This paper is part of a broader project whose aim is to present a coherent unified approach to natural language dialogue semantics using tools from type theory. Here we explore aspects of our approach which relate to situation theory and situation semantics. We first point out a relationship between type theory and the Austinian notion of truth. We then… (More)
Language Proof and Logic is available as a physical book with the software included on CD and as a downloadable package of software plus the book in PDF format. The all-electronic version is available from Openproof at...
Chu spaces are a new model for information structure (cf. Their properties are usually developed as a form of category theory. In this note, we show how they may also be viewed as models for a two-sorted first-order language, and we determine the exact flow of information across the natural Chu transforms. Our analysis is akin to that of process graphs via… (More)
All rights reserved iii Acknowledgments There are many people that I would like to thank. First of all, I would like to express my gratitude to my thesis advisor, Larry Moss. His encouragement, enthusiasm, and the countless hours that he spent discussing my work with me have made this thesis possible. In addition, I would like to express special thanks to… (More)
A representation of relation algebras is given by modifying the Routley-Meyer semantics for relevance logic. This semantics is similar to the Kripke semantics for intutionistic logic, but it uses a ternary accessibility relation instead of a binary one. The representation is foreshadowed in the work of Lyndon, as well as by the representation of Boolean… (More)
Brief overview Hyperproof is a Macintosh program designed to help students learn how to reason logically, using either sen-tenccs of first-order logic, or diagrams, or both. 1 An ilhistration of a typical Hyperproof screen is shown in Figure 1. Hyperproofis a descendant of our earlier courseware Tarski's World . Tarski's World uses diagrams to help teach… (More)
erations, I take it, severely shake the relevance of C&H's example. But even if these considerations prove to be on the wrong track, the following point still can be made: given the important dialectical role the example plays, the conclusion they want to draw is simply jeopardized without more being said in order to rule out the considerations mentioned. I… (More)
Surrogate reasoning is reasoning whose task is partially taken over by operations on external aids, such as sentences, diagrams, physical models , mathematical models, and computers. Drawing on the basic concepts in situation theory, we present a semi-formal model of surrogate reasoning. We claim that the relative advantages and disadvantages of different… (More)