We outline a formal foundation for a \structural " (or \symbolic") object/event representation, the necessity of which is acutely felt in all sciences, including mathematics and computer science. The proposed foundation incorporates two hypotheses: 1) the object's formative history must be an integral part of the object representation and 2) the process of object construction is irreversible, i.e. the \trajectory " of the object's formative evolution does not intersect itself. The last hypothesis is equivalent to the generalized axiom of (structural) induction. Some of the main diculties associated with the transition from the classical numeric to the structural representations appear to be related precisely to the development of a formal framework satisfying these two hypotheses. The concept of (inductive) class representation|which has inspired the development of this approach to structural representation|diers fundamentally from the known concepts of class. In the proposed, evolving transformations system (ETS), model, the class is dened by the transformation system|a nite set of weighted transformations acting on the class progenitor| and the generation of the class elements is associated with the corresponding generative process which also induces the class typicality measure. Moreover, in the ETS model, a fundamental role of the object's class in the object's representation is claried: the representation of an object must include the class. From the point of view of ETS model, the classical discrete representations, e.g. strings and graphs, appear now as incomplete special cases, the proper completion of which should incorporate the corresponding formative histories, i.e. those of the corresponding strings or graphs. 1 Concepts which have proved useful for ordinary things easily assume so great an authority over us, that we forget their terrestrial origin and accept them as unalterable facts. They then become labeled as \conceptual necessities", a priori situations, etc. The road of scientic progress is frequently blocked for long periods by such errors.

Speech recognition has been a very active area of research over the past twenty years. Despite an evident progress, it is generally agreed by the practitioners of the field that performance of the current speech recognition systems is rather suboptimal and new ap-proaches are needed. The motivation behind the undertaken research is an observation that the notion of representation of objects and concepts that once was considered to be central in the early days of pattern recognition, has been largely marginalised by the ad-vent of statistical approaches. As a consequence of a predominantly statistical approach to speech recognition problem, due to the numeric, feature vector-based, nature of rep-resentation, the classes inductively discovered from real data using decision-theoretic techniques have little meaning outside the statistical framework. This is because deci-sion surfaces or probability distributions are difficult to analyse linguistically. Because of the later limitation it is doubtful that the gap between speech recognition and lin-guistic research can be bridged by the numeric representations. This thesis investigates an alternative, structural, approach to spoken language representation and categorisa-

We outline a formalism for "structural", or "symbolic", representation, the necessity of which is acutely felt in all sciences. One can develop an initial intuitive understanding of the proposed representation by simply generalizing the process of construction of natural numbers: replace the identical structureless units out of which numbers are built by several structural ones, attached consecutively. Now, however, the resulting constructions embody the corresponding formative/generative histories, since we can see what was attached and when.

[W]e may again recall what Einstein stressed: that given a sufficiently powerful formal assumption, a fertile and comprehensive theory may... be constructed without prior attention to the detailed facts, or even before they are known. L. L. Whyte, Internal Factors in Evolution, 1965 We outline a formalism for structural, or symbolic, representation, the necessity of which has been acutely felt in all sciences, particularly biology, for quite some time now. At the same time, biology has been gradually edging to the forefront of sciences, although the reasons obviously have nothing to do with its state of formalization or maturity—which is quite primitive as compared, for example, to that of physics. Rather, the reasons have to do with the growing realization that the objects of biology are not only more important and interesting, but that they also more explicitly exhibit the evolving nature of all objects in the Universe. It is this view of objects as evolving structural processes that we aim to address here, in contrast to the ubiquitous mathematical view of objects as points in some abstract space. One can gain an initial intuitive understanding of the proposed representation by generalizing the (Peano) process of construction of natural numbers: replace the single structureless unit out of which a number is built by multiple structural ones. An immediate but critical consequence of the distinguishability/multiplicity of units in the construction process is that we can now see which unit was attached and when. Hence, the resulting representation for the first time embodies temporal structural information in the form of a formative, or generative, history.

What is a structural representation?