Diagrams, Logic and Representation

The main thesis of this dissertation is that there are principled logical explanations behind valid and invalid uses of diagrams in reasoning. In particular, the logic involved in reasoning with diagrams can be studied in the same way that the logic of linguistic inference has been analyzed by Frege, Tarski, and others. Four logics are studied whose well-formed representations consist of diagrams rather then sentences. Syntax and semantics are provided for each diagrammatic system. Rules of inference for reasoning with the diagrams are provided in each case, and basic logical results such as completeness are established. Preliminary conceptual and philosophical questions are also treated