  The note is devoted to an interactive game theoretic formalization of
dialogues as psycholinguistic phenomena and the unraveling of a hidden dialogue
structure of 2-person differential interactive games. In the field-theoretic
description of interactive games the dialogues are defined naively as
interactive games of discrete time with intention fields of continuous time;
the correct mathematical formulation is proposed. The states and the controls
of a dialogue correspond to the speech whereas the intention fields describe
the understanding. In the case of dialogues the main inverse problem is to
describe geometrical and algebraical properties of the understanding. On the
other hand, a precise mathematical definition of dialogues allows to formulate
a problem of the unraveling of a hidden dialogue structure of any 2-person
differential interactive game. Such procedure is called the verbalization. It
means that the states of a differential interactive game are interpreted as
intention fields of a hidden dialogue and the problem is to describe such
dialogue completely. If a 2-person differential interactive game is
verbalizable one is able to consider many linguistic (e.g. the formal grammar
of a related hidden dialogue) or psycholinguistic (e.g. the dynamical
correlation of various implications) aspects of it.
