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Auteur: Hiroyuki NISHINA

The Complexity of the Motion Planning for Actions as Possibly Equivalent to That of Phrase Structure Grammar

Abstract/Résumé: Minimalist theory attempts to reduce evacuate UG from syntax, installing its properties into lexical items as grammaticalized functional features [Chomsly2001]. After linearization, merger leads to a sequence of subphrase structures, though their derivation mechanism is different from the tree-to-tree mapping type of derivation adopted in the parametric syntax [Boecks2011]. Both still maintains that human sentences are syntactically represented in some types of tree structure. We argue for the hypothesis that human language necessitates human kinetic ability by comparing the complexity of the grammar of human language. We show that we can approximately represent a human action as a sequence of tree structures constructed from the relevant action planning for a humanoid robot. The following inclusion relations of the languages generated by grammars are known as Chomsky hierarchy [Chomsky1956]: Regular Language⊂Context-Free Language⊂Context-Sensitive Language [6]. Swiss German, with its appropriate case-marking even within the cross-serial-construction, was demonstrated as weakly context-sensitive [Shieber1985]. This leads us to conclude that human grammar is at least a bit more powerful than that of context free grammar. There is evidence that a Bengalese finch’s song has a regular grammar [Okanoya2004]. We elsewhere constructed a denotative semantics of action verbs, in which all the rotations around each joint in each action are defined in terms of a joint’s causation of another or an endpoint to “move” [Nishina2007]. In the present analysis, we collected the rotations from the action planning data for the programmable humanoid robot, and converted them into causation relations. We constructed a phrase structure grammar of motion causation from an action planning, in which all the rotations involved in the intervals in the relevant action are described as to joints, degrees and periods of rotation. Its main rule is recursive, enabling embedding: C→V MOV C, expressing that causing V to C to MOVe is also C, where V is a vertex, joints and endpoints, and C is a spatiotemporal connection between two vertices. We need a sequence of phrase structure trees to describe a whole action, which suggests that the complexity of actions exceed that of phrase structure grammar. Monkeys can sign, but why they cannot speak languages [Cheney&Seyfarth1997]? The biped structure with free upper limbs seems crucial. Nevertheless, tamarins, biped, are unable to process a simple phrase structure [Fitch&Houser2004]. Rhesus monkeys, chimpanzees and gorillas were reported not to modify their supralaryngeal vocal tracts by tongue maneuvers, thus leading to the poor variety of vocalization [Liberman1968].