Konrad Eckes

In addition to the commonly known stable legal relationships between persons or institutions and fragments of the Earth's surface (real estate), there are widely applied ad hoc relationships to real space, with significantly varying durations. They are a function of acquired rights and remain valid for a strictly defined period of time. They are common in everyday life and take on diverse forms, the basic attribute of which is a reference to a broadly understood fragment of geographical space. Emerging technological achievements, such as digitisation of payments, algorithmisation of procedures, identification of documents and people, autonomous traffic and artificial intelligence - pose a challenge to provide ad hoc relationships to space with formalised notation. The problem of formal notation of legal rules applicable in local space will be presented on the example of the right of entry to the university campus, together with local traffic and parking rules. The space is divided into zones and then into smaller units – parking spaces, according to the hierarchical structure. Social groups that have relationships with these zones are also formed into hierarchical sets. Individual groups have different rights to space – hierarchically – at the zone level. The established hierarchy is the first factor considered. The second factor is variability over time. Relationships to local space change over time, most often in a cyclical form. It can therefore be concluded that in this case the law is a function of time. Parking spaces, as objects in spatial sets, are occupied randomly and subsequent users must start the procedure of searching the remaining objects belonging to the set. This procedure has been written in the form of a flowchart and graph. Objects removed from the set (as they are occupied) may randomly return, so for the purposes of effective searching, this process is presented as repeatable – as a whole or locally (cascading search). The third aspect considered are differences in the way users move around the local road network and in elementary spatial fields. The network structure is represented by intersections, which are noted as node matrices. In order to define how to behave in the local space, a list of rules was prepared and standardised. From a practical point of view, a form of prohibition is advantageous because it can be logically linked to a list (set) of consequences. Following these assumptions, the general form of the behavioural test algorithm was formulated. The presented issues demonstrate complex relationships to space and its integrating rule in relation to legal rules. This approach to law allows for space management using IT methods. The notation of the spatial structure and of legal relationships related to time enable the definition of rules of conduct for diverse groups of local societies. Dissimilarity from equality of law for all and stability over time, occurs in local environments and raises the relationships between community, space and time to a higher level of generality.

In daily life there are many relationships between human being and the local space. A typical feature of the state register (cadastre) is stability in time. But in other relationships to the local space – the role of time can be crucial.
In this paper the task of defining the relationships to the space in a formal way was undertaken. The method of making the conditions (facts) for the selected examples of relations was applied, and then the procedures (algorithms) were carried out, building the relationships to the local space, making it active for an individual or a group.
As examples, at first the relationships to 2D objects was presented, regarding the addressed fragment of the local space and the defined time when the relationship is active. Then the hierarchic structure of the space was taken into account by dividing it into smaller final units using a developed address recorded in the set of base conditions.
A reverse case was discussed – hierarchic increase of the area in subsequent steps of the procedure of defining the relationships between the activity and space. In this case the access to the subsequent larger and larger areas is the function of the eligibilities of individuals or social groups to the subsequent stage of extending the area up to its final maximal form. Such relationships take place in industrial companies, where the gradation of eligibilities is a form of protecting the production details.
Another relationship to the space is the relationship of the individual or group to linear objects, for example to the network of roads and marked trails. The example of the relationship to the network of trails and the complex case of the relationship, regarding additional conditions were presented.
The next section developing direct relationships to multistep relationships is discussed. It extends the feature only for the sequence of pedestrian movements combined with the traffic. In this case two relationships occur: the relationship to a spatial object and relationship to a linear object (the route of the vehicle).
In almost all the cases the time factor plays an important role in the relation to space, which is defined as one of the conditions in the set of base facts.
The contemporary time is the era of digitalisation of data and processes. The space we live, is a unique good. This good should be managed in a sustainable way Hence the need to explore, analyse and formalise various relationships to the space.