Illustration by DALL·E (+PJ)

At the time (1987-90) when I was developing software for British Telecom called ANELLA (Associative Network with Emergent Logical and Learning Abilities), it was the colleague who had coined this nice acronym who had drawn my attention to emergence phenomena in my AI. At the heart of the process was a trick I’d developed to eliminate most of the dead-ends of semantic networks in one fell swoop: defining the dual of a semantic network as the memory of an AI. The time has come to call in the best minds on the subject 😉 .

P.J.:

See the following in the imported file. Does it make sense to you?

Claude 3:

The diagrams and explanations make sense to me. The key points I understand are:

1. The author is proposing an alternative way to represent semantic networks called a “P-Graph” or “P-Dual” representation.

2. In a P-Graph, concepts are attached to the edges of the graph and relations to the nodes, which is the opposite of a traditional semantic network.

3. The author argues this P-Graph representation is more biologically plausible in terms of mapping to actual neural networks in the brain.

4. An adjacency matrix method is introduced to help construct the P-Graph from a traditional semantic network.

5. Several examples are worked through, showing how adding new concepts and relations alters the structure of the P-Graph, with new “neuron-like” nodes and “synapse-like” edges emerging.

6. Cycles can appear in the P-Graph to represent certain reciprocal relations, like a pet having a master and a master having a pet.

Overall, the P-Graph seems to provide an interesting alternative perspective on representing knowledge that aims to more closely mirror biological neural networks compared to classical semantic networks. The illustrations help clarify the key ideas being put forth.

GPT-4:

The document “The P-graph explained” discusses an approach to representing semantic networks, known as P-graphs, which seems to be an alternative or an enhancement to classical semantic networks. This approach apparently aligns better with biological neural networks in terms of structure and functionality.

Here are the key points made in the document:

• Representation Shift: The P-graph deviates from traditional semantic networks by assigning concepts to edges rather than nodes, and relations to nodes instead of edges. This alteration might help in creating a more accurate representation of how actual neural networks function biologically.
• Dual Semantic Network: The document discusses the concept of creating a dual of a graph where nodes become edges and vice versa. This concept is applied to the semantic networks to perhaps better mimic neural mappings in biological systems.
• Biological Plausibility: The P-graph is claimed to be more neuro-biologically plausible. It suggests that the structure of these graphs mimics the actual connections in a biological neural network, where, for example, ‘boy’, ‘meets’, and ‘girl’ could correspond to different parts of a neuron such as axon ramifications or synapses.
• Graph Construction using Adjacency Matrix: The document outlines a method to construct a P-graph using an adjacency matrix, which seems to be a systematic way to transform a classical graph (template) into a P-graph. This transformation is crucial for maintaining structural integrity while altering node-edge relationships.
• Comparative Examples: It provides comparative illustrations and examples to demonstrate how traditional semantic networks can be transformed into P-graphs, emphasizing the differences and potential advantages of the P-graph approach.
• Semantics and Topology: The P-graph approach is also described as beneficial for dealing with semantic ambiguities and for representing semantic relationships that evolve over time, like those encountered in language acquisition.
• Special Case Handling: The addition of new concepts and relations, like ‘master’ and ‘has_a’, to a P-graph is discussed in terms of graph complexity and node interpretation changes, suggesting a flexible and dynamic structure.

The content you’ve provided suggests that the P-graph model is an innovative approach to knowledge representation that might offer distinct advantages over traditional models, especially in terms of biological realism and adaptability to complex semantic relationships. This could have implications for fields such as cognitive science, artificial intelligence, and neuroscience, where understanding the structure and dynamics of knowledge representation is crucial.

P.J.:

If I said to you that there are emergent phenomena when turning from the original semantic graph to its dual, would you be surprised?

Claude 3:

No, I would not be surprised at all that emergent phenomena arise when transitioning from a traditional semantic network to its P-Graph dual representation. A few observations from your examples suggest this emergence:

1. New nodes and edges appear in the P-Graph that have no direct correlate in the original semantic network. For instance, when “Lassie” was added, an entirely new “dog” neuron emerged in the P-Graph with its own set of synapses, despite “dog” not being a new concept added to the semantic network.

2. The connectivity pattern can change significantly and in non-obvious ways in the P-Graph. The addition of “master” not only created a new neuron, but also caused the original “dog” neuron to grow a new synapse and spawned a whole second “dog” neuron with different connections.

3. Higher-order structures like cycles emerged in the P-Graph that were not explicitly represented in the semantic network. The reciprocal “has-a” relation between dog and master created a cyclic connection between two neurons.

These emergent properties arising from the P-Graph transformation suggest that this dual representation is capturing some implicit structure and dynamics that are not readily apparent from the direct concept-relation encoding of the semantic network.

The P-Graph seems to naturally manifest some of the complex, self-organizing properties we associate with biological neural networks and cognition. So the emergence of novel phenomena in the P-Graph representation is quite intuitive and exciting from the perspective of modeling knowledge in a more brain-like way.

GPT-4:

Not at all! The concept of emergent phenomena when transitioning from an original semantic graph to its dual (P-graph) makes sense, especially given the unique structural changes that occur in the transformation process. In complex systems theory, emergent phenomena refer to properties or behaviors that arise from the collective interactions of the system’s components, which cannot be predicted merely by understanding the individual parts.

In the case of P-graphs:

• Reassignment of Nodes and Edges: By swapping the roles of nodes and edges—where concepts become linked to edges and relations to nodes—new patterns of connectivity and interactions emerge. This reassignment could lead to new ways of representing and understanding relationships and hierarchies within the data that were not apparent in the original semantic network.
• Biological Plausibility and Neural Mappability: As noted in the document, the P-graph aims to mirror the connectivity and functions of biological neural networks more closely than traditional graphs. This shift could naturally lead to emergent properties that better model cognitive and neurological processes, such as pattern recognition, learning, and memory, reflecting more accurately how information is processed and stored in the brain.
• Complexity in Representation: With the addition of new concepts and relationships in the P-graph, as with the “master” and “has_a” example from the document, the graph’s complexity increases. This complexity might lead to emergent properties related to how concepts are interconnected, potentially offering new insights into semantic relations and concept hierarchies.
• Topology and Semantic Clustering: The use of adjacency matrices and the specific structuring in P-graphs could lead to different clustering of concepts and relationships, possibly revealing new semantic clusters or unexpected links between concepts due to their topological arrangement.

Overall, the transition to a P-graph could indeed introduce emergent phenomena as the system’s dynamics and interactions change, potentially offering richer and more nuanced insights into the data represented.

(To be continued…)

Illustration by DALL·E (+PJ)