How to Structure an Ontology Andrew U. Frank Geoinformation TU Vienna frank@geoinfo.tuwien.ac.at Overheads at: http://www.geoinfo.tuwien.ac.at/presentations/frank.htm Andrew Frank 11/23/2018

Overview My approach Separate ontology in tiers Formal ontology as a theory Construction of ontology Andrew Frank 11/23/2018

My approach Temporal ontology: individuals and processes! Practical consistency is important: Level of detail must correspond in different parts. Error and uncertainty in description is important (not discussed today) Andrew Frank 11/23/2018

Why a multi-tier ontology? Most efforts to structure ontologies strive for maximum generality. Ontology with capital O (singular only!). Philosophers propose a single set of rules applicable to everything. e.g. Aristotle's categories, mereology Our experience shows that no single proposed ontology covers all areas important in a GIS. Andrew Frank 11/23/2018

Multiple tiers to integrate different approaches Tiers are similar to the top level classes in DOLCE, But: Each tier follows its own logic. The connections between tiers is formalized. Andrew Frank 11/23/2018

Overview of the tiers 0. The physical environment Observations of the environment and activities The reality of objects a. Objects and actions b. Generalizations: classes and operations 3. Social reality Legal reality Subjective Reality Communication 1 .. 3 are rather epistemologies, projected ontologies or e-ontologies. Andrew Frank 11/23/2018

Tier 0: Physical environment Only part which is truly an Ontology, the world as it is, without the presence of cognitive agents. There is little we know about this! Andrew Frank 11/23/2018

Assume a field construction of world Physical properties for every point in space and time: f (x,y,z,t) = a Not all functions are continuous, but space and time is assumed continuous. Physical laws (laws of nature) can be expressed as partial differential equations in properties of points. Many properties are determined; not all of these are observable (or known) to us! Andrew Frank 11/23/2018

Tier 1: Observation of physical environment by agents Observations for every point in space yield a quantitative value. obs (x,y,z, obs-type) = value Differentiation between environment and observing agent, properties of the environment and observation Connections to tier 0: observation functions and activities of agents Andrew Frank 11/23/2018

Tier 1: Activities change the environment Agents can act on the environment and effect change in it. The change in the environment can be observed. Andrew Frank 11/23/2018

Feedback loops ground semantics: There are two linked feedback loop (morphism) Physical activity – observed change Body feeling of activity – sensory activity Andrew Frank 11/23/2018

Observations types: Point observations – values for material properties, local motion, forces, temperature etc. Andrew Frank 11/23/2018

A Landscape Andrew Frank 11/23/2018

What was shown? 3 types of observations: wave energy in 3 frequency bands for each observation type, 2.1 million observations in a regular grid (central perspective from a point) Neither my sensor, nor the representation contains any hint of mountains, trees, buildings etc. Did you see any? Andrew Frank 11/23/2018

Tier 2: The Reality of Objects People have a strong tendency to form objects which maintain identity in time. Objects are formed to maintain invariant properties in time. Object formation reduces bulk of representation and leads to economic reasoning: From many point observations we deduce a single object with properties related to the point observations. Andrew Frank 11/23/2018

Andrew Frank 11/23/2018

Connection to tier 1: Objects form areas of uniform observation values Areas of uniform value for an observation are merged to objects. Uniformity in values of observation can be in same color same speed or direction of movement same material Objects are constructed to have identity and continue in time. This reduces the load on memory enormously. Andrew Frank 11/23/2018

Lifestyles of Objects Object continue in time. Objects are created and destroyed. Living things are born and die. Some objects can have their existence suspended. Damir Medak (TU Wien) and Kathleen Hornsby (U Maine) Andrew Frank 11/23/2018

A Table Top Andrew Frank 11/23/2018

Granularity The observations where made with a certain resolution. Objects are formed from observations – sometimes the resolution is reduced, because less granularity is sufficient for the task at hand. Examples: Noodle dish is resolved into single noodles only when you are eating it. And what to do with the sauce? Andrew Frank 11/23/2018

Object formation (2) Philosophers talk a lot about natural kinds living objects, animals or plants. These are easy, but there are other cases – very natural as well: Andrew Frank 11/23/2018

Andrew Frank 11/23/2018

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Andrew Frank 11/23/2018

Objects as uniform areas Objects form partition of space (and time). Multiple ways of subdividing space: Different observations or combinations of observations Different spatial, temporal or observation granularity. Typically problems result from objects formed from different observations. Andrew Frank 11/23/2018

Connections from tier 2 to tier 1: The actions change properties in some spatial-temporal region. The property values of objects are the integration of the observable property values for spatial regions. Andrew Frank 11/23/2018

Tier 3a: Subjective Reality- Individual cognitive agents Individual internal reality Feelings are subjectively real The beliefs agents from about the world resulting from observations vary, even if two agents observe the same reality. Andrew Frank 11/23/2018

Reflection We observe the actions of other and assume similar causes (invisible feelings). Socialization is a process at a hierarchically slower pace than observation-action. Connection to fixed point semantics of denotational semantics. Andrew Frank 11/23/2018

Tier 3b: Social reality Much what we consider part of reality is only a social convention. Most important are the conventions in language: (applies to natural language or expert slang) Names of things Objects are named, individual names like ‘Stella’, ‘John’, etc. or classes, like ‘plate’, ‘fork’ , dog Andrew Frank 11/23/2018

Institutional objects Abstract objects are formed, to facilitate social interactions: Money, Parcels.. John Searle: An object X counts as Y in the context of C. Andrew Frank 11/23/2018

Example: Money This is ‘legal tender’, but physically only printed paper. Social convention: can be used to buy things. Rules for physical objects apply to the paper, other rules apply to the ‘legal tender’ For example: temporal extend of physical object and ‘legal tender’ is not the same. Andrew Frank 11/23/2018

An Example: Communication with Maps: A map-making agent explores an environment, Draws a map, Map using agent uses map to navigate. Andrew Frank 11/23/2018

Connection between tier 3a and 3b: Social processes externalize in symbolic form the individual socialization: Cultural Reality Andrew Frank 11/23/2018

Grounding and practical consistency in Taxonomies Most ontologies are hierarchies of classes with an is_a relation between them and not much else. Existing taxonomies are lists of words for which an is_a relation is assumed; for their understanding they rely on the readers pre-existing understanding of the natural language terms Andrew Frank 11/23/2018

Polysemy Words do not have fixed meaning. Meaning varies with context. In this context, you would use the words car and bicycle Andrew Frank 11/23/2018

A different meaning of bicycle (ordinary) bicycle vs. tandem Andrew Frank 11/23/2018

And this? A motor tricycle and a water tricycle: to differentiate from the land bicycle before. Observation: Words often mean a class and the (ordinary) subclass of it. Andrew Frank 11/23/2018

Two classification trees possible: Just different order of applying distinctions! Andrew Frank 11/23/2018

Distinctions between classes: Classes must be in some respect different from other classes. The two taxonomies are constructed with the same distinctions: Land – Water Motorized – Human-powered Bi-, tri- or four wheeled Andrew Frank 11/23/2018

Order of distinguishing matters The two taxonomies are different only in the order in which the distinctions between properties are applied. Which one should one prefer? It does matter: Intermediate class definitions do not correspond and cannot be translated. Andrew Frank 11/23/2018

Lattice structures avoid this choice Distinctions are applied in any order, Not a hierarchy! Andrew Frank 11/23/2018

Integration of taxonomies possible The integration of taxonomies to produce a lattice is easy with a 4 valued logic: Andrew Frank 11/23/2018

Grounding in distinctions Only the descriptions of the distinctions must be explained. The classes follow automatically. Only few distinctions are necessary for large taxonomies! Andrew Frank 11/23/2018

Difference from mainstream ontologies Founded in observable properties not in the assumption of preexisting (ideal) classes. Individuals are ‘areas of uniform properties’ and have observable attributes. Classes are constructed as sets of individuals with same properties. Classes constructed form a lattice (not a hierarchy). Andrew Frank 11/23/2018

Formal Formal Ontologies I want to consider a mathematical theory with a small set of the relations and operations in an ontology: is_a, subclass_of, … Avoid debatable, philosophical assumptions and ontological commitments. Andrew Frank 11/23/2018

Andrew Frank 11/23/2018