<?xml version="1.0" standalone="yes"?>
<Paper uid="J89-2004">
  <Title>Technical Correspondence On the Logic of Category Definitions ON THE LOGIC OF CATEGORY DEFINITIONS</Title>
  <Section position="2" start_page="0" end_page="0" type="ackno">
    <SectionTitle>
ACKNOWLEDGMENTS
</SectionTitle>
    <Paragraph position="0"> This paper was written while I was at the Centre for Cognitive Science in Edinburgh. I wish to thank Jaap van der Does for encouraging me to write this proof down and for proofreading it. I also wish to thank G. Gazdar for remarks on an earlier version of the paper and an anonymous referee for further suggestions.</Paragraph>
  </Section>
  <Section position="3" start_page="0" end_page="0" type="ackno">
    <SectionTitle>
NOTES
</SectionTitle>
    <Paragraph position="0"> 1. Unfortunately, they do not distinguish between the language Lc and the logic, which defines a subset of that language, namely the set of its theorems. We make this distinction here by calling the logic as well as the set of theorems it defines A c.</Paragraph>
    <Paragraph position="1"> 2. We define a logic as a set of rules, which are pairs A&amp;b, where A is the set of premises of that rule and ~b its consequence. Modus Ponens thus takes the form ~b,~b ~ ~/~. Rules are closed under substitution. Axioms are rules because we can take A = 0. The modal fragment of A c is then simply the subpart of rules that only involve modal formulas, i.e. no type 1 features.</Paragraph>
    <Paragraph position="2"> 3. Remember that type 1 features take propositions as values, whereas type 0 features only take atoms.</Paragraph>
  </Section>
class="xml-element"></Paper>