Abstract
This work aims to develop a novel BDI agent programming framework, which embeds the reasoning under uncertainty (probabilistic logic) and is capable of a realistic simulation of human reasoning. We claim that such a development can be addressed through the adoption of the mathematical and logical formalism derived from Quantum Mechanics: a scheme fulfilling the necessary requirements is described, useful for both the interpretation of some peculiarities in human behavior, and eventually the adoption of ‘quantum computing’ formalism for the agent programming. This last possibility could exploit the power of quantum parallelism in practical reasoning applications. Integration with the BDI paradigm enables the straightforward adoption of efficient learning algorithms and procedures, enhancing the behavior and adaptation of the agent to the environment.
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Notes
Also known as BWI: ‘Belief-Wish-Intentions’
In the following, with the word cognitive, we will refer in general to the ensemble of learning, training and reasoning processes.
E.g. a robot’s sensor, able to measure the external temperature, permits the robot to have a belief about the real, current value of this variable. If the sensor’s reading is 50 ∘C, one can not infer that this is certainly the actual value: the sensor may be out-of-service.
It is possible to extend the formalism developed to the case of continuous variables, but this poses some difficulties which prevent a straightforward extension.
I.e. its mental state, according to its beliefs, at a certain moment of the reasoning.
This characterization descends from describing these states as Hilbert space basis vectors: if one is certainly TRUE, than all the others must be FALS E.
It is skipped here the particular case of a pure separable global state, represented by a diagonal density operator, as it can be reduced to the trivial case where the density matrix in (14) has only one non-vanishing diagonal element, i.e. the global state is an eigenstate of the global density matrix. All other considerations done for Example 1 would nevertheless hold for this specific case.
It is worth to briefly comment also the more general case where the global density matrix is separable as \({\rho }_{MS}= {\sum }_{i} \lambda _{i} {\rho }_{i(B)} \otimes {\rho }_{i(I)}\). Here correlations among the subsystems are expected; nevertheless, for this case it would be still possible to describe two-system probabilities as classical probabilities [35].
Notice ho w the reduced density matrix ρ (I), given the separability outlined, coincides with the term in the product of (15).
I.e. the only information supposed directly accessible.
Which is the same as a change in the basis used for ρ (B).
Indeed, an agent requires near real-time decision-making.
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Bisconti, C., Corallo, A., Fortunato, L. et al. A Quantum-BDI Model for Information Processing and Decision Making. Int J Theor Phys 54, 710–726 (2015). https://doi.org/10.1007/s10773-014-2263-x
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DOI: https://doi.org/10.1007/s10773-014-2263-x