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Quantum computation and cognition: a logical approach

Giulia Battilotti

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

We show a logical calculus where massive quantum parallelism is expressed. This is possible within an inconsistent logical framework, analogous to the logic of the unconscious of I. Matte Blanco. We hypothize that inconsistency is necessary to intelligence, since it gives strong computational and then cognitive advantages to our mind.

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This review presents an overview of cognitive systems, quantum phenomena and possible connections between them. The focus will be the artificial cognitive systems and briefly touch the discussion of possible benefits from quantum counterparts. The nonclassical features of Quantum Theory introduced as quantum resources which enables possible speed ups or advantages over classical computational tasks. Quantum computation is introduced as a powerful computational tool over its classical counterparts by also covering possible applications of cognitive phenomena in the framework of quantum cognition. Also different attempts in order to implement decision making processes for cognitive purposes mentioned.
Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic Turing machines and quantum Turing machines.possible applications of the quantum computational semantics to cognitive problems.parallelism in music.
Abstract There is something fundamentally disturbing about contemporary philosophy of mind and philosophical cognitive science. Almost without exception (exceptions such as Lockwood (1989) and Chalmers (1996, see esp. p. 349) ), the philosophical theories are logically inconsistent with the most well-confirmed theory ever developed by humans, namely, quantum mechanics. Why do philosophers develop theories of the mind-brain as if quantum mechanics does not exist, or as if it is utterly irrelevant to theories of the mind-brain? I believe this epistemic situation has arisen due to a series of questionable philosophical arguments about the role of philosophy of mind/cognitive science and quantum mechanics in our overall theoretical framework. In sect. I explain some of these arguments and contend they are unsound.
There are inherent limits in classical computation for it to serve as an adequate model of human cognition. In particular, non-commutativity, while ubiquitous in physics and psychology, cannot be sufficiently handled. We propose that we need a new mathematics that is capable of expressing more complex mathematical structures to tackle those hard X-problems in cognitive science. A quantum mind approach is advocated and we hypothesize a way in which quantum computation might be realized in the brain.
In the last years, quantum computational logics have been developed in order to describe the logical setting of quantum computation [1]. An important challenge is the development of proof theoretical tools for quantum computation, so that the physical process of computation can correspond to a logical process of computation. In particular, the challenge is that quantum computational speed up, due to superposition and entanglement, can find an explanation in terms of logical proofs. The object of our research is a sequent calculus developed in the framework of basic logic, that is a logical platform to study extensional logics, including quantum logics [2, 3]. In basic logic, logical connectives and their rules are the result of importing suitable links at the metalevel into the object level. We suppose that a particular kind of dynamics between the object level and the metalevel is created when considering a quantum system rather than a classical one. This is due to a specific treatment of variables, that, in our view, can create the logical setting for a holistic, rather than compositional, treatment of information, proper of entangled states [4]. Then we develop a predicative sequent calculus. In it, superposition is built by quantifying a propo-sition, associated with a quantum system, on a first order domain determined by the experiments on such system. Then a convenient treatment of variables can create dynamically entangled states in logical