Chrystopher L. Nehaniv

Motivated by computational efficiency in algebraic automata theory here we define the cascade product of permutation groups as an external product, as a generic extension. It is the most general hierarchical product that uses arbitrary total functions to combine a linearly ordered set of permutation groups. Algebraically speaking, cascade products are explicitly constructed substructures of the iterated wreath product. We show how direct, semidirect and wreath products can be described as cascade products and we also discuss examples of composite groups that can only be constructed exactly as generic extensions by cascade products. The cascade construction naturally generalizes to the transformation semigroup case by leaving out the details of defining inverse operations.

`No' belongs to the first ten words used by children and embodies the first active form of linguistic negation. Despite its early occurrence the details of its acquisition process remain largely unknown. The circumstance that `no' cannot be construed as a label for perceptible objects or events puts it outside of the scope of most modern accounts of language acquisition. Moreover, most symbol grounding architectures will struggle to ground the word due to its non-referential character. In an experimental study involving the child-like humanoid robot iCub that was designed to illuminate the acquisition process of negation words, the robot is deployed in several rounds of speech-wise unconstrained interaction with na\"ive participants acting as its language teachers. The results corroborate the hypothesis that affect or volition plays a pivotal role in the socially distributed acquisition process. Negation words are prosodically salient within prohibitive utterances and negative intent interpretations such that they can be easily isolated from the teacher's speech signal. These words subsequently may be grounded in negative affective states. However, observations of the nature of prohibitive acts and the temporal relationships between its linguistic and extra-linguistic components raise serious questions over the suitability of Hebbian-type algorithms for language grounding.

As we endow cognitive robots with ever more human-like capacities, these have begun to resemble constituent aspects of the ‘self’ in humans (e.g., putative psychological constructs such as a narrative self, social self, somatic self and experiential self). Robot’s capacity for body-mapping and social learning in turn facilitate skill acquisition and development, extending cognitive architectures to include temporal horizon by using autobiographical memory (own experience) and inter-personal space by mapping the observations and predictions on the experience of others (biographic reconstruction). This ‘self-projection’ into the past and future as well as other’s mind can facilitate scaffolded development, social interaction and planning in humanoid robots. This temporally extended horizon and social capacities newly and increasingly available to cognitive roboticists have analogues in the function of the Default Mode Network (DMN) known from human neuroscience, activity of which is associated with selfreferencing, including discursive narrative processes about present moment experience, ‘self-projection’ into past memories or future intentions, as well as the minds of others. Hyperactivity and overconnectivity of the DMN, as well as its co-activation with the brain networks related to affective and bodily states have been observed in different psychopathologies. Mindfulness practice, which entails reduction in narrative self-referential processing, has been shown to result in an attenuation of the DMN activity and its decoupling from other brain networks, resulting in more efficient brain dynamics, and associated gains in cognitive function and well-being. This suggests that there is a vast space of possibilities for orchestrating self-related processes in humanoids together with other cognitive activity, some less desirable or efficient than others. Just as for humans, relying on emergence and selforganization in humanoid scaffolded cognitive development might not always lead to the ‘healthiest’ and most efficient modes of cognitive dynamics. Rather, transient activations of self-related processes and their interplay dependent on and appropriate to the functional context may be better suited for the structuring of adaptive robot cognition and behaviour. As we endow cognitive robots with ever more human-like capacities, these have begun to resemble constituent aspects of the ‘self’ in humans (e.g., putative psychological constructs such as a narrative self, social self, somatic self and experiential self). Robot’s capacity for body-mapping and social learning in turn facilitate skill acquisition and development, extending cognitive architectures to include temporal horizon by using autobiographical memory (own experience) and inter-personal space by mapping the observations and predictions on the experience of others (biographic reconstruction). This ‘self-projection’ into the past and future as well as other’s mind can facilitate scaffolded development, social interaction and planning in humanoid robots. This temporally extended horizon and social capacities newly and increasingly available to cognitive roboticists have analogues in the function of the Default Mode Network (DMN) known from human neuroscience, activity of which is associated with selfreferencing, including discursive narrative processes about present moment experience, ‘self-projection’ into past memories or future intentions, as well as the minds of others. Hyperactivity and overconnectivity of the DMN, as well as its co-activation with the brain networks related to affective and bodily states have been observed in different psychopathologies. Mindfulness practice, which entails reduction in narrative self-referential processing, has been shown to result in an attenuation of the DMN activity and its decoupling from other brain networks, resulting in more efficient brain dynamics, and associated gains in cognitive function and well-being. This suggests that there is a vast space of possibilities for orchestrating self-related processes in humanoids together with other cognitive activity, some less desirable or efficient than others. Just as for humans, relying on emergence and selforganization in humanoid scaffolded cognitive development might not always lead to the ‘healthiest’ and most efficient modes of cognitive dynamics. Rather, transient activations of self-related processes and their interplay dependent on and appropriate to the functional context may be better suited for the structuring of adaptive robot cognition and behaviour. As we endow cognitive robots with ever more human-like capacities, these have begun to resemble constituent aspects of the ‘self’ in humans (e.g., putative psychological constructs such as a narrative self, social self, somatic self and experiential self). Robot’s capacity for body-mapping and social learning in turn facilitate skill acquisition and development, extending cognitive architectures to include temporal horizon by using autobiographical memory (own experience) and inter-personal space by mapping the observations and predictions on the experience of others (biographic reconstruction). This ‘self-projection’ into the past and future as well as other’s mind can facilitate scaffolded development, social interaction and planning in humanoid robots. This temporally extended horizon and social capacities newly and increasingly available to cognitive roboticists have analogues in the function of the Default Mode Network (DMN) known from human neuroscience, activity of which is associated with selfreferencing, including discursive narrative processes about present moment experience, ‘self-projection’ into past memories or future intentions, as well as the minds of others. Hyperactivity and overconnectivity of the DMN, as well as its co-activation with the brain networks related to affective and bodily states have been observed in different psychopathologies. Mindfulness practice, which entails reduction in narrative self-referential processing, has been shown to result in an attenuation of the DMN activity and its decoupling from other brain networks, resulting in more efficient brain dynamics, and associated gains in cognitive function and well-being. This suggests that there is a vast space of possibilities for orchestrating self-related processes in humanoids together with other cognitive activity, some less desirable or efficient than others. Just as for humans, relying on emergence and selforganization in humanoid scaffolded cognitive development might not always lead to the ‘healthiest’ and most efficient modes of cognitive dynamics. Rather, transient activations of self-related processes and their interplay dependent on and appropriate to the functional context may be better suited for the structuring of adaptive robot cognition and behaviour.

We describe a new notation for finite transformations. This compact notation extends the orbit-cycle notation for permutations and builds upon existing notations. It gives insight into the structure of transformations and reduces the length of expressions without increasing the number of types of symbols.

We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty lies in the strict separation of several different ideas appearing in the holonomy method. The steps of the proof and the constructions are illustrated with computed examples.