University of Washington

Graduate Student, Linguistics

Undergraduate Researcher

Arts and Sciences

About

Please also see my CV to the left.

Research Interests Summary

General:
    cognitive science, formal philosophy, analytic theology

    Cognitive Science: issues that arise when a human and
    computer team up to represent the meaning of a text
    and reason about what is said
   
    Formal philosophy: How methodologies from cognitive
    science can augment philosophical inquiry
   
    Analytic Theology: How might theological inquiry
    likewise benefit methodologically from cognitive science

Specific:
    computational semantics, automated reasoning,
    functional programming, ancient Hebrew and Greek
    linguistics

Statement

Past Research

The primary area of research I pursued at the University of Kentucky was the computational modeling of morphology. I was fortunate to have access to faculty at UK with expertise in this area. Dr. Andrew Hippisley at UK has expertise in the DATR programming language and instructed me on how to use it. DATR uses default inheritance to model relations between inflection classes and generates the language’s paradigms as theorems of the model. It is a nice tool to reduce the redundancy in one’s grammar and to capture regularity and irregularity. It also makes it necessary to be explicit, and the generation of theorems allows one to refine the theory against mistaken conjectures.

During my summer research, I was able to design a working model of the Classical Greek noun system including 24 classes of nouns in a hierarchical default inheritance theory. Through that work, I was able to capture some interesting theoretical insights. The shape of my theory shows a completely different view of the organization of Greek nouns. While traditional Greek pedagogy has the nouns grouped into three declensions, my theory has seven nodes in a treelike hierarchy. At the top, one generic noun node is the root of three branches, each containing a mother and daughter node. The first branch holds the first and second declensions where second declension is a daughter of first declension. My second and third branch split the traditional third declension in two.

Later on I began work on a second theory in Ancient Greek verbs. This theory is not as fully developed as the first, but did yield some interesting results. Both of my Greek morphology projects were supported by the school.

Logic is another area of research that I have worked on, though independently. I started with Lewis Carroll’s Symbolic Logic and developed it into an interesting formalism. It is able to capture the Aristotelian system of inference in just a few rules. I also imported some set theoretic and sentential connectives which make it more expressive. Furthermore, I modeled the syllogistic system as a logic circuit and translated that model into a working program that performs syllogistic inference. In the near future, I hope to develop some metatheory about the logic as well. I have also been working on extending the logic to make it capable of capturing inferences based on relations that had been lacking in traditional Aristotelian logic. In the same vein, I am looking at how this makes it possible to pin down the logic of active and passive voice and transitive and ditransitive verbs.

Background and Achievements

Next I will mention some miscellaneous but relevant parts of my education. I worked on Ancient Greek syntax for a term project with feature based grammar in the Python Natural Language Toolkit. For a semantics project, I wrote a program to generate combinations of tense, aspect, and mood to test English speakers’ intuitions. I wrote a program in J (a descendent of APL) which generated random graphs for an SAT graph coloring experiment for my logic and theory of computation class. Throughout my time at UK, I have worked with python, perl, C++, J, PHP, and have some experience with haskell and prolog. I have studied two semesters of calculus and am currently in a course on linear algebra. I’m also taking a class on statistics and probability and one on databases. I’ve taken four courses where logic or proof is a major part of the course, and I’m currently in the second semester symbolic logic course. In Philosophy, I’ve had ancient and medieval philosophy, ethics, an epistemology seminar, and currently a metaphysics and epistemology class. I’ve had an array of linguistics courses (my major). I have studied Spanish, French, and Ancient Hebrew and Greek. During my time at UK I have taken course loads from 14 to 19 hours. I have maintained an almost perfect grade point average throughout, achieving induction into the Phi Beta Kappa honor society. Now I’m on track to graduate summa cum laude in August. Moreover, I was awarded three competitive scholarships, two of which were for research.

Future Research

The next section outlines some ideas about my future research directions. Since I have listed a broad range of interests, I’d like to mention here what would be my focus if I were asked to narrow it down to the essential parts. In essence, I wish to develop technology which assists the user to take syntactically annotated linguistic corpora, compositionally capture semantic representations from them, utilize automated reasoning to draw out implicit knowledge from the texts, and store and organize the knowledge in databases. In short, I’d like to compute at the semantics-reason interface.

Logic, Linguistics, and Computer Science

The two types of cognition I am most interested in are linguistic meaning and reasoning. One of my most important interests is in the usefulness of logic as a tool across approaches to linguistics, programming languages, and reasoning. I am particularly interested in certain types of logic commonly associated with programming language theory such as type theory, category theory, lambda calculus, and combinatory logic. In addition to providing a basis for programming languages, these mathematical theories are utilized in grammatical formalisms, logics for automated reasoning, and natural language semantics.

Here are a few examples of these applications. Lambda calculus is the source of such programming languages as Lisp and also is central to the Montague paradigm of formal linguistic semantics. Type theory is likewise at the foundation of many programming languages, notably Haskell, and also the grammatical formalism type logical grammar. Type theory is also useful for logical frameworks, such as Twelf, which are used to implement logics in automated reasoning software and to reason about the metalogical properties of those logics. Combinatory logic is similarly used in programming languages and is also incorporated in the combinatory categorial grammar formalism. Category theory is foundational to the Maude programming language which is a logical framework, and category theory also plays a role in the Lambek calculus grammatical formalism.

I find it fascinating that there is a small set of related mathematical tools that have such wide ranging application in modeling and augmenting human cognitive functions. What I am curious about is to investigate what makes this connection so fruitful and to exploit the connection as a methodology for forging tools for computing at the syntax-semantics-reason interface. Hopefully this will also give us new insight into the mind; it might also result in more natural programming languages.

In addition to focus on the grammatical formalism, I am also interested in approaches to semantics which focus on the logical formalism. Natural logic, for instance, was developed with natural language semantics in mind and has metalogical appeal in addition. Moreover, there are many logics of interest for semantics other than first order logic: temporal, modal, and intentional, for instance. A major part of my inquiry is to develop logics that more closely mirror features of natural language, test them for metalogical properties, and implement them in automated and interactive deduction systems.

I also wish to complement these logic based interests with other methodologies, specifically probabilistic, statistical approaches to NLP and machine learning. These interest me for more than one reason. For one thing, statistical NLP is known to be a successful approach in such applications as machine translation. For another, it will give me an inductive perspective on the cognition of language to complement my marked deductive focus. Hybrid methodologies like Markov logic are also attractive to me.

Philosophy

I’d like to investigate how metaphysical doctrines affect logic and semantic theory.[i] How does one’s view of possible worlds affect the way one thinks about modality in natural language? How does the philosophy of time affect the way one thinks about tense and aspect? The question for me then becomes whether any adjustments make computing meaning more feasible.

Automated reasoning is a natural companion to philosophy. Logical argumentation has always been an ideal in philosophy, but the modern computer greatly augments the modeling and proving capabilities of humans. One particularly interesting application is axiomatization and theory building in metaphysics. The Stanford Computational Metaphysics Lab has been pursuing similar work for some time. It is also interesting to me to look into the formalization of scientific theories.  Automated reasoning can be used to develop such theories from axioms, check the theory for consistency, make predictions, and identify unconscious assumptions.[ii] Such modeling has the advantage of forcing us to make our claims explicit, and it makes us more able to confirm that our theories do work. Automated reasoning techniques can also work in cooperation with computational semantics in philosophy.

Computational semantics applications include modeling the semantics of paradoxes or analyzing historical and contemporary texts in philosophy to model the arguments and theories of their authors. Beginning with a logical model of, e.g., Plato's theory of forms, one can then draw out inferences and prove theorems with the aid of a computer.

Religious Informatics

I am interested in applying my skills as linguist, philosopher, computer and cognitive scientist to advance the state of the art in religious informatics. It is a very important task among religious communities to interpret their sacred texts using the very best tools. On one hand, modern tools of cognitive science are not very widely used in theology and biblical studies to my knowledge. On the other, interest has been increasing in the recent years. I will mention a few examples. Matthew O’Donnell published his important book on the use of corpus linguistics for the Greek New Testament.[iii] Logos Bible Software is being a catalyst for innovation by hosting the annual Bible Tech conference. Moreover, there is a new interest in academia for the adoption of a more analytic as opposed to continental mode of methodology in theology. The Templeton Foundation awarded a large grant to Dr. Michael Rea of Notre Dame Philosophy to further research in analytic theology. It would seem that computer aided analysis of the semantics and logic of sacred texts fits well with those aims.

Thus, in accord with these trends, I propose a computational theology, a type of religions informatics. In my conception, theology is a foundational subset of a comprehensive Christian philosophy. I take inspiration mainly from Dr. Gordon Clark in this regard. At this point, all my interests converge. I endeavor to utilize techniques described above to mine and model the Christian system of thought based on the statements, i.e., the axioms, in the Biblical corpus. Computational theology is, perhaps, what Augustine would have done if there had been computers in his day: seeking answers to philosophical questions that cohere with Scripture and using computers to augment his capabilities.

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  [i] For an example of some contemporary work in this area, see Peter Ludlow,  Semantics, Tense, and Time: An Essay in the Metaphysics of Natural Language, Cambridge, Mass: MIT Press, 1999.
  [ii] See Jaap Kamp, A Logical Approach to Computational Theory Building with Applications to Sociology, in ILLC Dissertation Series, Amsterdam: 2000. Retrieved from: http://staff.science.uva.nl/~kamps/publications/2000/kamp:logi00.pdf , accessed Feb 15, 2011.
  [iii] Matthew Brook O'Donnell, Corpus Linguistics and the Greek of the New Testament, Sheffield: Sheffield Phoenix Press, 2005.



I also enjoy electronic music and talking about nothing.

Try out my personal station on Last.fm:

http://j.mp/ga6P28

I presented at the Bible Tech 2010 and 2011 conferences:

http://www.bibletechconference.com/speakers.htm

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