Structural induction: towards automatic ontology elicitation

Induction is the process by which we obtain laws (and more encompassing - theories) about the world. This process can thought as aiming to derive two aspects of a theory: a Structural aspect and a Numerical aspect respectively. The Structural aspect is concerned with the entities modeled and their interrelationship, also known as ontology. The Numerical aspect is concerned with the quantities involved in the relationships among the above-mentioned entities along with uncertainties either postulated to exist in the world or inherent to the nature of the induction process. In this thesis we will focus more on the structural aspect hence the name: Structural Induction: toward Automatic Ontology Elicitation. In order to deal with the problem of Structural Induction we need to solve two main problems: (1) We have to say what we mean by Structure (What? ); and (2) We have to say how to get it (How?). In this thesis we give one very definite answer to the first question ( What?) and we also explore how to answer the second question (How?) in some particular cases. A comprehensive answer to the second question (How?) in the most general setup will involve dealing very carefully with the interplay between the Structural and Numerical aspects of Induction and will represent a full solution to the Induction problem. This is a vast enterprise and we will only be able touch some aspects of this issue.The main thesis presented in this work is that the fundamental structural elements based on which theories are constructed are Abstraction (grouping similar entities under one overarching category) and Super-Structuring (grouping into a bigger unit topologically close entities - in particular spatio-temporally close). This thesis is supported by showing that each member of the Turing equivalent class of General Generative Grammars can be decomposed in terms of these operators and their duals (Reverse Abstraction and Reverse SuperStructuring, respectively). Thus, if we are to believe the Computationalistic Assumption (that the most general way to present a finite theory is by the means of an entity expressed in a Turing equivalent formalism) we have proved that our thesis is correct. We call this thesis the Abstraction + SuperStructuring thesis. The rest of the thesis is concerned with issues in the opened by the second question presented above ( How?): Given that we have established what we mean by Structure, how to get it?