Conceptual Space profiles
Sandro Rama Fiorini
I would like to kick off the discussion in this group by posing the following question to all.
During the CS Conference, we have seen many distinct formulations of the Theory of Conceptual Spaces in terms of mathematical and computational models (e.g., Adams & Raubal, Aisbett & Gibbon, and etc). It seems to me that all these approaches have different profiles, in the sense that they have distinct representational capabilities within the TCS. For instance, some provide better formulation of prototypes, others of categories and properties, others of conceptual operations and concept change, and so on. My question is: how one should organize these profiles? Can we talk about a fundamental CS profile? That is, is there a fundamental set of characteristics that any TCS formulation should preserve? Also, if we accept a fundamental profile, what would be extension profiles?
Best regards,
Sandro Rama Fiorini
inf.ufrgs.br/~srfiorini
lucs.lu.se
Joel Parthemore
...Can we talk about a fundamental CS profile? That is, is there a fundamental set of characteristics that any TCS formulation should preserve?
Quoting from my thesis ;'):
The central tenets of conceptual spaces theory I take to be:
- Neither associationist (including connectionist) nor symbolic accounts of cognition, and likewise neither empiricist nor rationalist approaches, can, on their own, do adequate justice to the nature of concepts. The former are too reductionist, the latter too rarefied. Associationist and symbolic accounts should be understood as two different levels of explanation of cognition, which a theory of concepts should then try to bridge.
- Just as a conceptual account of cognition bridges these two levels of explanation of cognition, concepts themselves bridge two levels of cognition. That is, they sit in the middle between directly sensorimotor-grounded cognition on the one hand, symbolically and propositionally structured thought on the other. The former is more unconscious and automatic, and shades over into the subpersonal; the latter is indisputably personal, and much if not most of the time conscious and deliberate. Concepts are beholden to neither one level nor the other.
- “There is no unique correct way of describing cognition” (Gärdenfors, 2004, p. 2). “In brief, depending on which cognitive process we are trying to explain, we must choose the appropriate explanatory level” (Gärdenfors, 2004, p. 57). Likewise, there is no unique correct perspective on concepts. Depending on which aspects of them we are trying to explain, they may look more like words of a language, say, or more like patterns of association.
- Furthermore, there is no unique correct perspective on any particular concept, not least because concepts change: with the agent who is using them and with the context in which they are used. Gärdenfors specifically includes the so-called natural kinds concepts.
- A metaphor for physical objects in physical space, concepts are (best understood as) either:
- points (or associated sets of points) within conceptual spaces, whose dimensions (e.g., hue, saturation, and brightness in the case of colour) may be acquired in a bottom-up activity-driven manner or a top-down intentionally-driven one8; or as
- shapes (or associated sets of shapes) within those same spaces.
- The upshot of this is, as I read it, that there is no principled class/instance distinction to be made: any particular instance of a concept (a point) can, within practical limits, be expanded to a shape (a “class” or set of points, each one a more particular instance), and any shape can be collapsed to a point (i.e., treated as an instance of some, more general, concept).
- Those shapes are typically (though not always) convex shapes: that is, for any two points that lie within the concept x, all points on a straight line between them should also lie within that concept. (Some concepts are defined as the negation of other concepts, within a certain domain: e.g., Gentiles are anyone who is not Jewish. Fodor uses the example of NOT A DUCK. If the one concept [JEWISH or DUCK] is convex, its negation [GENTILE, NOT A DUCK] within a domain cannot be.)
- Individual convex shapes (or individual points) denote a particular type of concepts, namely properties – what I have preferred to call (see Section 4.2.2.3) property concepts. Property concepts relate only to a single domain: e.g., COLOUR can only be described in terms of the integral dimensions HUE, SATURATION, and BRIGHTNESS (or their equivalents), and never according to some entirely different set of integral dimensions such as MASS and DENSITY. Other types of concepts (what I have referred to as object concepts or action/event concepts) are associated sets of these shapes (or points) across multiple domains. Note that, just as individual shapes can be collapsed to points, so, too, associated sets of these shapes can be collapsed to a single shape: i.e., all concepts can be treated as property concepts. This is not explicitly stated, but I take to be implicit in Gärdenfors’ account.
- The structure of concepts need not in any way be consciously introspectible: “. . . For many words in natural languages that denote properties, we have only vague ideas, if any at all, about what are the underlying conceptual dimensions and their geometrical structure” (Gärdenfors, 2004, p. 168).
- The process of “carving up” a conceptual space into various shapes and sub-domains is the process of categorization: “. . .Where (possible) objects are represented as points in conceptual spaces, a categorization will generate a partitioning of the space and a concept will correspond to a region (or set of regions from separable domains) of the space” (Gärdenfors, 2004, p. 60).
- At the same time, that “carving up” imposes a Voronoi tessellation on the space. A Voronoi tessellation tiles a plane that is initially populated by a set of points (the Voronoi sites), which in conceptual spaces theory are taken to represent the most prototypical members of a category. The plane is then divided up according to which of those points the remaining points in the plane are closest to (the Voronoi cells). Boundaries arise wherever there is equidistance to two of the existing points, junctions wherever there is equidistance to three (or more) points. Although these tessellations are [commonly presented] in two dimensions, a three- or n-dimensional Voronoi tessellation can also be done.
-- ----------------------------------------------------------------------- -- J. Parthemore - Centre for Cognitive Semiotics, Box 201 ------------ -- 22100 Lund SWEDEN -- +46 702 723 849 (mobile) ---------------------- -- research: http://www.informatics.scitech.sussex.ac.uk/users/jep25 -- -- home page: http://www.parthemores.com -- AOL/Yahoo!: ghanavolunteer- -- blog: http://jack_of_lantern.livejournal.com ----------------------- -- The point of philosophy is to start with something so simple as not- -- to seem worth stating, and to end with something so paradoxical ---- -- that no one will believe it. - Bertrand Russell -------------------- -----------------------------------------------------------------------
Ronald Stamper
Dear c-spaces colleagues,
I’ve joined your list as a result of a communication on the ontolog list. I shall listen attentively to your discussions looking out for key ideas that I must be sure to cover in the book I am now completing.
I’ll tell you a little about my work to invite you to throw challenges in my direction
My attention is focused on information systems as social constructs. I’m interested in applying IT to organisational problems. Over a long period, with colleagues at the London School of Economics and then U. of Twente, we studied the specification of organisations as systems of social norms. Currently I am making a final pass through a book on semantics for which I have tried to supply a strictly engineering approach. With that goal in mind, I have eschewed the notion of ‘concepts’. That may horrify c-spaces members unless you see it as an attempt to put the notion of ‘concepts’ on as thorough an empirical basis as possible.
The practical results of our research are very successful in practice. In particular we have introduced a notion of ontological dependency that governs the construction of schemas so strictly that they display an empirical canonical form of great stability. That stability and rigour have demonstrated massive reductions in systems lifetime costs.
Our primitive notion is that of ‘affordances’ in lieu of ‘concepts’.
I had my fill of concepts on the IFIP WG 8.1 FRISCO Task Group where a majority attempted to base a FRamework of Information Systems Concepts on them. Each relevant concept was defined strictly formally in terms of others until they reached the foundational notion: the concept.
As an engineer, I asked to be taken to see some of these concepts. As they reside in the minds of people, I wanted to know in whose mind I should probe.
This approach tried to combine the incompatible assumptions of an objective reality with a psychological basis for knowledge of reality.
Our research looked at the construction of reality by members of a community, starting with their social reality, by investigating social norms as exhibited in legal norms. On reading James Gibson’s work on perception, the construction of models of the material world fitted into a unified framework. Gibson’s notion of affordances (= invariant repertoires of physical behaviour) that correspond to the things we perceive unites with the notion of social norms (that define invariant repertoires of social behaviour) in a satisfying theory. As engineers, we can know and deal only the reality we can perceive as physical and social affordances.
There are two papers on my inadequate website: www.rstamper.co.uk
One sketches the key theoretical ideas and the other is a brief account of the application of the theory to requirements engineering.
Best wishes with your discussion about conceptual spaces. I’m sure you will throw up problems that I must solve in my own work on perceptual space.
Ronald Stamper
Sandro Rama Fiorini
I agree this complete set of tenets may be
part of a particular
CS formulation. However, I would say that there is a subset of
it that is more
fundamental to any CS formulation, while the rest is more
"implementation"
specific, or just "extensions" to the fundamental notion of CS.
Let me explain my point-of-view.
First I would say that what is stated about one particular CS
formulation is
not valid for others. For instance, I am not sure
that voronoi tesselations are necessary for defining
conceptual spaces; we have examples of CS formulation not
including it. That said, how do you compare
different formulations?
It seems we need to systematize their features. Besides,
applications of CS
have different representation requirements. How one can as well
systematize
these requirements? That's why I am suggesting the "profiles".
Being very brave, I would say that
concepts, prototypes and distances
are the primitive constructs of any approach to CS. In
principle, you don't need to talk about dimensions and
domains, at least not explicitly. If the framework
provides an way of grouping prototypes under concepts and an effective
procedure to measure
the distance from inputs to these prototypes, then I would say
we already have a
conceptual space. That's what I would call fundamental
profile
(F) of CS;
I would agree you cannot do much with it, but it forms a base
that can be
expanded in many ways.
The fundamental profile can be then extended by a lattice of
additional
profiles. A given formulation may give support to quality
domains (D). These
domains can be linear (D), circular (Dc), numeric (Dn), lexical
(Dl), etc.
Then you can have a profile which define
contrast classes (CC) and how they operate. That may need a more
specific construction for concept regions (R), like polytopes
(Rp)
If you can organize these sets of features, you can: (a) define
clear
separation to them; and (b) compare combinations of features in
a systematic
way. For instance, we can refer to a given CS representation
framework
"supporting FDc", to another one "supporting FDn" and
compare then. I can say that my domain requires an FDcRp
framework.
Ultimately, I can analyze the formal, cognitive and
computational properties of
a given profile.
To some extent, I am taking inspiration on the idea
of expressibility labels you find in Description Logics. I
believe that more the CS field grows, we will need this kind of
systematization to be able to communicate.
regards,
Sandro
Joel Parthemore
I agree this complete set of tenets may be part of a particular CS formulation.
However, I would say that there is a subset of it that is more fundamental to any CS formulation, while the rest is more "implementation" specific, or just "extensions" to the fundamental notion of CS.
First I would say that what is stated about one particular CS formulation is not valid for others. For instance, I am not sure that voronoi tesselations are necessary for defining conceptual spaces; we have examples of CS formulation not including it.
That said, how do you compare different formulations? It seems we need to systematize their features.
Being very brave, I would say that concepts, prototypes and distances are the primitive constructs of any approach to CS.
Second, I seriously question whether one can have prototypes without some substantive notion of conceptual boundaries. That said, I realize that this is open to debate. Note that there are many prototype-based theories, going back at least to Eleanor Rosch's work in the '70s (and, realistically, even further); so there must be something to distinguish CS from other prototype-based theories.
Finally, distance is, agreed, essential to CS; but, again, it seems to be in common with all prototype-based theories. Certainly Rosch had and has an assumption of distance built into her work. Note that distance seems to require two further things: dimensions (which I take to be integral dimensions, but you can quibble) and metric.
In principle, you don't need to talk about dimensions and domains, at least not explicitly.
If the framework provides an way of grouping prototypes under concepts and an effective procedure to measure the distance from inputs to these prototypes, then I would say we already have a conceptual space. That's what I would call fundamental profile (F) of CS
The fundamental profile can be then extended by a lattice of additional profiles. A given formulation may give support to quality domains (D). These domains can be linear (D), circular (Dc), numeric (Dn), lexical (Dl), etc.
Note that I have no objection in principle to setting up a taxonomy of CS-based or -inspired systems (theoretical systems or concrete implementations). It could, indeed, be very useful.
Joel