A. C. Varzi. Parts, wholes, and part-whole relations: the prospects of mereotopology. Data and Knowledge Engineering, 20:259--286, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....[10] for a survey on pointless geometry. The fact that relations such as part of , overlap , non tangential inclusion and others can be defined in terms of the connection relation relates some pointless geometries to the field of mereology [16] and to its fusion with topology mereotopology [26]. The latter is closely related to naive or qualitative physics, introduced by [12] in particular, to its subfield Qualitative Spatial Reasoning (QSR) 3] It has been realised that searching for models of mereological systems, methods of lattice theory and the theory of relation algebras can be ....

VARZI, A. C. Parts, wholes, and part--whole relations: The prospect of mereotopology. Data & Knowledge Engineering 20 (1996), 259--286.

....new theories for most spatial and geometrical concepts. Several studies have been devoted to the building of mereo topological theories on that basis (for instance the well known RCC theory [Randell et al. 1992] see also [Fleck, 1996] Asher and Vieu, 1995] and for a survey of mereo topology [V arzi, 1996] as mereo topology (essentially, the modeling of connection and part hood) is regarded as the basis of common sense geometry. Very little work has been done on motion in such a qualitative framework. Even works done under the banner of socalled qualitative physics usually make use of the ....

....However these logics are often based on two primitives, for precedence, and either inclusion or overlap. If we want to keep the topological distinction between connection and overlap made on the spatio temporal entities, we need to have topological concepts on the temporal level as well (and Varzi [V arzi, 1996] has shown this is not possible with only overlap or inclusion, i.e. mereology) This distinction is part of Allen s common sense theory of time [Allen and Hayes, 1985] and Galton [Galton, 1993] has shown it is necessary to account for continuous motion. But Allen s theory assumes selfconnected ....

A. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20(3):259--286, 1996.

....spatio temporal regions that arguably addresses and solves some of the issues mentioned before. This theory enables us to define a topology of extended spatial and temporal entities and to propose an ontology for (topological) motion. We place ourself in a mereo topological framework (see [38] and [42] for a general presentation of available theories along this line) We think this theory then gives a good basis for a theory of objects having spatio temporal referents. In the following we present in section 2 a survey of different approaches to motion representation. Section 3 defines the ....

....extent of objects. Section 6 gives some elements as to how these issues can be addressed in our framework if it is to become a theory of objects. A more serious criticism of this version of mereo topology is the absence of boundary entity, which has been considered a serious flaw by [38] and [42]; we will see that It has been argued that physics of the relativity theory would justify such an approach as being closer to the real universe, but we think the debate has nothing to do with this since relativity is still far from being part of the layman s common sense knowledge and brings ....

[Article contains additional citation context not shown here]

A. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20(3):259--286, 1996.

....phenomena. Mereology was developed as an alternative to set theory, and the part whole relation is one of the ontological basic relations needed to describe the world. But a purely mereological outlook is too narrow to describe spatial entities and the structure of spatial localizations. In Varzi[47] several strategies are expounded to cope with this problem of expressivity; we take here the most obvious approach, namely to add further space relevant basic relations to the mereological basic relation . Topology provides a natural next step after mereology in the development of a comprehensive ....

Varzi, A.C. Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology; Datas and Knowleldge Engineering 20, (1996), 259-286.

....and transitive; thus, P is a strict partial order. It has been recognised that mereology is often more suitable as a language for reasoning about complex objects than first order logics based on Cantorian set theory; applications of mereological systems arise, for example, in spatial reasoning [4, 78] and natural language processing [32] A model of rough mereology is a structure # # #X; n; Fu#, such that X is a collection of objects, # X # X # ##; ## a function, and n # X;wedenotebyX # the set X ##n#.Furthermore, Fu## # # # X is a function, called fusion, such that x # Fu#U# ## ....

Varzi, A. C. (1996). Parts, wholes, and part--whole relations: The prospect of mereotopology. Data & Knowledge Engineering, 20, 259--286. 24

.... as the spatial referent of an object (i.e. the portion of space occupied by the object) Basic spatial concepts like those of mereology (part whole relations) and topology (connection relations) are then easy to represent with such ontological elements, and various authors studied these aspects [1 4]. In order to obtain an expressive power similar to classical geometries, the following notions also have to be represented: distance, orientation and shape. This paper deals with the representation of shape and to some extent with orientation. The necessary metrical concepts are introduced ....

Achille C. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20:259--286, 1996.

....of objects Several works have been devoted to the study of mereological and topological relations. The main contributions in the domain are the RCC8 theory [ Randell et al. 1992 ] and the framework of Asher and Vieu [ Asher and Vieu, 1995 ] For a complete review of the domain, refer to [ Varzi, 1996 ] Fewer works in qualitative spatial reasoning deal with the more complex notions of distance, shape and orientation. Distance is a well studied notion in classical geometry, all the way back to Euclid, but it is hardly applicable to a region based system. There are several interesting works ....

Achille C. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20:259--286, 1996.

....linguistic motivated work of Asher and Vieu [ AV95 ] These different approaches differ only in the choice of the primitives and the domain to be represented. All these approaches are based on mereological and topological relations (for a very detailed review on mereology and topology, see Varzi [ Var96 ] and can henceforth be used to represent basic positions of connected (by a part or by a point) objects. These relations are nevertheless insufficient to express metrical and morphological notions. Borgo, Guarino and Masolo, added in [ BGM96 ] a primitive CG of congruence (same shape modulo ....

Achille C. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20:259--286, 1996.

....stand in the development of region based theories of space: mereotopology. Mereology is concerned with parts of entities, and was originally developed by Le sniewski [31] In the spatial context the part of relation between regions is important, and systems of mereotopology have been developed [46, 47, 54, 1, 8] which axiomatize spatial regions based on the part of relation among regions and additional topological structure. BCAs clarify the mereotopological content of the RCC axioms. In a BCA hA; C i the partial order in A models the notion of part, so the requirement that A be a Boolean algebra is the ....

A. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20:259--286, 1996.

....81. Mereology and Topology Although mereology (being the theory of the partwhole relationship) would seem at first sight simply to be a subtheory of topology (and indeed is presented thus in the topological theories mentioned so far in this section) there are arguments against this view. Varzi [126] has discussed the issue and notes that whilst certain mereology is not sufficient by itself, there are three main ways in which theories in the literature have proposed integrating topology and mereology: 1. Generalise mereology by adding a topological primitive. This is the approach taken by, ....

A Varzi. Parts, wholes, and part-whole relations: the prospects of mereotopology. Data and Knowledge Engineering, 20(3):259--286, 1996.

.... For a discussion of the ontological issues we refer the reader to Simons (1987) Cohn et al. 1997) Pratt Lemon (1997) and to the special edition on ontology of the International Journal of Human Computer Studies 43 (1995) an overview of current development in mereology can be found in Varzi (1996). Before we properly define contact relations, we should like to recall a few facts of binary relations. Relations and their algebras have been studied since the latter half of the last century, e.g. by de Morgan (1864) Peirce (1870) and Schroder (1890 1905) Tarski (1941) who, incidentally, ....

Varzi, A. C. (1996). Parts, wholes, and part--whole relations: The prospect of mereotopology. Data & Knowledge Engineering, 20, 259--286.

....requirements for inter operability it becomes feasible to consider multi agent systems with heterogeneous agents. Communicative actions between such agents is usually based on speci c ontologies [3] Various ontologies have been conceived and their properties studied, including general part whole [16] and speci c ontologies for particular domains. Several frameworks for collaboration models [10, 17] for multi agent systems have been advanced, like cooperative problem solving using joint intentions [7] collaborative plans for complex group action [6] or social reasoning through dependence ....

....in the following we shall consider just samples of such ontologies, so sticated enough to illustrate the mechanism. A ground mereology that gives a common basis for all part whole theories treats usually parthood as a partial ordering, that is a re exive, antisymmetric, transitive relation [16]. For our pupose, the schema below de ning a basic mereology is more convenient. BasicMereology immedPartOf ; partOf ; subpart : Device Device 8 x ; y ; z : Device immedPartOf (x ; y) partOf (x ; y) partOf (x ; y) partOf (y ; z ) partOf (x ; z ) subpart(x ; y) partOf (y ; x ) ....

[Article contains additional citation context not shown here]

Achille C. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20:259-286, 1996.

....new theories for most spatial and geometrical concepts. Several studies have been devoted to the building of mereo topological theories on that basis (for instance the well known RCC theory [Randell et al. 1992] see also [Fleck, 1996] Asher and Vieu, 1995] and for a survey of mereo topology [V arzi, 1996] as mereo topology (essentially, the modeling of connection and part hood) is regarded as the basis of common sense geometry. Very little work has been done on motion in such a qualitative framework. Even works done under the banner of socalled qualitative physics usually make use of the ....

....However these logics are often based on two primitives, for precedence, and either inclusion or overlap. If we want to keep the topological distinction between connection and overlap made on the spatio temporal entities, we need to have topological concepts on the temporal level as well (and Varzi [V arzi, 1996] has shown this is not possible with only overlap or inclusion, i.e. mereology) This distinction is part of Allen s common sense theory of time [Allen and Hayes, 1985] and Galton [Galton, 1993] has shown it is necessary to account for continuous motion. But Allen s theory assumes selfconnected ....

A. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20(3):259--286, 1996.

....by the parts with respect to the whole Notice that in order to understand the various forms of part whole relation [Winston et al. 1987, Artale et al. 1996] the general theory of parts must be supplemented with a theory of wholes. Together, the two theories form what may be called mereotopology [Varzi 1996]. Theory of identity. The theory of identity builds up on the theory of parthood and the theory of wholes, studying the conditions under which two entities exhibiting different properties can be considered as the same. Relevant questions that must be addressed are: How can an entity change ....

....exact spatial location is less obvious, and it is however bound to the location of the participating continuants. In the following, when mentioning the location of an occurrent, I shall refer to its temporal location. For a thorough review of the philosophical work on occurrents, see [Casati and Varzi 1996]. Abstract objects are objects which do not have a spatial nor a temporal location. They are included here just for completeness, but are in fact kept outside the current analysis. Notice however that I refer here to abstract particulars, such as Pitagora s theorem or (maybe ) the empty set. Most ....

Varzi, A. 1996. Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology.

....frame based systems. 5 of individuals belonging to C2. This corresponds considerably with the union of necessary and possible component relations in our terminology. Theoretical aspects of part whole relations are generally based on mereology [Lesniewski, 1984; Simons and Dement, 1996, see also Varzi, 1996] or mereotopology [Varzi, 1996; Smith, 1996] that study only composed objects instead of types or concepts. From the conceptual modeling perspective we can consider the objects of a domain by simply considering the connections of objects. Another modeling choice is the use of an attribute ....

....belonging to C2. This corresponds considerably with the union of necessary and possible component relations in our terminology. Theoretical aspects of part whole relations are generally based on mereology [Lesniewski, 1984; Simons and Dement, 1996, see also Varzi, 1996] or mereotopology [Varzi, 1996; Smith, 1996] that study only composed objects instead of types or concepts. From the conceptual modeling perspective we can consider the objects of a domain by simply considering the connections of objects. Another modeling choice is the use of an attribute has component when connections ....

Achille Varzi, Parts, wholes, and part-whole relations: The prospects of mereotopology, Data and knowledge engineering. Vol. 20, No 3, 1996. 259286

....In the whole paper, free variables are assumed to be universally quantified. 3 standard way, by means of a single binary predicate P restricted to hold only between substrates of the same kind: A2. Pxy (Mx My) Rx Ry) The following axioms equivalent to Closed Extensional Mereology [23,27] are assumed for P : A3. Pxx A4. Pxy Pyx x =y A5. Pxy Pyz Pxz A6. xy z(z = x y) A7. Pxy z(z = x y) A8. Pxy zPzx Ozy where the following definitions hold: D1. Oxy = df z(Pzx Pzy) Overlap) D2. x y = df iz w(Owz (Owx Owy) Sum) D3. x y = df iz w(Pwz (Pwx Pwy) ....

....how the notion of contingent parthood is defined for physical objects. 4. SPACE 4.1 Topological Level Besides the parthood relation, we introduce in the domain of space a further primitive to account for topological properties. We follow with this move the first of the strategies discussed in [27] (the others being adopting topology as a basis for mereology, as in [5,21,1] and adopting mereology as a basis for topology, as in [10] our approach differs however from those inspired to Clarke s work, since we don t take topological connection ( C ) as a primitive: rather, we adopt the notion ....

Varzi, A. 1996. Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology. Data and Knowledge Engineering: (in press).

....by confining ourselves to the mereotopology of their spatiotemporal locations. Whatever the applicative agenda here, there is serious work to be pursued. The puzzles may be bizarre. But the study of limit cases is often the best starting point for understanding the ordinary cases. Notes See [54] for an introduction and review of mereotopology and [47] for the link with formal ontology. On the demarcation between these two components (and a taxonomy of the main options) see [53] See e.g. 15, 27] The objection to P extensionality goes back to [25] and [40] while the objection ....

Varzi A. C., 1996a, `Parts, Wholes, and Part--Whole Relations: The Prospects of Mereotopology,` Data and Knowledge Engineering 20, 259--86.

....and Vieu 1995 and Smith and Varzi, forthcoming. Casati and Varzi 1994 argue that holes, in particular, are bounded from the outside: the boundary of a hole is the surface of its material host. For other families of examples see Jackendoff 1991. 9 This point expands on an argument put forward in Varzi 1997, 7. 10 2) A worm drills a hole in a log of wood and breaks through to the other side. Once again, an abrupt change takes place at the termination of such a process: a sphere becomes a doughnut; the topology of the object undergoes a qualitative transformation. Or consider a piece of soft plasticine (a ....

....from the outside. See again TB4, which effectively represents the Bolzanian view of contact. If, by contrast, the boundary through which x and y are connected is a fiat boundary, i.e. if they are externally C connected: 19 On the difference between location and occupation, see Casati and Varzi 1996, 1999. 20 Our axioms for are adopted from Smith 1997. They differ slightly from those given by Chisholm, who takes coincidence to pertain exclusively to boundaries. In particular, reflexivity and transitivity do not hold unrestrictedly for Chisholm (see his 1984) 21 DB 4 EC (x, y) C (x, y) O(x, ....

Varzi, A. C., 1996a, `Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology, ` Data and Knowledge Engineering 20, 259--86.

....on the head of a pin. Chisholm [1973: 590] also considers shadows and holes as counterexamples to Locke s principle. For another example, J. M. Shorter [1977] mentions the intriguing case of intersecting clouds produced by two distinct cloud projectors . For a general discussion, see Casati and Varzi [1996] 10 does not seem to be implied by the Minimalist View. And how can we possibly deny the second premise (the premise that Tib Tail will or would still include Tail after the accident, if it survives at all) Perhaps we could say that after the accident Tib Tail ceases to exist insofar as its parts ....

Varzi A. C., 1996a, `Parts, Wholes, and Part--Whole Relations: The Prospects of Mereotopology `, Data & Knowledge Engineering, 20, 259--286.

....Vieu 1995 and Smith and Varzi, forthcoming. Casati and Varzi 1994 argue that holes, in particular, are bounded from the outside: the boundary of a hole is the surface of its material host. For other families of examples see Jackendoff 1991. 9 This point expands on an argument put forward in Varzi 1997, 7. 10 3) A bed of coral starts growing a finger somewhere. The finger continues to grow until it eventually comes round to meet the main body again, forming a sort of handle. At the instant that it does so, the topology of the object changes: where once we had a sphere, now we have a torus. All ....

....can be perfectly colocated one with another. 19 On this interpretation, coincidence is clearly an equivalence relation, i.e. a reflexive, symmetric, and transitive relation: 20 A1 x x A2 x y y x A3 x y y z x z. 19 On the difference between location and occupation, see Casati and Varzi 1996, 1999. 20 Our axioms for are adopted from Smith 1997. They differ slightly from those given by Chisholm, who takes coincidence to pertain exclusively to boundaries. In particular, reflexivity and transitivity do not hold unrestrictedly for Chisholm (see his 1984) 20 To these axioms we add two ....

Varzi, A. C., 1996a, `Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology, ` Data and Knowledge Engineering 20, 259--86.

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A. C. Varzi. Parts, wholes, and part-whole relations: the prospects of mereotopology. Data and Knowledge Engineering, 20:259--286, 1996.

No context found.

A. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20(3):259--86, 1996.

No context found.

A Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20:259--86, 1996.

No context found.

A. Varzi. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20(3):259--286, 1996.

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Varzi A C. Parts, wholes, and part-whole relations: The prospects of mereotopology. Data and Knowledge Engineering, 20:259--286, 1996.

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