TITLE:
Model Theories of Set Theories and Type Theory
AUTHORS:
Robert Murray Jones
KEYWORDS:
Models; Set Theory; Quantified Modal Logic; Existence Predicate
JOURNAL NAME:
Open Journal of Philosophy,
Vol.4 No.1,
February
27,
2014
ABSTRACT: This paper is divided into three parts. In the
first part, we review the historical background of a system
of logic devised by Henry S. Leonard to allow for reasoning using existence as
a predicate. In the second part, we consider various directions
in which his logic could be further developed, syntactically, semantically, and
as an adjunct to quantifier elimination and set theory. In the third and final
part, we develop proofs of some underlying results of his logic, using modern
notation but retaining his axioms and rules of inference.