Computational Implementation of a Model of Category-Theoretic Metaphor Comprehension

In this study, we developed a computational implementation for a model of metaphor comprehension based on the theory of indeterminate natural transformation (TINT) proposed by Fuyama et al. We simplified the algorithms implementing the model to be closer to the original theory and verified it through data fitting and simulations. The outputs of the algorithms are evaluated with three measures: data-fitting with experimental data, the systematicity of the metaphor comprehension result, and the novelty of the comprehension (i.e. the correspondence of the associative structure of the source and target of the metaphor). The improved algorithm outperformed the existing ones in all the three measures.

Quantum-like cognition and decision making in the light of quantum measurement theory

We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects, cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely {\it sharp repeatable non-projective measurements} - ${\cal SR\bar{P}}. $ This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modeling isn't automatic borrowing of the quantum formalism. Exploring the class ${\cal SR\bar{P}}$ highlights the role of {\it noncommutativity of the state update maps generated by measurement back action.} Thus, ``non-classicality'' in quantum physics as well as quantum-like modeling for cognition is based on two different types of noncommutativity, of operators (observables) and instruments (state update maps): {\it observable-noncommutativity} vs. {\it state update-noncommutativity}. We speculate that distinguishing quantum-like properties of the cognitive effects are the expressions of the latter, or possibly both.