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Formal Languages, Part Theory and Change


Benson, David Bernard (1968) Formal Languages, Part Theory and Change. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MY2Y-F179.


A general definition of interpreted formal language is presented. The notion “is a part of" is formally developed and models of the resulting part theory are used as universes of discourse of the formal languages. It is shown that certain Boolean algebras are models of part theory.

With this development, the structure imposed upon the universe of discourse by a formal language is characterized by a group of automorphisms of the model of part theory. If the model of part theory is thought of as a static world, the automorphisms become the changes which take place in the world. Using this formalism, we discuss a notion of abstraction and the concept of definability. A Galois connection between the groups characterizing formal languages and a language-like closure over the groups is determined.

It is shown that a set theory can be developed within models of part theory such that certain strong formal languages can be said to determine their own set theory. This development is such that for a given formal language whose universe of discourse is a model of part theory, a set theory can be imbedded as a submodel of part theory so that the formal language has parts which are sets as its discursive entities.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Engineering Science and Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Thompson, Frederick B.
Thesis Committee:
  • Unknown, Unknown
Defense Date:8 September 1967
Record Number:CaltechTHESIS:03072016-161303982
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9608
Deposited On:08 Mar 2016 18:32
Last Modified:25 Mar 2024 21:54

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