Hello M. Asterios Chardalias,

I am sorry but I discover the CIT with your question because I am working on a similar question. In fact, I work on abstraction processes (mainly Newell and Floridi's theories of abstraction and Godel's numbering function) not on analogy process. In particular, I try to formalize a method of abstraction that I called TOM4A (Time Observation Method for Abstraction) so that I could code it in an abstraction process. To this aim, I developed a new mathematical framework called the Timed Observation Theory.

Looking for the CIT, I discover that I used similar principles of the CIT to define a knowledge modeling methodology called TOM4D (Timed Observation Modeling for Diagnosis) and I find that there exist strong similarities between these two types of processes, abstraction and analogy. But in both cases, the difficulty of operationalization is huge since the principles to link two conceptual spaces are not clearly established. In my opinion, not only rules are required but also an algebra so that a Godel numbering function could be implemented (not only Dempster’s rule as in the Structure Mapping Theory).

As a consequence, as many Authors says, there is still a long run to operationalize CIT (and Abstraction theories). But your question is interesting since there can be some one, some where, that made a trial on this road. And sharing such trials is very important.

Sorry to bring no concrete answer to your question, but thank you for asking it!

Best regards,

Marc

Do you have annotated data for expected operation results and for different operation scenarios?

I don't work on linguistics but my works on knowledge engineering is close to CIT: modeling a knowledge corpus is an interpretation process of text and schemata with the particular goal of producing a usable model for a given cognitive task.

You can find the example described in the publication "Reducing the Gap between Experts’ Knowledge and Data: The TOM4D Methodology" in my ResearcheGate publication list. This paper models a system from a set of 9 rules coming from the CommopnKads book (you will find the reference in the paper). The model is made for a diagnosis task of a (very) simplified car. I worked also on others examples, more complicated, notably an hydraulic dam, but these examples have not been completely published yet. You can find some paper about these other examples in my publication list.

Hoping these examples will help you,

Bets regards

Marc

Article Reducing the Gap between Experts’ Knowledge and Data: The TO...

@ Marc Le Goc

Abstraction is a part of the blending process for sure. Especially during the construction of the Generic Space. I haven't come across the term "Knowledge Engineering" before. It sounds like a pretty interesting field. :)

@ Ignacio Arroyo

I haven't got into annotation schemes yet. But since CIT has a strong 'evolutionary' undercurrent running through it., they'll need to reflect it somehow.  A simple static semantic tag won't work. I'm thinking something more along the lines of vectors and graphs. 

Information retrieval and extraction requires vectors and/or graphs. Depending on the task you want to perform. That's why it is my question. Blending or integration are Cognitive science terms. However, it is possible that in modeling we can define kinds of blending by learning the combinatorics of simple summations. Probably, also the combinatorics of selectional preferences* allowed in new mental spaces (contexts?).

Actually I'm not a semanticist or linguist, but I have studied Faucunnier-Turner theories in some moment at past. Actually It seems to be not as unreachable as some scientists assert, I think. Also Im working on mathematical definition of vector representations which are driven by semantic criteria. One of challenges taking place is to encode the two language constraints of Harris, which involve indeed different combinatories depending on context.

Any way, if you'd have some different intuition about mental space representation (mainly considering you said it is not sufficient with vectors and graphs), it would be great hearing about it.

Erk, Pado, (2008) A Structured Vector Space Model for Word Meaning in Context.

One of the basic advantages of CIT is the notion of  'emergent structure'. When elements project from the input spaces to the blend, they do not just 'combine', they 'integrate' . What arises has its own noncompositional ontology. That is why I don't feel that combinatronics can help bring out the best of CIT. 

Erk & Pado (2008) suggest factoring in syntactic structures. I'm reluctutant to go down that path, since I'm coming from a Cognitive Linguistic tradition, which rebelled against traditional Chomskyan generative linguistics and their obsession with syntax. 

My problem with vectors and graphs is that they seem to entail locality (all things similar are close to each other or somehow connected), single-originality (all things new are created for the first time in one place only and then spread from there) and single-directionality. But, for me, meaning is non-local, multi-original and multidirectional. Interesting theories that appear to help overcome these shortcomings are Chaos Theory and Quantum Information Theory.

Hello Asterio,

The debate between syntactics and semantics is an old debate. In my mind, the most difficult problem is to control the introduction of semantics from a particular arrangement/combination of symbols. That is to say defining the principles and the means to control the introduction of semantics in an interpretation process.

I don't want to make the publicity of my works but the paper I suggest describes some ways to make stuctures emerging from a given arrangement of symbols. You can see in the example that it is a long and difficult process which requires a lot of steps thats are based on simple but general and strong principles. The problem of the automation of such a process is still open but I think that some parts can be usefully automated so that, in a near future, the difficulty will decrease significantly.

As a consequence, I think that the best way to operationalize CIT is to to define a global process and to decompose it in steps so that some part of these steps could be formalized and automated. Next, linking together the formalized parts would lead to a specific (in the sense of not general) but efficient process that will clarify the operationalization of the CIT. And the best way to do that is to take a simple example.

Best regards,

Marc

It is interesting you have explored theories from other areas, thereby making associations between components of these, apparently, very separated concepts. It is indeed which we (humans) perform according to CIT. However, firstly, given you are trying to infer the way to induce this kind of behavior into a computer, I think it is needed to taking into account its inherent limitations. The major thing this device would to do is approximating (probably idealized) models by using data structures exclusively. There are probably many methods for simulating or approximating non-data-structured objects, but these would be uniquely simulations. 

Secondly, theories you are taking into consideration are totally comprehensible whenever you make the needed effort to do it. Then you can make more concrete associations. It can even be an interesting life project.

Thirdly in the case of chaos theory, personally I think there are fundamental disagreements to CIT: clearly CIT establishes the concept of the aiming of a sequence of blending processes, thereby implying the equilibrium (convergence) of a potentially infinite process. The above also imply the convergence of any involved operational process among concepts (e.g. attribute merging). Chaos theory is contrary to these principles because of, how then we can learn if it is not by equilibrium stages? In this sense it is important to seriously consider a basic concept such as 'convergence' in vector spaces, in order to be able to associate it to cognitive theories. Also I suggest you reviewing chaotic cellular automata, which are suitable for computer simulations and really have more agreements with what you have in mint. The disadvantage of this theory is that it is still a black box in many fundamental aspects, e.g. what initial configuration converges to any desired final configuration? Convergence and desired structures exist, but it is unknown the initial structure(s) can generate it from basic operations (also seemed to inverse problem solution).

Forth in the case of quantum information theory (QIT), Im not sure what kind of associations you probably made. What I can see in QIT, are generalizations of classical theories. Not much more (bit -> qbit, state --> qstate, etc. They are data structures still). In the case of Godel theories, really I can't tell you anything. In these two cases, it would be interesting to hear more about it from you. What kind of associations you are considering relevant.

Lastly, I consider the approach of Pado & Erk very useful for exploring because they are not precisely focused on syntax, but rather in predicate structures which are indeed what languages use for telling something about something (indeed the main objective of communication). It is independent from what we say is correct or incorrect or from ideas are rational or irrational. They indeed also critiqued pure syntax theories.

Regarding to the multidirectional behavior of CIT, in fact Pado & Erk proposed this kind of behavior in their model, by using their example of "catching a ball", which shows agreement with an important feature of CIT: completion. It is clear their model has many limitations, because of only a limited number of cases were addressed, but it can be visualized its suitability for generalization to many interesting cases in CIT. 

I know this is not a discussion forum (but a space for Q&A), but the question is very interesting and probably there are not answers for it.

@Marc Le Goc

Breaking it down and working on it one piece at a time should work, if only CIT specified autonomous procedures. Alas, they are 'integrated' and they'll reconfigure as soon as you try to post-assemble them. You need the entire network pre-assembled and operational  before you run any blendings to get accurate simulations. As for the 'one simple example' as a starting point, CIT is only valuable when it comes to handling complex figuration. When one tries to take away complexity, other cognitive linguistic theories become optimal. 

@Ignacio Arroyo 

Chaos has the property to 'synchronize' under the right conditions. That's when a blend emerges, what you call 'convergence'. But before that, there is a state where the network simultaneously holds an infinitesimal number of possibilities (Pereira, 2007 calls these alternative probable states 'blendoids'). What is more, CIT appears to apply no principled criteria to select mental spaces and that's where one of the many challenges for an effective computational model for it lies. When we need to describe a process that appears 'random', but intuition tells us there has to be a recognizible pattern somewhere, I think chaos pretty much fits the bill.

The out-of-sync chaotic state ("when everything is still possible") can be described as quantum, from my layman's understanding of Quantum Theory. I only mention Quantum Information Theory because we are dealing with concepts (aka information), not particles. Perhaps standard Information Theory, of which QIT is an extension, is not a pretty good fit for CIT modeling beccause it adopts the Conduit Metaphor for communication (a message is carried from a transmitter to a receiver through a medium), while CIT talks of meaning construction. But Quantum Theory also gives me non-locality and entanglement, which I deem useful for bringing together mental spaces across great conceptual distances.

I just casually glanced over Erk & Pado (2008) and I may have overlooked the direction you mention. I will look it through again. :)

@Asterios

If you read my paper about TOM4D, you will see how a very simple set of 9 rules, linking together only 10 elementary propositions, leads to a great complexity: behind the apparent simplicity, always resides an incredible complexity for the one that knows looking at it!

To be operationalized, any process must make elementary associations between piece of information, even in a chaotic manner. If the CIT does not define these elementary association, there is no solution to your problem: no theory will help!

In the contrary, if there exists a network, then there exists nodes and binary relations. Typically, a binary relation is an elementary process establishing a link between two pieces of information: defining the nodes and the elementary processes (i.e. relations), then defining categories of nodes and processes (the critical point!) so that semantic relations between these categories will emerge, is the first step to the "operationalization" of any theory. Generally speaking, doing so cannot be done in only one cycle: the cycles must be repeated again and again until a global coherence emerges within the interpretation of the resulting network. To my mind, what you call "integration" is the establishment of such a global coherence within a given set of elementary processes (i.e. relations). This is one of the lessons the Knowledge Engineering discipline produced. And that is why, in my opinion, you are expecting from Chaos Theory and Quantum Information Theory: looking for overall consistency through a steady state defined as an optimal distribution of information over a network.

Personally, my researches on Knowledge Engineering and Machine Learning lead me to consider that it is not possible to think the complexity with the notion of state in mind. I consider that complex systems are defined by the fact that they have no "state" or, in other words, the state notion of complex system has no meaning: causality is not the principle withing complex dynamic systems. This is obvious when looking at nature ... or any network like a brain! I think then that coherence is one of the basic principle of complexity.

Up to now, I am not able to demonstrate this point but what I learned during my (too long, alas!) experience is that it is very powerful when introducing semantics within a network of symbols.

:)

I understand your intuition about complexity and randomness of possible results from any blending procedure. However, although in chaos theory a pattern should to emerge, this has not any possibility of convergence (at least in known computer-tractable vector spaces). Even the explanation about blendoids sounds quite far away from chaos, because of the infinitesimal cardinality of the blendoid set. This set seems to be a latent subset of a infinitely cardinal set of much lesser probable blendings, whose usefulness for some specific aiming approaches to zero. That is, the blended set could be seen as a task-driven (aiming) selected set. This latter statement fits even more to the regularization theory (Tikhonov, 1966) -generalized to unimaginable levels.

Any way, I will read the Pereira's paper in order to get out from simple glance.

@ Marc Le Goc

‘Network’ is the terminology applied by the theory to express multiple concurrent interdependent operations. That brings along ideas of connectivity, topology, alignment and other similar Euclidean space construals. The introduction of space concepts allows for graph representation that can get us a long way for an accurate operationalization. However, it also traps the theory in some entailments that need not necessarily hold. Conceptual relatedness as physical proximity, binary relations, relational ontologies (relations thought as existing independent of their actual predicates) are instances that come to mind.

True, the notion of ‘state’ cannot hold any substantial merit in a discussion of dynamic systems. An alternate, perhaps more suitable, term is ‘mode’. ‘State’ however is popular in (particle) physics. Since cognitivists regard cognition as grounded in the environment (both natural and social), physics emerges as a more relevant paradigm than engineering. Computational approaches, on the other hand, remain mostly blind to more organic, holistic organization systems and that’s why their models of cognition come out as somewhat ‘autistic’. Bridging the gap is certainly not easy.

Both ‘state’ and ‘mode’ are concepts meant to introduce ‘order’, so an ecological lexicon -including such lemmas as ‘pattern’, ‘construct’ and ‘relation’- can become meaningful. ‘Coherence’ (or ‘convergence’ Ignacio brought up) is another such concept. But here again blends are tricky: they are mostly ‘innovative’ (thus ‘incoherent’ with or ‘divergent’ from current state of affairs). Blends are ‘subversive’ both in terms of how they come about and what they come to be. Yet they are not completely random!

@ Ignacio Arroyo

I may be somewhat deluded in my understanding of ‘chaos’ and I certainly miss out on most –if not all of its mathematical aspects. But its imagery in modeling fluodynamics comes pretty close to my personal view of cognition. Li, Zook, Davis & Riedl (2012) talk of goal-driven blending so the blend as an aiming selected set makes absolute sense. I have not come across ‘regularization theory’ either. You guys keep feeding me new buzzwords! I’ll have a look at it as well. It seems, though, I need to brush up on my math skills for good first...

@Asterio: 2 remarks.

First, only time introduces an order in a dynamic system. The notion of state (or mode, if you prefer) has been introduced by humans to model the behaviors of dynamic systems. In other words, there is no state in artificial or natural artifact but only in models.

And second, an innovation is a modification of the current state of affairs that must be coherent to be new and so, subversive: if the modification does not bring its own and new coherence, it is only an effect of the stochastic properties of a dynamic system (nothing new, nothing subversive, nothing can be learned)

:)