Research

My active areas of research include the following, much of which can be characterized as Logic in Computer Science.

• Finite Model Theory & Descriptive Complexity
• The use and application of Abstract State Machines
• Logic Programming Semantics

I'm hoping to use my results here to create a new method of static source code analysis, allowing developers to more quickly and easily reason about large code bases.

Other areas of research which are active, but not primary, include:

• Philosophy of language with formal semantics à la Montague and Hogan semantics.
• Notions of intentional algorithmic equivalence

Applicable:

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

-- Ludwig Wittgenstein (with a shameless modification of my own)

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 endeavors shortly, as I'm currently busy finalizing my PhD!

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.

More is forthcoming.

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.

History of my Research Interests

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!?

After that, I began researching various areas of mathematical foundations and the foundations of computation. In 2006 I came upon the areas of Finite Model Theory and Descriptive Complexity. Since then my research has focussed on these areas, with application in formal methods.