In the present paper we make s o m e c o n tributions to the theory of upper level ontologies. Every domain-speci c ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. It turns out that the top-level ontology of the well-known standard modelling languages KIF (Knowledge Interchange Format), F-logic (Frame-Logic), and CyCL, is based on set-theoretical construction principles, so that the latter are essentially limited by the extensionalism of set theory. In the current paper we outline a new approach to upper-level ontologies which is based on recent results in formal ontology. W e formulate some criteria which a n y upper-level ontology should satisfy although we shall not give a de nite de nition. Every such o n tology should include the three ontological categories of sets, universals, individuals and a system R of formal relations. R contains, among others, membership, part-whole and inherence. The individuals are divided in substantoids, moments and situoids. We review a modelling language GOL (General Ontological Language) whose top-level ontology satis es these criteria. Finally, w e compare our toplevel ontology to others, in particular to KIF, and to the ontologies of Russell-Norvig, J.Sowa, and to the standardization project SUO.
The current paper is devoted to an analysis of upper level categories. Upper level ontologies are concerned with theories of such highly general (domainindependent) categories as: time, space, inherence, instantiation, identity, processes, events, attributes, etc. The development of a widely accepted and wellestablished upper level ontology is an important and ambitious task, important because it determines a framework for the construction of domain-speci c and generic ontologies, ambitious because it is concerned with highly debated philosophical problems. An upper level ontology could be considered as an integral part of a knowledge modelling and representation language. In our approach w e assume the point of view of realism, i.e. the position that the kind of things we are speaking about have objective existence hence, ontological research should address reality itself. Thus, ontological research is not limited to building up conceptual schemes. We believe that the real world itself plays an important role to achieve a uni ed and consistent top-level ontology. W e use the term category to denote collections of entities. We classify the collection of all entities into the categories sets, individuals, universals, and formal relations. In section 2 we study the categories of sets, individuals, and universals. Section 3 is devoted to formal relations. The categories of section 2 and section 3 present the highest level of generality. In section 4 the category of individuals is further classi ed and some formal relations are considered in more detail. In section 4.2 conditions are formulated that -in our opinion-should be satis ed by every upper level ontology, and in section 4.3 a formal modelling language GOL is reviewed whose ontological basis satis es the criteria of an upper level ontology. G O L i s an ongoing research project at the University o f Leipzig, 10]. In section 5 we compare our ontology to other upper-level ontologies.
In our approach the entities of the real world can be partitioned in sets and urelements. Urelements are entities which are not sets, and urelements are classi ed into individuals and universals. Individuals are thought of as a realm of concretely existing things in the world (not sets), within the con nes of space and time. An individual is a single thing located in some single region of spacetime. A universal is an entity that can be instantiated by a n umber of di erent individuals which are similar in some respect. Universals are patterns of features which are not related to time and space. We assume that universals exist in the individuals which instantiate them (thus they exist in re) thus, our attitude is broadly Aristotelian in spirit. Individuals are correlated with universals via the formal relation of instantiation. W e w r i t e a :: u to denote that the individual a is an instance of the universal u. In the philosophical tradition there are several conceptions of universals and individuals, respectively, 13].For example, universals have been conceived as sets of individuals and individuals have been conceived as sets of universals. If one adopts both conceptions, then individuals are sets of sets of individuals and universals are sets of sets of universals. And so on. We conclude that not both conceptions are admissible. Which o f t h e t wo conceptions has to be given up? We think that both have t o b e g i v en up. A detailed justi cation of this view is long and will be expounded in the full version of the paper.
We assume that sets are neither in Space nor in Time. Hence, sets are not individuals. A universal is determined by its intention which captures among others a certain granularity and a certain view of its instances. We assume the basic axiom that sets, individuals and universals are pairwise disjoint categories.
According to the present standard doctrine, every n-ary relation is a set (or class) of ordered n-tuples. This conception is applied indiscriminately to both so-called empirical and mathematical relations. Thus, when John is kissing Mary, the ordered pair hJohn, Maryi is an element of a certain set A of ordered pairs that is denoted by "kissing". Also, that 2 < 5 is analysed by 6 2 5i 2 B where B is the set f 6 x yi : x < y g of ordered pairs. This uniform analysis harmonizes with conceiving of both sent e n c e s a s h a ving the same syntactic form, namely R(a b).
The usual semantics of rst-order logic, i. e. the semantics with respect to which G odel's completeness theorem is proved, interprets any s e n tence R(a 1 : : : a n ) as stating that ha 1 : : : a n i 2 R.
Admittedly, the sentences "John is kissing Mary" and "2 < 5" have sucient super cial similarity t o w arrant the same syntactic and semantic analysis. However, these sentences have radically di erent linguistic environments. For instance, "John is kissing Mary" can be extended to "John is kissing Mary twice", but "2 < 5" cannot be extended to "2 < 5 twice". Furthermore, the sentence "John is kissing Mary" is implied by "John is kissing Mary twice". We have therefore to use a logical form that will support this implication. While for 2 and 5 to be related as 2 < 5 no further entities are required to exist, there have to exist entities beyond John and Mary if "John is kissing Mary (twice)" is to be true, namely at least one (at least two) kiss(es). A plausible formulation is the following: 1. 9x(x i s a kiss ^does(J x ) ^su ers(M y)) 2. 9x y(x i s a kiss^x i s a kiss^:x = y^does(J x )^it does(J y )^su ers(M x)ŝ u ers(M y)) Obviously 2. implies 1. in rst-order predicate logic. These considerations lead to the distinction between formal and material relations. A relation is formal if it holds as soon as its relata are given. Formal relations are called equivalently immediate relations since they hold of their relata without mediating additional individuals. The smaller-than relation < for numbers, the instantiation relation, and membership are formal relations. Also the relations denoted by "does" and "su ers" in (1) and (2) are formal. In contradistinction to this, the kissing relation does not hold as soon as its relata exist a kiss (understood as an individual event) must happen in addition to its relata. Therefore, we call the kissing relation a material relation. Formal relations may be classi ed with respect to the main categories: sets, universals and indviduals. Membership is a formal relation between sets and between urelements and sets, and instantiation is a formal relation between individuals and universals. Universals and sets are connected by the formal relation of extension. Examples of formal relations between individuals are inherence, occupation, framing, containment which will be explained in section 4.1.
In this section further categories of individuals are introduced, and some formal relations are considered in more detail. We call all these categories as ontologically basic because they are the most fundamental.
The individuals are further subcategorized into moments, substantoid, chronoids, topoids and situoids1 -terms which will be explained in more detail in what follows. This yields (at least) the following ontologically basic predicates (also called basic types): Mom(x), Subst(x), Sit(x), Chron(x), Top(x). Chronoids can be understood as temporal durations, and topoids as spatial regions with a certain mereotopological structure. A substance is that which bears individual properties or is connected to other substances by relational moments. Every substance possesses matter. The ultimate (or prime) matter of a substance has no moments or qualities. This implies that an ultimate matter cannot appear since every appearance has to take place via individual moments inhering in the appearing matter. We use the term substantoid to cover the whole range between prime matter and those pieces of matter (called substances in the proper sense) which possesses moments including forms, motions and qualities. An alignment ha 1 : : : a n i is a sequence of substantiods a 1 : : : a n , t h e a i 's are called components. An alignment is an individual in contradistinction to a list which is a set.
The origin of the notion of moment lies in the theory of \individual accidents" developed by Aristotle in his Metaphysics and Categories 1]. An accident i s a n individualized property, e v ent or process which is not a part of the essence of a thing. We use the term \moment" in a more general sense and do not distinguish between essential and inessential moments. Moments include individual qualities, actions and passions, a blush, a handshake, thoughts and so on moments thus comprehend what are sometimes referred to as \events". The loss of a moment in this more general sense may c hange the essence of a thing. Moments have i n common that they are all dependent on substantoids. Relational moments are dependent on a plurality of substantoids.
A situoid is a part of the world that can be comprehended as a whole and which takes into account the courses and histories of the ontological entities occurring in it. Situations are special types of situoids: they are situoids at a time, so that they present a snap-shot view of parts of the world. Situations can be de ned as projections of situoids onto atomic (or very small) time intervals or equivalently as situoids with an atomic (or very small) framing chronoid. An elementary situation is composed of individual substances and the relational moments which glue them together. Situations are constituted by using further ontologically basic relations such as causality and intentionality. Analogously, w e distinguish elementary situoids from situoids. We assume that every situoid is framed by a c hronoid and by a t o p o i d . F or every situoid s there is a nite number of universals which are associated with s. ass(s u) has the meaning: s is a situoid and u is a universal associated with s. There is a basic predicate S i t e l (x) for elementary situoid, and a predicate S i t (x) for situoids in general. Our approach to situations di ers essentially from that of Barwise 2], 3]. Barwise did not elaborate an ontology of relations thus in particular, the relation of inherence is missing from his theory.
What are the ontologically basic relations needed to glue together the entities mentioned above? Basic relations are membership denoted by 2, and part-of relations, denoted by <, (re exive part-of). Other basic relations are denoted by s y m bols starting with a colon. In the current paper we additionally consider the basic relation of inherence, denoted by : , the relativized ternary part-of relation, symbolized by : , the instantiation relation, denoted by ::, the framing relation, designated by : <, the containment relation, denoted by : , and the foundation relation, denoted by : ?.
The phrase \inherence in a subject" can be understood as the translation of the Latin expression in subjecto esse, in contradistinction to de subjecto dici, which m a y be translated as \ predicated of a subject". The inherence relation : -sometimes called ontic predication -glues moments to the substances, which are their bearers, for example it glues your smile to your face, or the charge in this conductor to the conductor itself. The part-of relations < should have i n every case an individual as its second argument, i.e. if a < b a b, t h e n b is an individual. The ternary part-whole relation : (x y z) has the meaning: \z is a universal and x qua instance of z is a part of y". Obviously, : (x y z) implies x y, but not conversely. These universal-dependent part-whole relations are important in applications. The symbol :: denotes the instantiation relation, its rst argument is an individual, and its second a universal. The instances of a universal u are \individualizations" of the time-and space-independent pattern of features captured by u. The containment relation : captures the constituents of a situoid. x: y means \x is a constituent of the situoid y". Among the constituents of a situoid s belong the occurring substantoids and the moments inhering in them, but also the universals associated to s.
The binary relation : < glues chronoids or topoids to situations. We presume that every situation is framed by a c hronoid and a topoid, and that every chronoid or topoid frames a situation. The relation x: < y is to be read \the chronoid (topoid) x frames the situation y". The de ned binary relation :?(x y) expresses the foundation relation between a substance and a moment. :?(x y) has the meaning that x is the foundation of y or x founds the moment y, a s f o r example your hair founds the moment o f y our being hairy, and the moment o f being hairy inheres in your person. The de ned binary relation :occ(x y) describes a relation between substances and topoids having the meaning: the substantoid x occupies the topoid y.
We f o r m ulate certain neccessary criteria which an upper level ontology -in our opinion-should satisfy.
Upper-Level Ontology. E v ery upper level ontology includes at least the three ontological categories: sets, individuals and universals and a system R of rela-tions and predicates containing the basic relations and basic types described in section 4.1. 2We consider the described system of basic categories as a constituent core ontology because individuals are composed of substances and moments or are contained in situoids. This system has to be extended by further basic relations for treating space, time, and shapes. One possibility i s t o i n troduce the relation x i s b oundary of y, and the coincidence r elation 17].
The core ontology should be extended by unity conditions and comprehension principles. Unity conditions are universals capturing kinds of wholes. An example of a unity condition is the universal substantoid having a boundary. Comprehension principles allow to construct new universals from given universals. One method to de ne comprehension principles is to introduce a language L whose expressions can be used to formally specify universals. Then, certain expressions can be understood as formal representations of universals. A L-comprehension principle determines which o f t h e L-expressions represent (specify) universals.
Using the core ontology (extended by some mereotopological notions) one may i n troduce following categories: substrate , process, event, state, and continuant. Here, substrate is a universal, and processes, events and states are parts of situoids. A continuant can be understood as a substantoid with boundary.
In this section we expound the partially axiomatized ontology underlying the modelling language GOL (General Ontological Language). GOL is an ongoing research project at the university o f Leipzig 6] which is carried out in collaboration with ontologists at the University of Bu alo 15]. GOL includes the categories which are considered in section 4.1. The modelling language GOL is formalized in a rst-order language. We presume a basic ontological vocabulary, denoted by Bas, c o n taining the following groups of symbols:
Symbols for binary and ternary basic relations.
: ass(x y) ( y ass. to y) : (is contained in) : occ(x y) ( x occupies y) ext(x y) (is extension) 5 Comparison to other Upper-level Ontologies 5.1 Knowledge Interchange Format.
Knowledge Interchange Format (KIF) is a formal language for the interchange of knowledge among computer programs, written by di erent programmers, at di erent times, in di erent languages. KIF can be considered as a lower-level knowledge modelling language.
The ontological basis of KIF can be extracted from 9] we summarize the main points. The most general ontological entity in KIF is an object. The notion of an object, used in KIF, is quite broad: objects can be concrete (e.g. a speci c carbon, Nietzsche, the moon) or abstract (the concepts of justice, the number two) objects can be primitive or composite, and even ctional (e.g. a unicorn). There is no ontological classi cation of the basic entitities. In KIF, a fundamental distinction is drawn between individuals and sets. A set is a collection of objects an individual is any object that is not a set. KIF adopts a version of the Neumann-Bernays-G odel set theory, GOL assumes ZF set theory. The functions and relations in KIF are introduced as sets of nite lists here the term \set" corresponds to the term "class". Obviously, the relations and functions in KIF correspond in GOL to the extensional relations. KIF does not provide ontologically basic relations like our inherence, part-whole and the like. Hence, the ontological basis of KIF is much weaker than that of GOL. GOL can be considered as a proper extension of KIF KIF can be understood as the extensional part of GOL.
The most general categories of this ontology are Abstract Objects and Events 14]. Abstract objects are divided into Sets, Numbers, Representational Objects events are classi ed into Intervals , Places, Physical Objects, and Processes. This ontology does not satisfy the criteria of section 4 because there is no clear distinction between sets, universals, and individuals. Also, there is no category of formal relations. The class of universals (here called \categories") is a subclass of sets. This pure extensional view of universals seems to be not correct. Furthermore, numbers are considered as di erent from sets. But, it seems to be plausible to introduce numbers as special sets, as in GOL. Obviously, classical mathematics can be reduced to set theory. The instantiation relation is identied with membership. Besides this the ontology provides the part-of-relation. The categories of events may b e reconstructed within the category of situoids in GOL. An event in the Russell-Norvig ontology is a \chunk" of a particular universe with both temporal and spatial extent. An interval is an event that includes as subevents all events occurring in a given time period. Such i n tervals can be, in a sense, understood as situoids. But the di erence is, that situoids are parts of the real world that can be comprehended as a whole. This implies that to situoids are associated certain universals capturing the granularity a n d the view of this part of the world.
Sowa's ontology 19] does not satisfy the conditions of section 4.2. There is no clear distinction between sets, universals and individuals. A main distinction is made between classes and entities. Since these notions are interpreted in KIF they can be understood within GOL as sets and urelements. There are the following two-place primitive relations: has, instance-of, sub-class of, temp-part, spatial-part. The instance-of relation is interpreted by the membership-relation, and the ontological status of the has-relation is unclear. Since these notions are interpreted in KIF they are considered as set-theoretical notions. We want to emphasize that formal relations of the real world are not relations in the sense of set-theory. S o wa's ontology uses further two epistemic non-KIF operators: nec and poss but the ontological character of these modal operators is not clear.
In our opinion, modal operators should be eliminated from ontology. I n S o wa's ontology several classes are introduced, as for example relative, mediating, physical, abstract, continuant, ocurrent. These notions may be rede ned within GOL giving them a clear ontological status.
In the papers 12] and 8] some principles for a top-level ontology are outlined.
The rudimentary top-level ontology, implicitly given in these papers, partially satis es our criteria of 4.2. Formal relations are considered in 8] as relations involving entities in all \material spheres" these have a di erent meaning from formal relations in our sense which w e understand as being \immediate". Then certain formal relations are discussed: intantiation and membership, parthood, connection, location and extension, and dependence. The considered formal properties include concreteness, abstractness, extensionality, u n i t y, plurality, dependence and independence. Intantiation, membership, and parthood are basic relations in our sense the inherence relation is missing. The extension relation E(x y) = x is the extension of y can be modelled by our relation occ(x,y) (the entity x occupies the topoid y). The connections relation from 8] can be de ned in GOL by using the coincidence relation and the notion of boundary.
SUO is a project recently intiated by the Institute of Electrical and Electronic Engineers to develop a \Standard Upper level Ontology" based on KIF 18]. This is designed to provide de nitions for between 1000 and 2000 general purpose terms in such a w ay as to yield a common structure for low-level domain ontologies of much larger size and more speci c scope. The ontologies were rst divided into two classes, those de ning very high-level concepts and those de ning lower-level notions. The highest level contains J. Sowa's upper-level ontology and Russell-Norvig's upper-level ontology, and the second level contains a number of further concepts. From this and the above considerations of sections 5.2 and 5.3 follows that the SUO-ontology does not satisfy our criteria for an upperlevel ontology.
The development of an axiomatized and well-established upper-level ontology is an important step towards a foundation for the science of Formal Ontology in Information Systems. Every domain-speci c ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. For this purpose it is important to understand what an upper-level category means, and we proposed some conditions that every upperlevel ontology should satisfy. The development of a well-founded upper-level ontology is a di cult task that requires a cooperative e ort to make signi cant progress.
Furthermore, we use the following symbols:Sub (for the universal \substance"), Time (for the universal \time"), Space (for the universal \space"). To the basic vocabulary we may add further symbols used for domain speci c areas the domain speci c vocabulary is called an ontological signature, denoted by . A n ontological signature is determined by a set S of symbols used to denote sets (in particular extensional relations), by a set U of symbols used to denote universals, and by a set K of symbols used to denote individuals. An ontological signature is summarized by a tuple = ( S ,U K).
The syntax of the language GOL( ) is de ned by the set of all expressions containing the atomic formulas and closed with respect to the application of the logical functors _ ^ ! : $, and the quanti ers 8 9. W e use untyped variables x y z : : : terms are variables or elements from U S K r s s i t denote terms.
Among the atomic formulas are expressions of the following form: r = s, t 2 s, r : h s 1 : : : s n i, v :: u, t: < s, t: s.
The language includes an axiomatization capturing the semantics of the ontologically basic relations. We do not present the axiomatization in full here, but rather illustrate the main groups of axioms by selecting some typical examples. We i n troduce three groups of axioms, whose union form the axioms Ax(GOL) associated with the language GOL. Besides the logical axioms we h a ve t h e f o llowing groups of axioms.
(a) Sort and Existence Axioms 1. 9x(Se t (x)), 2. 9x(U r (x)) 3. 8x(Se t (x) _ U r (x)) 4. :9x(Se t (x) ^U r (x)) 5. 8x(U r (x) $ I n d (x) _ U n i v (x)) 6. :9x(I n d (x) ^Univ(x)) 7. 8xy(x 2 y ! S e t (y) ^(Se t (x) _ U r (x))) (b) Instantiation D. ext(x y) = df Univ(x) ^Se t (y) 8 u(u :: x ! u 2 y).
1. 8xy(x :: y ! I n d (x) ^Univ(y)) 2. 8x(U n i v (x) ! 9 y(S e t (y) 8 u(u 2 y ! u :: x))) (c) Axioms about sets 1. 8uv9x(Se t (x) ^x = fu vg) 2. f Se t j 2 Z F g, where Se t is the relativization of the formula to the basic symbolS e t (x). 3 3 In the formula Se t all variables and quanti ers in are restricted to sets. Z Fis the system of Zermelo-Fraenkel. By 1. and 2. there exists arbitrary nite sets over the urelements. Furthermore, we m a y construct nite lists. Note, that lists and alignments are di erent sorts of entities. (d) Axioms for Moments, Substances, and Inherence