writing sample submitted
Feb. 7th, 2007 04:44 pmI just submitted Ch. 8 of my Master's thesis as a writing sample. To give my readers more background, I wrote the following:
This seems interesting:
Pearce, Rantala - Approximative Explanation is Deductive-Nomological
Background for the Writing Sample
The following writing sample is a chapter taken from my Master's thesis, which I wrote in Amsterdam in 2005.
The idea was to create a corpus of scientific derivations (taken from undergraduate textbooks) in the form of derivation trees, and use that corpus to create problem-solving AI that is simultaneously a cognitive model of scientists who have that set of "puzzle solutions" in their mind.
The central idea of the thesis was to model scientists' reuse patterns. A result can be seen as a "chunk", a memoized consequence of a set of higher-level laws (and model-specific conditions). If the goal of scientific explanation is to link hypotheses to higher-level laws (as in the Deductive-Nomological (DN) view), then the reuse of a previously-seen result is a shortcut: that path has already been traced for us. Why bother proving a lemma that has been proven before?
This is analogous to my advisor's research area, Data-Oriented Parsing (DOP), in which analyses of natural language utterances are memoized (chunks are subtrees of parse trees). DOP has a number of interesting properties, including the ability to model chunk salience and extra-grammatical utterances. Are extra-grammatical utterances analogous to deviations from strictly DN derivations (i.e. derivations that use approximations, fudge factors, etc.)? This was one of the main questions I investigated.
My thesis was a failed attempt to apply DOP to the domain of scientific reasoning. While language behavior (production and interpretation) can be said to reuse previously-seen subtrees as chunks, the same is not the case for derivation trees: scientists do not need to know how a lemma was proven in order to use it. While language approximately obeys the principle of compositionality (the meaning of the whole is a function of the meaning of its parts), the same in not true for derivations.
Furthermore, given the nature of the task, I was unable to get a decent-sized corpus with which to estimate usage frequencies for scientific results, let alone evaluate the resulting system. Nevertheless, the thesis contains significant work on equational reasoning and formalization of physics.
This chapter focuses on issues of how to best formalize textbook derivations. It proposes a strong ontology, e.g. “(force gravitational Earth Moon)” instead “F_moon”, which enables the further formalization steps of adding preconditions (formalized as predicates) to formulas, representing constraints given by the model; and tagging axioms with the theory that they came from.
Gustavo Lacerda
This seems interesting:
Pearce, Rantala - Approximative Explanation is Deductive-Nomological