 2015) an intriguing argument is presented in favor of data and knowledge. of the usage of a natural semantics in an advanced ecological theory Results: Basic categories and relations of Whitehead’s Process of perception. We hold that the same is valid for image processing, and Reality are analyzed and specified by axioms in FOL. We too. As Albertazzi accentuates, it is necessary to express phenome- outline a representation of the informational character of a datum nal qualities not in an objective manner, but rather in the way they as a prehension. This approach needs to be completed in order are perceived subjectively. Whiteheadian subjective forms are the to grasp the process of transforming data into knowledge in more key to represent how contemporary entities are perceived. Their de- detail. scriptive character allows applications to not only represent appear- ances as dispositions, since they are capable to encode functionality *Contact: sebastian.siemoleit@imise.uni-leipzig.de and affections. Subjective forms are the result of a sense-making process and how visual data are perceived according to a perceiver. 1 INTRODUCTION We defend the conception that theory is needed and should be In the current paper we present an approach, inspired by ideas of regulated as well as tested by practical applications.1 Conveniently, Whitehead’s philosophy in Process and Reality, which supports the the neuro-ecological model of the brain described in (Northoff analysis of the categories of knowledge and data. This investigation 2016a) does not only withstand ontological discussion in (Northoff was stimulated by the boom of Big Data and the need to gain a 2016b) but also an impressively successful comparison to empirical deeper understanding of the relation between data and knowledge. data. This model is based on the Whiteheadian notions of subject We believe that this boom precipitates, serious misinterpretations and object and explains how they are subsequent phases of perceiv- about the role of data and its expected power to generate real ing entities. These notions will be discussed later in this paper and knowledge. From some circles of computer scientists and software provide a foundation for this model in a formal guise. Such work engineers, but also statisticians, emanates the idea that empirical sci- emphasizes the important role of formal ontology as it is pointed out ence and its methods are obsolete in the age of Big Data, because all in (Martin 1999), which can be summarized by: All what exists falls the knowledge is in the data and can be extracted by mining algo- prey to ontology. rithms and statistics (Anderson 2008). 1 Hamming (1997) "In science, if you know what you are doing, you should not be doing it. In engineering, if you do not know what you are doing, then you should not be doing it:” 1 Siemoleit et al 2 APPROACH point of an object’s life time, its object-data exhibits entities, being wholly present at this time point. This means that an individual qual- ity of an object, say an individual red, can be wholly accessed at time 2.1 Basics of an Ontology of Data points. The composition of an object with some of its qualities ex- We use the top level ontology GFO as a reference ontology and hibits more complex data, called object-facts. framework for our investigation (Herre 2010; Herre et al. 2007). In The bearers of processual data are processes. Processual data are GFO the existence of four ontological regions, called ontological classified into presentic and global. Presentic processual data are as- strata, are postulated. The temporal regions include the material stra- sociated to process boundaries. They must be wholly accessible at tum, the stratum of societal entities, and the psychological stratum. time points. The isolated presentic data of process boundaries do not The ideal region includes entities which are independent from space need any reference to a process. They can be completely reduced to and time, including mathematical objects and universals; in White- object qualities. These are typically qualities of objects participating head’s philosophy they correspond to the eternal objects. In GFO in the process. An example of a non-isolated datum of a process is the entities of the world are classified into categories and individu- the velocity of a moving body at a time-point. This datum cannot be als. Categories can be instantiated; individuals are not instantiable. determined and specified without a preceding process. GFO allows for categories of higher order, i.e., there are categories The global qualities of processes are the richest class of processual whose instances are categories themselves. Spatiotemporal individ- qualities. A systematic classification of these qualities is in its initial uals, also called concrete individuals, are classified alongside two stage. Their main feature is that it does not make any sense to specify axes: the first one explicates the individual’s relation to time and them at a process boundary. One type of such qualities is abstracted space, and the second one uses the relation of existential dependency from time series in form of curves. Examples are electro-cardio- between individuals. grams or a long term blood pressure measurement. There are many Spatiotemporal individuals are classified into continuants, presen- other global qualities of a process which are not derived from time tials and processes. Continuants persist through time and have a life- series. Examples are the duration of a process, its temporal extension time; they correspond to ordinary objects, such as cars, balls, trees or its occupied space. Physics provide many examples of this kind, etc. At any time-point of its life time, a continuant exhibits a presen- e.g. the average velocity of moving bodies. tial, which is an entity that is wholly present at that time-point. Pro- The non-phenomenal data open a rich field of data, from which cesses are temporally extended entities that happen in time; they can we select relational data only. Relational data are based on relations, never be wholly present at a time point. Processes have temporal which are categories (universals), the instances of which are relators. parts, which are processes themselves. A relator, being a cognitive creation, is an attributive which is com- Concerning the second axis, attributives depend on bearers which posed of (relational) roles. We consider the following expression can be objects (continuants, presentials) or processes. Situations are 𝐺 ∶= “𝐽𝑜ℎ𝑛’𝑠 𝑑𝑟𝑖𝑛𝑘𝑖𝑛𝑔 𝑎 𝑏𝑒𝑒𝑟”. The subterm “𝑑𝑟𝑖𝑛𝑘” denotes a parts of reality which can be comprehended as a coherent whole relation, denoted by 𝑅𝑒𝑙(𝑑𝑟𝑖𝑛𝑘). Let 𝑝 be an instance of (Barwise et al. 1983). There is a variety of types of attributives, 𝑅𝑒𝑙(𝑑𝑟𝑖𝑛𝑘), then from this we may derive two roles, the role 𝑞1 of among them qualities, roles, functions, dispositions, and structural the drinker, and the role 𝑞2 of the drunken. John plays the role of the features. Categories the instances of which are attributives are called drinker and the beer plays the role of the drunken. These constituents properties. According to the different types of attributives (relational are composed to a complex entity, a relational fact expressed by roles, qualities, structural features, individual functions, disposi- “𝐽𝑜ℎ𝑛`𝑠 𝑑𝑟𝑖𝑛𝑘𝑖𝑛𝑔 𝑎 𝑏𝑒𝑒𝑟”; the fact, denoted by this expression 𝐺, tions, factual, etc.) we distinguish quality properties (intrinsic prop- is denoted by 𝐹𝑎𝑐𝑡(𝐺). The bearers of a relator are determined resp. erties) and role properties (extrinsic properties). The latter are clas- specified by the players, which play the corresponding roles. The sified into relational role properties (abr. relational properties), so- roles themselves occur as unary attributives, though they cannot be cial role properties (social properties). separated from the relator of which they are a part of. GFO includes a part that is GFO-Data, which is a top level ontol- Relators and roles are considered attributives, being more abstract ogy of data (Herre 2016). The semantics of data is captured by prop- than phenomenal data, as for example qualities. These data cannot erties, the instances of which need a bearer. The syntax of data uses be accessed by perception and measuring instruments. Relators can symbol structures and tokens, which can be saved on a material me- be classified with respect to the bearers; the role players may be ob- dium, for example a hard disc. The relation between the semantics jects or processes. and syntax of data is investigated in (Uciteli 2011). A similar ap- proach is presented in (Ceusters 2015). In the following we consider the semantics of data only. According to GFO-Data, we distinguish three levels of infor- mation: phenomenal data, factual data and propositions, whereas the term information is used informally to cover both data and knowledge. Data depend on bearers, and we assume that the bearers are concrete individuals. In GFO-Data, atomic data are covered by attributives and the corresponding properties; they are constituents for complex data. The elementary form and the origin of phenomenal data are sense Fig. 1 Categorical Basic structure of GFO-Data data, but also data which can be measured by instruments. These data correspond to qualities. With respect to the bearers, we distin- We hold that propositions are more abstract parts of the world guish between object-data and processual data. Object-data are clas- than facts. Elementary relational propositions correspond to rela- sified into presentic object-data, and non-presentic data. At any time 2 A Whiteheadian approach to data and knowledge tional facts. Let us consider the fact 𝐹𝑎𝑐𝑡(𝐺), associated to the ex- a basic datum anymore, it is already a product of 𝑎’s mental pole, as pression 𝐺 ∶= “𝐽𝑜ℎ𝑛’𝑠 𝑑𝑟𝑖𝑛𝑘𝑖𝑛𝑔 𝑎 𝑏𝑒𝑒𝑟. ” By an operation of ab- well as a probably unconsciously made proposition about 𝑏 and 𝑐. straction the mind transforms the fact 𝐹𝑎𝑐𝑡(𝐺) into the proposition The creation of such mental entities mark the first step on the way 𝑃𝑟𝑜𝑝(𝐹𝑎𝑐𝑡(𝐺)) ∶= “𝐽𝑜ℎ𝑛 𝑖𝑠 𝑑𝑟𝑖𝑛𝑘𝑖𝑛𝑔 𝑎 𝑏𝑒𝑒𝑟. ” The modes of ex- to the creation of knowledge from data. istence of 𝐹𝑎𝑐𝑡(𝐺) and 𝑃𝑟𝑜𝑝(𝐹𝑎𝑐𝑡(𝐺)) are different: 𝐹𝑎𝑐𝑡(𝐺) is a part of spatiotemporal reality, whereas 𝑃𝑟𝑜𝑝(𝐹𝑎𝑐𝑡(𝐺)) is an ab- stract entity having an indirect relation to reality, mediated by the Eternal Objects, corresponding fact. Propositions can be satisfied or disproved, Universals, Properties hence, they can be true or false. We emphasize that the interface between data and knowledge oc- curs at the transformation from facts to propositions. Relational propositions are very simple expressions which can be used to rep- resent small pieces of knowledge. The development of a full-fledged ontology of knowledge, which includes complex propositions, the- ories and knowledge fields, is an important task for the future. Fig- ure 1 summarizes the basic categories of GFO-Data. 2.2 Process and Reality Fig. 2 Physical entity 𝑃, energy pattern on the retina 𝑅, and the mind 𝑀, being dependent on the brain, are actual entities, which are connected by the The crucial part of the ontology in Process and Reality is the becom- prehend-relation, whereas the vase 𝑉 is a perceptual object which is created ing of actual entities. These actual entities, being in space and time, by the mind by integrating the input of the retina and certain eternal objects, are the only components reality consists of from a physicalist point to which 𝑀 has access. The perceptual object belongs to the internal structure of view. All other entities are abstract objects or parts of actual en- of the mind 𝑀. In the picture those attributes (resp. eternal objects) of the tities. These parts form the inner structure of each actual entity and vase are left out which refer to the tactile phenomena. determine its perceivable attributes. What Whitehead refers to as process lies in the becoming of each actual entity and plays an inte- We argue that there are similarities between the Whiteheadian pro- gral part in how the inner structure of such an entity is created. The cess ontology and the GFO-approach to an ontology of data and becoming is the evaluation of the sense data which an actual entity knowledge, as sketched in section 2.1. The justification of this claim can perceive and how the information, created out of this data, is needs a deeper analysis of the structural aspects of Whitehead’s pro- composed. Furthermore, this information determines how the entity cess ontology within the GFO-framework. In this paper, we focus can be perceived by other entities. on a partial representation of those entities types only, which White- Whitehead refers to the cycle of perceiving and being perceived head subsumes under his Category of Existence. In the future work, as principle of advance. Each actual entity fulfills two tasks. Firstly, we intend to give a complete description of all these types and will in its role as a subject, it transforms data into knowledge and sec- define a relational structure in which they coexist to form a contin- ondly, in its role as an object, it provides this knowledge as data for uously evolving reality. other entities. The process itself is the transformation of data into Figure 2 displays the relevant components which are associated knowledge. Data is a result of perception and no object is perceived with the perceptual system. This can be described by using the no- directly, but it is grasped by its attributes. Likewise, an actual entity tion of actual entity, the relation of prehension, and eternal objects, does not directly perceive other actual entities; it perceives its sur- which correspond to attributes being universals. rounding world as prehensions about the actual entities the world consists of. Therefore, each attribute will be reflected as a part of the prehension its carrying actual entity effects. This part is the universal 3 FORMAL REPRESENTATION the attribute instantiates. Whitehead’s Category of the Ultimate specifies the principles which Whitehead calls them eternal objects as they are more than just are presupposed in the three other categories, defined in Process and object-universals. Each of them is used relative to the prehending Reality. The so-called Category of Existence aggregates all types of subject, whereas an object-universal is the same for each subject. As existing entities. The subsequent Category of Explanation and Cat- an example we consider the situation that a dog is prehended as egory of Obligation describe the notion of these types and their basic frightening; the eternal object, used by the subject to describe this functional properties, as well as relations between their instances. dog, is not the object-universal dog only. The corresponding eternal Subsequently, we summarize how actual entities, prehensions, and object is a composition of the object-universal dog and fear as a sub- eternal object must be specified to support applications in the theory jective emotional component which is another eternal object. In Pro- of data and knowledge. cess and Reality these compositions are called subjective forms. These subjective forms resemble aspectual derivatives, as presented 3.1 Data and discussed in (Herre 2013). If an actual entity 𝑎 perceives the actual entities 𝑏 and 𝑐 and pre- In the Whiteheadian approach, the basic elements of the categorical hends them by means of their common attributes 𝑋 only, then 𝑏 and scheme are actual entities, which form reality, and eternal objects 𝑐 are perceived as a single entity n, because a cannot distinguish that provide order and definiteness to them. them and assumes them to be the same. Whitehead calls this entity 𝑛 the nexus of 𝑏 and 𝑐, justified by the subjective form 𝑥 which is 3.1.1 Actual Entities the complex eternal object having all 𝑋 as its parts. This nexus is not Actual entities are defined in two different ways, depending on context. One context pertains to the evolution of developing entities, 3 Siemoleit et al where the actual entity presents an event, whereas the other refers to We introduce a first-order structure 𝐾𝑆 = an actual entity’s own process of becoming as subject. (𝑊, 𝑂𝑆, 𝑠𝑢𝑏𝑗𝑒𝑐𝑡, 𝑑𝑎𝑡𝑢𝑚, 𝑓𝑜𝑟𝑚), called knowledge structure, be- A becoming subject analyzes the data provided by the world and cause it aggregates the main components taken from Whitehead’s gains spatiotemporal extensiveness during this process. This exten- philosophy, which are crucial for the elucidation of data and siveness is effected by the resulting information of this analysis. The knowledge. Here, 𝑊 denotes the universe, consisting of spatiotem- becoming itself has no extension on its own, but results in an actual poral entities, which include the set actual entities 𝐴𝑐𝑡𝑢𝑎𝑙 and the occasion representing extensiveness. These actual occasions are a prehensions, 𝑂𝑆 is an ontology structure as introduced above and special kind of event, consisting of one unique actual entity only. 𝑠𝑢𝑏𝑗𝑒𝑐𝑡, 𝑑𝑎𝑡𝑢𝑚, 𝑓𝑜𝑟𝑚 are binary relations to be explained later. We argue that these two entities are equivalent. If a reference is Prehensions are a special form of composite entities. made to an actual entity's extensiveness, i.e. its position in time or The earlier mentioned subject-object-form-relationship is crucial space, we are talking about its corresponding actual occasion. Since to the definition of prehensions. A subject objectifies a datum by it has no temporal extension, we argue that each becoming resem- assigning a subjective form to it. In this context, objectification bles an instantaneous change. An effected change is only to some means making a datum graspable by assigning abstract universals degree specific to the actual entity, because an external determina- and emotions to it. Prehensions encode such objectifications, i.e. tion exists. how entities generate information out of data. In the following we focus on those entities described in Process and Reality, which are 3.1.2 Eternal Objects relevant for the analysis of data; these are prehensions of actual en- The determination of actual entities is provided by eternal objects. tities, and eternal objects. These types are sufficient to describe the These objects are able to describe actual entities and thus, the anal- acquisition of data, the evaluation by the subject, and to outline the ysis of a becoming subject results in information as a composite eter- mental operations realizing the creation of data and knowledge. nal object. The existence of such complex objects implies an order- ing between all eternal objects enabling actual entities to evaluate ∀𝑥 (𝑃𝑟𝑒ℎ𝑒𝑛𝑠𝑖𝑜𝑛(𝑥) ∶↔ ∃𝑢, 𝑣, 𝑤(𝑠𝑢𝑏𝑗𝑒𝑐𝑡(𝑢, 𝑥) ∧ 𝑑𝑎𝑡𝑢𝑚(𝑤, 𝑥) ∧ their analysis regarding the relevance of the results. Whitehead pre- supposes the existence of a unique actual entity which is final; it 𝑓𝑜𝑟𝑚(𝑤, 𝑥))) (4) exists initially and its internal structure implies a binary relation on ∀𝑥, 𝑦(𝑠𝑢𝑏𝑗𝑒𝑐𝑡(𝑥, 𝑦) → 𝐴𝑐𝑡𝑢𝑎𝑙(𝑥) ∧ 𝑃𝑟𝑒ℎ𝑒𝑛𝑠𝑖𝑜𝑛(𝑦)) (5) the set of all eternal objects. We argue that this relation is a partial ordering; it resembles the ordering between concepts, introduced ∀𝑥, 𝑦(𝑓𝑜𝑟𝑚(𝑥, 𝑦) → 𝐸𝑡𝑒𝑟𝑛𝑎𝑙(𝑥) ∧ 𝑃𝑟𝑒ℎ𝑒𝑛𝑠𝑖𝑜𝑛(𝑦)) (6) and investigated in (Herre 2007). The system of eternal objects, to- gether with a binary relation ≤, is called ontology structure, and is ∀𝑥, 𝑦 (𝑑𝑎𝑡𝑢𝑚(𝑥, 𝑦) → (𝐴𝑐𝑡𝑢𝑎𝑙(𝑥) ∨ 𝐸𝑡𝑒𝑟𝑛𝑎𝑙 (𝑥)) ∧ presented by the pair 𝑂𝑆 = (𝐸𝑡𝑒𝑟𝑛𝑎𝑙, ≤). We stipulate the follow- 𝑃𝑟𝑒ℎ𝑒𝑛𝑠𝑖𝑜𝑛(𝑦)) (7) ing axioms. ∀𝑥(𝑥 ≤ 𝑥) (1) ¬∃𝑥 (𝐴𝑐𝑡𝑢𝑎𝑙(𝑥) ∧ 𝐸𝑡𝑒𝑟𝑛𝑎𝑙(𝑥)) (8) ∀𝑥, 𝑦, 𝑧(𝑥 ≤ 𝑦 ∧ 𝑦 ≤ 𝑧 → 𝑥 ≤ 𝑧) (2) ¬∃𝑥 (𝐴𝑐𝑡𝑢𝑎𝑙(𝑥) ∧ 𝑃𝑟𝑒ℎ𝑒𝑛𝑠𝑖𝑜𝑛(𝑥)) (9) ∀𝑥, 𝑦 (𝑥 ≤ 𝑦 ∧ 𝑦 ≤ 𝑥 → 𝑥 = 𝑦) (3) ¬∃𝑥 (𝐸𝑡𝑒𝑟𝑛𝑎𝑙(𝑥) ∧ 𝑃𝑟𝑒ℎ𝑒𝑛𝑠𝑖𝑜𝑛(𝑥)) (10) For each actual entity 𝑒 there is a unique eternal object, called its According to the type of its datum, we distinguish between physical subjective aim. This aim helps 𝑒 to choose valuable data during its and conceptual prehensions. Both of them have different sources. becoming by providing the abstraction of an ideal outcome. In addi- Physical prehensions emerge from actual sense data and can be seen tion, this aim determines which eternal object 𝑜 is selected as a sub- as raw data, whereas conceptual prehensions are products of an ac- jective form by 𝑒 to give meaning to a datum, i.e. another entity 𝑒’. tual entity’s mental pole which represents mental data. The eventual assignment of 𝑜 to 𝑒’ is called objectification of 𝑒’ and, thus, establishes a subject-object-relationship between 𝑒 and 𝑒’. This ∀𝑥 (𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙(𝑥): ↔ ∃𝑦(𝑑𝑎𝑡𝑢𝑚(𝑦, 𝑥) ∧ 𝐴𝑐𝑡𝑢𝑎𝑙(𝑦))) (11) relation characterizes 𝑒 as subject and 𝑒’ as object. 𝑜 provides a po- tential representation of 𝑒’ in the internal structure of 𝑒, as well as a ∀𝑥 (𝐶𝑜𝑛𝑐𝑒𝑝𝑡𝑢𝑎𝑙(𝑥): ↔ ∃𝑦(𝑑𝑎𝑡𝑢𝑚(𝑦, 𝑥) ∧ 𝐸𝑡𝑒𝑟𝑛𝑎𝑙(𝑦))) (12) valuation of 𝑒’, regarding the subjective aim of 𝑒. Thus, a subjective All other prehensions are called impure, because they integrate men- form is a possible composition of eternal objects, representing an tal and sense data. The question arises how it is possible to ac-quire objectified entity and its value for a specific subject. Since each mental data. According to Whitehead’s ontological principle, every composition of eternal objects is an eternal object, a subjective form datum has to be derived from an actual entity. Thus, there is a con- 𝑓 is a complex eternal object. 𝑓’s role of being a subjective form nection between the ontology structure 𝑂𝑆 and the actual entities. existentially depends on an actual entity 𝑠 playing the role of a sub- The answer is given by the Category of Conceptual Evaluation be- ject, and another entity 𝑒 playing the role of an objectified entity. cause it states that every conceptual prehension is a reproduction of This relation is a basic relation, which is denoted by the evaluation of its corresponding physical prehension. 𝑝𝑟𝑒ℎ𝑒𝑛𝑑(𝑠, 𝑒, 𝑓). ∀𝑥, 𝑦, 𝑧 (𝑃ℎ𝑦𝑠𝑖𝑐𝑎𝑙(𝑦) ∧ 𝑠𝑢𝑏𝑗𝑒𝑐𝑡(𝑥, 𝑦) ∧ 𝑓𝑜𝑟𝑚(𝑧, 𝑦) → 3.2.2 Prehensions ∃𝑢(𝑠𝑢𝑏𝑗𝑒𝑐𝑡(𝑥, 𝑢) ∧ 𝑑𝑎𝑡𝑢𝑚(𝑧, 𝑢))) (13) Informally, a prehension is an act of grasping something either by means of sense or mind. During the process of becoming, an actual Let us consider an observer 𝑜 and a loudspeaker 𝑙 facing him. 𝑙’s entity creates composite entities forming its internal structure. Each emission of a soundwave 𝑠 is an attributive and observable as a phe- of these entities is a reaction to other actual entities and to the eternal nomenal datum by 𝑜. Furthermore, assume a second loudspeaker 𝑙′ objects characterizing this reaction. next to 𝑙 which emits the same sound wave as 𝑙. According to the 4 A Whiteheadian approach to data and knowledge stereo effect, 𝑜 will recognize the emission of a unique sound wave are propositions. Since we have seen that data is the direct sensing 𝑠′ as phenomenal datum. 𝑜 is unable to distinguish between the of another actual entity resp. its conceptual evaluation, propositions soundwaves of 𝑙 and 𝑙’, but, because he faces them directly, he may are what we called impure prehensions. Knowledge arises if mental distinguish these concrete individuals visually, by grasping further and sense data are mixed to create propositions about the contempo- phenomenal data provided by the loudspeakers. Applying the for- rary world of a subject. malism, we define 𝑜, 𝑙 and 𝑙′ as actual entities and 𝑜 has a prehen- Let us reconsider the example of the observer and the two loud- sions 𝑝 and 𝑝′ corresponding to the respective loudspeakers. speakers and take away the light. 𝑜 is able to perceive the sound emission such that the perceivable attributives of 𝑙 and 𝑙’ are the same. The activity of perceiving two concrete individuals as one en- tity yields a special type instantiated by the abstract individual 𝑠’ that exists for 𝑜′ only as shown in Figure 4. In Process and Reality, in- dividuals like 𝑠′ are called nexūs which are similar to relators in GFO. Their purpose is to provide an abstraction from an exhaustive granularity or express missing differentiation between individuals. To formalize this notion, we need an alternative axiomatization of knowledge structures with the following axiom allowing us to define nexūs. An extended signature needs to contain the binary relation ∈ denoting that an actual entity is included in a nexus. Nexūs are used to describe the mereological fusion of a set of actual entities to a complex entity, according to their common prehensions. The com- plex eternal object, which is the common part of the subjective forms of these prehensions, is called the common element of form. Fig. 3 The prehensions of an observer 𝑜 regarding two loudspeakers 𝑙 and 𝑙’ ∀𝑥, 𝑦, 𝑧, 𝑢, 𝑣 (𝐴𝑐𝑡𝑢𝑎𝑙(𝑥) ∧ 𝑠𝑢𝑏𝑗𝑒𝑐𝑡(𝑦, 𝑧) ∧ 𝑑𝑎𝑡𝑢𝑚(𝑥, 𝑧) ∧ emitting the same soundwave. 𝑓𝑜𝑟𝑚(𝑣, 𝑧) ∧ 𝑢 ≤ 𝑣 → ∀𝑟, 𝑠, 𝑡(𝐴𝑐𝑡𝑢𝑎𝑙(𝑟) ∧ 𝑑𝑎𝑡𝑢𝑚(𝑟, 𝑠) ∧ 𝑠𝑢𝑏𝑗𝑒𝑐𝑡(𝑦, 𝑠) ∧ 𝑓𝑜𝑟𝑚(𝑡, 𝑠) ∧ 𝑢 ≤ 𝑡 ↔ ∃𝑚, 𝑛(𝑑𝑎𝑡𝑢𝑚(𝑚, 𝑛) ∧ In Process and Reality this situation would be modelled far more complex, because each soundwave is composed of actual entities, 𝑠𝑢𝑏𝑗𝑒𝑐𝑡(𝑦, 𝑛) ∧ 𝑟 ∈ 𝑚))) (14) and the eternal objects would resemble the laws of physics. How- Nexūs are the logical objects of propositions, and provide an ab- ever, we believe that the following simplification is expressive straction from the atomic view at the expense of accuracy. Proposi- enough for most use cases. Assume the existence of the eternal ob- tions are statements about groups of entities abstracted to a nexūs. jects 𝐿, 𝐿′ and 𝑆 representing the conceptualization of both loud- They consist of two parts, the earlier mentioned logical subject and speakers and the soundwave they are emitting. Figure 3 shows both a logical predicate. This predicate is a subjective evaluation about physical prehensions 𝑜 is perceiving. 𝐿; 𝑆 and 𝐿’; 𝑆 denote the sub- the logical subject and hence a complex eternal object. Some of the jective forms of 𝑙 and 𝑙’. It holds 𝐿 ≤ 𝐿; 𝑆, 𝑆 ≤ 𝐿; 𝑆, 𝐿′ ≤ 𝐿′; 𝑆 and created knowledge is chosen to constitute the internal structure of 𝑆 ≤ 𝐿′; 𝑆. Depending on 𝑂 and the subjective aim of 𝑜 the subjective this entity, since not every conceivable piece of knowledge is correct form of the conceptual evaluation of 𝐿; 𝑆 and 𝐿’; 𝑆 can be determined or consistent with other propositions. In order to reach this distinc- and define the conceptual prehensions of 𝑜. tion, an actual entity distinguishes positive and negative prehen- There are some striking parallels between GFO-Data and Process sions. The datum of a negative prehensions has no relevance for the and Reality. The physical prehension 𝑝 resembles the bundle 𝑏 of subject, while the datum of a positive prehension resp. feeling has all phenomenal data inhered by 𝑙, i.e. a set of object facts, and relevance. thereby each quality 𝑜 is able to perceive from them. 𝑝’s subjective The set of propositions of every actual entity in 𝐾𝑆 is its judge- form 𝐿; 𝑆 is the fusion of all categories instantiated by the elements ment about data in 𝐾𝑆. This implies that the truth of each proposition of 𝑏 as an eternal object. To perceive an individual quality of 𝑙, 𝑜 depends on its prehending subject, i.e. if it is a feeling, i.e. true for has to divide 𝑝 into atomic parts to create more granular prehensions. the actual entity creating it, but this does not imply universal truth. The prehensions 𝑝1 , 𝑝2 , … , 𝑝𝑛 of 𝑥 are inherited by 𝑜 as 𝑝1′ , 𝑝2′ , … , 𝑝𝑛′ To describe this relation, an extended interpretation of the concepts with modified subjective forms. There has to be a prehension 𝑝𝑖 in 𝑙 as theories approach, described in GFO-Data, has to be applied be- that is inherited by 𝑜 that effects its sound emission instantiating the cause this approach makes the same assumption about truth of prop- universal 𝑠𝑜𝑢𝑛𝑑 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛 corresponding to 𝑆. Thus, 𝑝’𝑖 ’s subjec- ositions. We intend to evaluate these Whiteheadian notions of tive form has 𝑆 as a part. Let us extend the inheritance to contain a knowledge, i.e. nexus and proposition, regarding a usage in GFO. historical way from the loudspeaker over the ears and cochlear nerves up to 𝑜’s brain, which is able to prehend sound emissions consciously. An analysis of 𝑝𝑖 and this historical way will enable us to analyze the principles of perception further. We plan to embed this procedural concept into GFO-Data to show how phenomenal data is acquired similar to the process shown in Figure 2. 3.2 Knowledge If we want to capture the notion of knowledge, we have to bear in Fig. 4 An observer 𝑜 with two loudspeakers 𝑙 and 𝑙’ facing him. The emission mind that knowledge is represented in prehensions whose objects of the equivalent soundwaves 𝑠 is perceived as the singular soundwave 𝑠’. 5 Siemoleit et al 4 RELATED WORK fledged ontology of knowledge we will use ideas in (Herre 2013), where a bridge between formal ontology and knowledge organiza- The process-ontological ideas of Whitehead’s Process and Reality tion was established. are well-recognized by many scientists of various disciplines be- yond philosophy. To the best of our knowledge, there are not many applications of it in computer science. Additionally, none of these REFERENCES are similar to the work presented here. Albertazzi, L. (2015). A Science of Qualities. Biological Theory, 10 The work in (Palomäki et al. 2010) copes with the application of (3), pp. 188–199. Whiteheadian philosophy in software engineering. The proposed Anderson, C. (2008). 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Cambridge University Press, Cambridge knowledge. The boundary between data and knowledge can be lo- UK. calized at that place, where facts are transformed into propositions. In our examples these propositions are very simple; they present only small pieces of knowledge. For the development of a full- 6