## 3 Engineering Formal Systems with Ontologies and Algebras
### Ontologies and Ontological Commitments  
Ontologies have been suggested and used as the basis for semantic interoperability of information systems [29]. Following [PERSON]'s characterization of an ontology (in the Artificial Intelligence sense), as an \"engineering artifact, constituted by a specific vocabulary used to describe a certain reality, plus a set of explicit assumptions regarding the intended meaning of the vocabulary words\" [29], assumptions can be stated using any formal theory. We will use an algebraic formal theory as explained below (Section 3.2).  
Any ontological theory has to commit to some basic distinctions. Our ontological commitments are based on the Descriptive Ontology for Linguistic and Cognitive Engineering (DOLCE) [30], in its simplified form of DOLCE Ultra Lite (DUL) [31] and its application to sensors in the skeleton of the Semantic Sensor Network (SSN) Ontology [32]. A comparison of the latter with other sensor ontologies has been provided by [PERSON] and [PERSON] [6]. All extensions that are introduced in this article are aligned with DUL and the SSN Ontology, _i.e._, no additional concept matching is required.  
DUL distinguishes four top-level categories of entities: objects, events, qualities, and information entities. Objects, for example lakes, participate in events, for example rainfalls. The categorization of an entity as object or event depends on the purpose and desired temporal resolution. On closer analysis, many phenomena involve both categories. For example, a water body can be conceptualized as a single static object, neglecting the flow of water, or as a collection of objects (amounts of water, terrain features) participating in water flow events.  
Properties are qualities that can be observed via stimuli by a certain type of sensors. Properties do not exist independently, but depend on other entities, the so-called features of interest. Physical properties belong to physical objects, temporal properties to events. For example, a temperature belongs to an amount of matter and a duration belongs to an event.  
An observation is seen here as invoking first a quale in the observer's mind, or an analog signal in a technical sensor. Our notion of qualia denotes a quality perceived by an observer and is not abstracted from the carrier of the quality. The red of the rose perceived by an observer belongs to that particular rose as well as to the observer; it is not abstracted from either. Thus, observation involves firstly the production of a quale (analog signal) and secondly its symbolization, _i.e._, a sequence of impression and expression.  
Measuring is distinguished here from observing by requiring measurements to have numeric results. [PERSON] considered measurement as \"the assignment of numerals to objects and events according to rule\" [33], but included names in his measurement scales. This required, at least in theory, to turn names into numbers by some rules. Here, the term measurement is restricted to quantification, and the term observation is used for sensing processes with results symbolized in any form, not just numerically. The defining property of both, observation and measurement is to map to well-defined symbol algebras, whether these are numeric or not.  
The result of an observation (as well as of a measurement) process is an information entity, which is commonly referred to as observation as well. It is considered a social object, expressed by abstract symbols. Apart from the value of the observed property, it can contain temporal and location as well as uncertainty information. We use the term _observe_ for the event and the term _Observation_ for its result.