Research

Throughout my undergraduate degree in computer science, I was fascinated with the then-buzz-field of artificial intelligence, and focussed on courses in these areas. Specifically, I was most interested in “organic” approaches to AI, including approaches using neural networks, cellular automata, genetic algorithms, and various biomoriphic approaches. My undergraduate senior design project SapioGo won the 2005 Senior Deisgn Project of the Year award for Computer Science.

My interests changed dramatically in 2004 after taking a Mathematical Logic course sequence, and I became more interested in formal approaches and, ultimately, logic in general... who doesn't find the Löwenheim-Skolem theorm, Skolem's “paradox”, and Gödel's theorems utterly fascinating when they first hear them!?

The limits of my language mean the limits of my world.

Current Research

As a graduate student, I've spent much of my time working in the areas of finite model theory & descriptive complexity, and more recently, evolving algebras and abstract state machines (ASMs)

I'll post more about my current endeavers shortly.

Other Research Interests

In addition to the above, I'm interested in the philosophy of language, specifically Montague semantics and other formal approaches (including “Hogan”-semantics).

Materials

Publications

• “Unfounded Sets and Autarkies,” a presentation accepted to LaSh during FLoC 2006 (16 August 2006), by John Schlipf and Ryan Flannery.
  Download: autarkies.pdf.

Studies in Logic Notes

After completing the Mathematical Logic course sequence in 2004, my good friend Neal Hogan and I spent the Summer reading about various foundational areas and put together the following set of notes.

Mathematical Logic & Model Theory

• Soundness and Completeness for Propositional Logic notes (by John Schlipf)
  Download: latex, dvi, ps, pdf.
• Σ₁ & Π₁ Definability, Recursiveness, and Incompleteness (by John Schlipf)
  Download: latex, dvi, ps, pdf.
• Incomplete! Herbert Enderton's A Mathematical Introduction to Logic, selected topics from Chapters 2 and 4 (by Ryan Flannery)
  Download: latex, dvi, ps, pdf.

Zermelo Frankel Set Theory

• Keith Devlin's The Joy of Sets Chapter 2, the Zermelo-Fraenkel Axioms (by Ryan Flannery)
  Download: latex, dvi, ps, pdf.
• Keith Devlin's The Joy of Sets Chapter 3, Ordinal and Cardinal Arithmetic (by Neal Hogan)
  Download: latex, dvi, ps, pdf.
• Keith Devlin's The Joy of Sets Chapter 5, the Axiom of Constructibility (by Ryan Flannery)
  Download: latex, dvi, ps, pdf.
• This paper outlines Gödel's half of the proof that GCH is undecidable in ZF Set Theory (by Ryan Flannery)
  Download: latex, dvi, ps, pdf.

Lambda Calculus

• Alonzo Church's The Calculi of Lambda Conversion (by Ryan Flannery)
  Download: latex, dvi, ps, pdf.
• H.P. Barendregt's The Lambda Calculus Chapters 1 through 5 (by Neal Hogan)
  Download: latex, dvi, ps, pdf.

Various Topics

• Dana Scott's A Mathematical Theory of Computation (by Neal Hogan)
  Download: latex, dvi, ps, pdf.
• Incomplete! Alfred Tarski's Concept of Truth in Formalized Languages (by Ryan Flannery)
  Download: latex, dvi, ps, pdf.