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A quantum logic

By Peter Bruza - posted Tuesday, 13 February 2007

Peter and Rupert pass in the hallway of an Australian ICT research organisation. Peter, a research scientist utters to Rupert, the business development manager, “How is it going with John?” This utterance is the tip of an ice-berg rich in implicit associations. Due to their shared context, Peter and Rupert both know that “John” refers to “John Smith” of “ACME Corp”, who is negotiating a commercial license for “Guidebeam”, a next generation web-based search technology.

In the not so distant future our information environment will feature all sorts of devices and displays. Imagine the existence of a technology looming in the background which processes the above utterance, draws appropriate context sensitive associations in order to flesh it out, and thereafter uses the result to query for emails, license documents, podcasts of relevant conversations and so on, and tacitly retrieves these to prime Rupert and Peter's immediate information environment.

For example, the licence document and associated emails could be brought up on the wall display should they be needed for further reference in Peter and Rupert's spontaneous hallway discussion.


The above scenario illustrates that human beings are adept at drawing context-sensitive associations and inferences across a broad range of situations ranging from the mundane to the creative inferences that lead to scientific discovery.

Such reasoning has a strong pragmatic character and is transacted with comparatively scarce cognitive assets. The question is how to get technology to reliably replicate this? The need for such technology is pressing. Paradoxically, the information explosion is leading to diminished awareness. Expertise is becoming ever more specialised: individuals, groups, communities, enterprises are consequently becoming increasingly insular.

We need computational systems which have the capability to enhance our awareness, for example, by suggesting associations in context that we could make, but increasingly don't, as we generally lack the cognitive resources to do so. We believe that information processing technology has to manipulate context sensitive meanings which accord with those we harbour.

In other words, the “meanings” manipulated by the technology should be cognitively motivated. This point of departure readily gives rise to the question of how to get access to the meanings we carry in our heads and have technology manipulate them to good effect.

The field of cognitive science has recently produced an ensemble of models which have an encouraging, and at times impressive track record of replicating human information processing, such as human word associations norms. For example, primed with the word “Beatles” a common associate produced by human subjects may be “band”, or “John Lennon”. These models are generally referred to as “semantic space models”. The term “semantic” derives from the intuition that the meaning of a word is derived from the “company it keeps'', a famous quote originally from the linguist J.R. Firth (1890-1960).

For example, the words “mobile” and “cellular” would exhibit a strong association in semantic space as the distribution of words they co-occur tends to be similar, even though the two words almost never co-occur themselves.


Although the details of the individual semantic space models differ, they all process a corpus of text and “learn” representations of words in high dimensional space. That is, the meanings of words are given a geometric representation. Semantic space models are interesting in light of the scenario presented above as they open the door to gaining some operational command of the meanings we carry around in our heads together with mechanisms to replicate our ability to draw relevant context-sensitive associations.

One of the big questions is how to effectively model the interplay between meaning, context and such human pragmatic inference mechanisms. Surprisingly, quantum mechanics may provide some innovative and ground breaking inspiration in relation to this challenging question.

Recently a highly speculative but potentially far reaching discovery was made by the theoretical physicist Diederik Aerts and his collaborators. In a letter to the editors of a journal dealing with mathematical physics, they showed the formalisation of quantum mechanics (QM) shows very strong connections with the mathematical basis of semantic space models.

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About the Author

Peter Bruza's research spans the fields of quantum mechanics (QM) and cognitive science, with a strong connection to applied logic and information processing and retrieval. Peter Bruza was a pioneer of applied logic for information retrieval via his PhD thesis in 1993.

Creative Commons LicenseThis work is licensed under a Creative Commons License.

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