General Formal Ontology (GFO)
Abstract individuals are independent from time and space (they are not in time and space). Examples: the number "2" or pi.
Actions are occurents which are caused by some presential (the agent) at every (inner and outer) time-boundary of the chronoid framing the occurent.
Categories satisfy the following conditions: (1) Categories can be instantiated; (2) Categories can be predicated of other entities. Categories are defined intensional-with-an-s. They are, therefore, closely related to language.
A change in the technical sense refers to a pair of process boundaries. Either at coinciding boundaries (then it comes close to notions like ``punctual'' or ``instantaneous event'' as well as ``moment'' -- in a temporal reading), or at boundaries at the opposite ends of a process of arbitrary extension. The notion of change is relative to contradictory conditions between which a transition takes place. These contradictions refer to some collection of pairwise disjoint universals.
Chronoids are entities sui generis. Every chronoid has exactly two extremal and infinitely many inner time boundaries which are equivalently called time-points.
Concrete individuals have a relation to time or space (they are in time and space).
We consider a collection of presential facts which exist at the same time-boundary. Such collections may be considered themselves as presentials, and we call them configurations. It is further required that configurations contain at least one material object.
Configuroids are, in the simplest case, integrated wholes made up of material structure processes and property processes.
For the purpose of formalizing continuous changes, a minimal chronoid universal D(c) is employed in order to capture the idea of observable differences during certain chronoids, whereas the change itself does not allow the observation of a difference. The predicate change(e1,e2, u1, u2, u, D(c)) is intended to formalize this approach. Continous changes occur over time (a chronoid).
Processes where all non-coinciding internal boundaries are intrinsic changes. These turn out as purely continuous processes, described e.g. in physics by differential equations.
Discrete processes are made up of alterations of extrinsic changes and states.
Everything which exists is called an entity.
Deprecated. Extrinsic changes are represented by change(e1,e2, u1, u2, u), where e1 and e2 are a pair of coincident process boundaries, and u1 and u2 are disjoint sub-universals of u.
A function F is a universal (conceptual structure) defined in purely teleological terms with respect to a given goal G which commonly is ascribed by means of has-function relation to entities that are the realizations of the function F, execute such a realization or are intended to do it.
Histories consist of a number of process boundaries. We assume that any history can be embedded into a process, which then forms a foundation of the history. If it were not for this foundation, one would face the problem of singling out the right boundaries in order to get a natural history: It is not sensible to measure the temperature of a patient first, then determine his weight, followed by measuring his blood pressure and to consider these strangely arbitrary process boundaries as a history of the patient's body data.
Individuals are entities which cannot be further instantiated.
Instantanuous changes are represented by change(e1,e2, u1, u2, u), where e1 and e2 are a pair of coincident process boundaries, and u1 and u2 are disjoint sub-universals of u. Instantanuous changes are therefore changes of properties on two coinciding time boundaries.
Deprecated. For the purpose of formalizing intrinsic changes, a minimal chronoid universal D(c) is employed in order to capture the idea of observable differences during certain chronoids, whereas the change itself does not allow the observation of a difference. The predicate change(e1,e2, u1, u2, u, D(c)) is intended to formalize this approach.
An item is everything which is not a set. Also called ur-element.
An ontological level, which is sth. more restricted and "part of" some gfo:Stratum.
A material structure is an individual which satisfies the following conditions: it is a presential, it occupies space, it is a bearer of qualities, but other entities cannot have it as quality, and it consists of an amount of substrate, and it instantiates a persistant ("has identity").
Material persistants are particular universals whose instances are material structures; they are related to those entities which are called sometimes continuants or objects, as apples, cars or houses. Material persistants capture the phenomenon of persistance through time of a material object. A material persistant P satisfies a number of neccessary conditions. For every material persistant P there exists a process P such that the set of instances of P coincides with the set of process-boundaries of P. This implies the existence of a chronoid c such that for every time-point t of c there exists exactly one instance of P at time point t.
According to (Poli,2001), the basic structure of the material stratum is a distinction of physical, chemical and biological levels. These levels can be further refined.
In accordance with the work of R. Poli, we divide the psychological/mental stratum into the layer of awareness and the layer of personality. Awareness comprises most of what is studied by cognitive science (perception, memory, reasoning, etc). Personality on the other hand concerns the phenomenon of will and the way in which someone reacts to her experiences.
Occurents have temporal parts and thus cannot be present at a time-boundary. Time belongs to them, because they happen in time and the time of the occurent is built into it. The relation between an occurent and a chronoid is determined by the projection relation. Occurents are also called generalized processes in the GFO.
Ontological_layer, all of its subconcepts and the properties layer_of and on_layer are work in progress in a premature beta state.
a collective term for gfo:stratum and gfo:level
Beta
Persistants are GFO's way to capture identity over time. GFO pursues an approach which accounts for persistence by means of a suitable universal whose instances are presentials. Such universals are called persistants. These do not change and they can be used to explain how presentials which have different properties at different times can nevertheless be the same.
A presential exists wholly at exactly one time boundary.
Processes are a special kind of occurent. Processes are directly in time, they have characteristics which cannot be captured by a collection of time boundaries.
Processual roles are dependent processes. They are roles with a process as context.
The concept of a property value reflects a relationship between the property of x and the same property as exhibited by another entity y.
Set is a category pertaining to the individuals in the ZFC set theory.
A situation is a special configuration which can be comprehended as a whole and satisfies certain conditions of unity, which are imposed by relations and categories associated with the situation. Herein, we consider situations to be the most complex kind of presentials.
Situoids are processes whose boundaries are situations and which satisfy certain principles of coherence, comprehensibility, and continuity. They are regarded as the most complex integrated wholes of the world. A situoid is, intuitively, a part of the world which is a coherent and comprehensible whole and does not need other entities in order to exist. Every situoid has a temporal extent and is framed by a topoid.
On the one hand, the social stratum is divided into Agents and Institutions. Agents are the bearers of the social roles that humans play. Institutions are defined as systems of interrelated social components. On the other hand, a social system can be seen as a network in which businesses, politics, art, language (and many other facets) both present their own features and influence each other.
Boundaries of regions are surfaces, boundaries of surfaces are lines, and boundaries of lines are points. As in the case of time-boundaries, spatial boundaries have no independent existence, i.e. they depend on the spatial entity of which they are boundaries.
Space regions are mereological sums of topoids.
A process without an instantanuous change at any of its inner time boundaries is called a state.
According to (Poli, 2001, 2002) (based on the philosopher Hartmann) we distinguish at least three ontological strata of the world: the material stratum, the mental/psychological stratum, and the social stratum stratum. Every entity of the world participates in certain strata and levels. We take the position that the layers are characterized by integrated systems of categories. Hence, a layer can be understood as a meta-category whose instances are categories of certain kinds. Among these levels specific forms of categorial and existential dependencies hold. For example, a mental entity requires an animate material object as its existential bearer.
Time Regions are defined as the mereological sum of chronoids, i.e. time regions may consist of non-connected intervals of time.
The time model of GFO is based on Brentano and the glass continuum of Allen&Hayes.
Time boundaries depend on a chronoids (i.e. they have no independent existence) and can coincide.
Topoids are connected compact regions of space. They have spatial boundaries.
Universals are immanent universals. They exist in re.
Property values usually appear in groups which are called value structures, value spaces or measurement systems. Each of these structures corresponds to some property. More intuitively, one could say that the property may be measured with respect to some measurement system. For instance, sizes may be measured with the values ``small'' ``big'' or ``very big'', which are the elements of one value structure. The notion of a value structure of a property is similar to a quality dimension in (Gardenfors, 2000). Further, value structures are related to quality spaces in DOLCE (Masolo, 2003}. A quality space consists of all ``quales'' (our property values) of some ``quality'' (our property). Often it seems to be the case that a notion of distance can be defined, and that certain layers of value structures are isomorphic to some subset of real numbers, which allows for a mapping of values to pairs of a real number and a unit, as in the case of ``10 kg''.
The abstract part-of relation is denoted by p(x,y); the argument-types of this relation are not specified, i.e. we allow arbitrary entities to be arguments. We assume that p(x,y) satisfies the condition of a partial ordering, .i.e. the following axioms: reflexivity, antisymmetry and transitivity.
This relation captures the notion of existential dependence.
"goal" here refers to "final state" in (Burek, 2006).
The instantiation relation holds between a category and an item. It is not a relation between categories and individuals due to higher order categories such as "species".
"requirement" here refers to "initial state" in (Burek, 2006).