Semiotic connectionism in artificial intelligence

Pieter Wisse

introduction

Polymath Charles S. Peirce (1839-1914) argues that a person’s particular belief directs some equally specific conduct. A belief, or interpretant as Peirce also calls it, is established through semiosis, or action of the sign. As a cognitive entity, belief is ... believed to exist in, say, an object. Peirce’s model of semiosis therefore exhibits sign, object and interpretant as elements of an irreducible system.[1]
The semiotic triad has recently been expanded to an enneadic model by the author.[2] Every element of the original triad changed to constitute a dimension. Along each dimension of the semiotic ennead (here reproduced as figure 5), three more finely grained, relative, elements appear. So, the object dimension is constituted by situation, identity and conduct. Deviating from Peirce’s terminology, the now more familiar term behavior substitutes for conduct.
Starting from situation, identity and behavior as elements, I outline a direction for artificial intelligence that might lead to a closer formal correspondence with natural intelligence.[3]

behavioral configurations

From Peirce I take the cue of cognition’s behavioral relevance. It follows that artificial intelligence is always artificial behavior, too. I’ll first develop an approach to behavioral variety as could be intelligently managed. For that purpose, the minimal cognitive system consists of three nodes. I’ll simply call them node a, b and c, respectively. Now one way of configuring them, is to interpret a as a situation, b as an identity and c as a behavior. Staying with simple nodes, their connections must not so much be quantitatively weighted but qualitatively determined. Then, proceeding with the configuration under discussion, between a and b there is a directional situation connection (determining, please note, for this configuration, a as a situation and b as a corresponding identity). Likewise, a directional behavior connection occurs between b as an identity and c as a corresponding behavior.
Including such qualitative connections, three original nodes can result in six different behavioral configurations, as figure 1 elaborates.

Figure 1: Permutation for configurations.

The permutation still leaves ambiguity unreconciled, though. With several s-, respectively b-connections extending from / reaching toward some identity, it is always a particular pair of them that constitutes some behavioral configuration. As an additional assumption, a connection is fitted with the reference to its complementary connection in the overall configuration. Figure 2 illustrates such extended connections for the left-side behavioral configuration in figure 1. Whereas the nodes remain general for my outline, that is, a, b and c, both connections are necessarily specified accordingly: for example, σ_n and β_n.

Figure 2: Shifting specificity from nodes to connections.

The configuration is disambiguated with

σ_n = {a, b, β_n} and, consequently, β_n = {a, b, σ_n}.

It might be argued that I am moving too far away from traditional connectionism to continue to properly apply the label. But then again, I’m only taking connections more seriously than ever.
From my semiotic perspective, I am now ready to explore some of the territory for artificial intelligence. I’d like to emphasize that mine is an initial outline, also with limited space. My tentative approach should be taken as an invitation to further exploration.

a quantification of behavioral variety

For accommodating situationally differentiated behaviors, at the minimum three nodes specify some particular behavior. For the moment, I also set the maximum behavioral configuration at three nodes. Then, given a cognitive system with p nodes, what behavioral variety can it entertain?
The number of different selections of three elements from a set of p elements is easily derived. It reads ‘p over 3’ and computes as: p! / ((p-3)!3!).
As seen above, every three nodes yield 3! behavioral configurations. It follows that p cognitive nodes may support p! / (p-3)! situationally differentiated behaviors.
This number of p! / (p-3)! configurations originating from p (general) nodes, is of course also precisely the number of (specific) situation connections, respectively behavior connections.

complicating connections

Explicitly investing connections with qualitative value might appear counterproductive, at least for mainstream connectionism. Yet, rather than trying to mitigate it as a risk, i.e. obstructing options for quantitative analysis etcetera, for new opportunities I confidently continue speculating in that direction. For it suggests, as I mentioned at the outset, increased convergence between models for natural and artificial intelligence.
Here I can only provide a flavor of enhanced semiotic connectionism. I already remarked taking situation, identity and behavior as relative. By that I mean more than that some node may appear in one of all three such capacities.
Relativism also entails the possibility of moving beyond three nodes for a behavioral configuration. On the left, figure 3 sketches a configuration the two hierarchically positioned nodes, a and b, to reflect a situation. It should be possible to differentiate d as c’s behavior from d occurring in, for example, ‘just’ b as the situation in question for c (see the right side of figure 3).
It might not enough to maintain that β_n = {c, d, σ_n}. For more nodes in a situational capacity, for precision of behavior all connections must be known. For the left side of figure 3 that means β_m = {c, d, σ_q, σ_r}.

Figure 3: Multi-level situational differentiation of behavior.

In figure 4, the configuration on the left of figure 3 reappears. To its right, a configuration consisting of the same nodes in the same order is added, but with the node acting in the capacity of an identity moved up one level. Of course, the situational representation has shrunk, respectively the behavioral representation has expanded accordingly. All specific connections should reflect the particular configuration they help constitute.

Figure 4: Additional variety though compounded situations and/or behaviors.

Combining nodes, even when limited to hierarchical compounds, for situations and/or behaviors of courses increases the behavioral variety to be accommodated by a cognitive system. At the minimum, a situation requires one node for its representation in a particular behavioral configuration. When p nodes are available, the maximum of nodes making up a situation is (p-2); one node is always reserved for an identity and the minimum for a behavior is, just like a situation, one node.
Suppose x nodes constitute a situation. A maximum of p! / (p-x)! situational subconfigurations results.
With x nodes in a situational capacity, the number of nodes constituting a behavior may vary from 1 to (p-x-1). Let k range from 1 to (p-x-1), then for any x the maximum number of behavioral subconfigurations equals the sum of k! over that range. The number of complete configurations for any x is their product.
All together,

The number of specific connections must be adjusted accordingly. With x nodes for situation there are of course x situation connections in a configuration. The same applies to k nodes for behavior. So,

I’ve amply shown, how differentially (inter)connected nodes might qualify at least as far as static variety goes. For now I’ll leave discussing several aspects of dynamics of artificial intelligence from my tentative perspective of semiotic connectionism. Let me just make some introductory remarks on a reinterpretation of AI’s well-known BDI orientation: belief, desire and intention.

motivation, etcetera

So far, I have more or less unproblematically applied terms such as identity. My approach is essentially semiotic because nine such concepts constitute an irreducible ennead. Without providing much comment, it is reproduced here as figure 5.

Figure 5: Semiotic ennead.

When the model of figure 5 is applied, the cognitive system (interpretation) involves elements that correspond to identity, situation and behavior. What is assumed to be inside cognition, are motive and concept revolving around focus. Then, a belief that is acted upon is a motivated concept. However, the same may be said about a desire. Or an intention. Belief, desire and intention are not atomic concepts. Their dynamics can only be recognized from the vantage point of an irreducible model.
Human language is a late evolutionary development. Cognition is a much older phenomenon. Abstracting from (human) language, the semiotic ennead helps to recognize that cognition essentially involves a behavioral function. Language use should comply with such a functional explanation, not the other way around.

references

1. Buchler, J., editor, Philosophical writings of Peirce, Dover, 1955.
2. Wisse, P.E., Semiosis & Sign Exchange: design for a subjective situationism, including conceptual grounds of business information modeling, Information Dynamics, 2002.
3. Wisse, P.E., Ontology for interdependency, steps to an ecology of information management, in: PrimaVera, working paper # 2007-05, Amsterdam University, 2007.