Aspects of the Logical Structure of Conceptual Analysis

Aspects of the Logical Structure of Conceptual Analysis Sourabh Niyogi MIT Cambridge, MA 02139 niyogi@mit.edu Abstract Patient, Perceiver passive, Phenomenon, etc. are unex- plained primitives with few constraints on their gener- ation (Fodor 1998, Newmeyer 1998). If the semantics problem is kicked upstairs, it is unclear what, exactly, is being accomplished. Modern day lexical databases are not constructive, but differential (Miller et al 1990). We outline the logi- cal structure of the task of a conceptual analyst who wishes to construct a constructive lexicon based on a Universal Theory Model of Concepts. Elementary no- tions of descriptive and explanatory adequacy are devel- oped within this model. The diverse streams of evidence available for the conceptual analyst to engage in empir- ical inquiry are reviewed in the domains of light and perception. Theories for Constructive Lexicons In this paper, we consider the task of the conceptual analyst who wishes to construct a theory-based lexicon that is constructive rather than differential. By a theory- based lexicon, we mean a lexicon based on a technical explication of the traditionally nebulous “theory theory” (Gopnik and Meltzoff 1997, Carey 1991). Recent devel- opments suggest that a technical explication of what is meant by “theory theory” is tractable (c.f. Gopnik et al 2003, Niyogi 2005). The simplest model of this is dia- grammed in Figure 1, which I call the Universal Theory Model of Concepts. Via a set of primitives and experi- ence, a Theory Acquisition Device (TAD) acquires some theory T ∗ , an explicit representation that attempts to explain the law-like regularities of domains and entities hypothetical and of the world. The TAD yields person P’s “naive theory”; If P’s TAD outputs T ∗ , then T ∗ is P’s theory, and generates the possible internal states his mind may have of a set of observable and unobserv- able variables in various domains. A concept generator G, applied to T ∗ , generates a hypothesis space of word meanings G(T ∗ ). Then, a Vocabulary Acquisition De- vice uses experience and G(T ∗ ) to output lexicon L. Major projects have been conducted for centuries to record, in one form or another, representations of word meanings. This has been in the form of the lexicogra- pher’s dictionary or the more modern computational lin- guist’s electronic databases (WordNet, FrameNet, Verb- Net) e.g. last year’s symposium (Miller, Fillmore, Palmer, Lenat and Hayes 2004). The degree to which computational linguists and cognitive scientists draw upon these resources as accurate descriptions of lexical knowledge is astonishing. Researchers speak of “putting meaning in your trees”, providing “deep semantics”, au- tomatically labeling “semantic roles”, or using Word- Net as the authority for word sense disambiguation, to name some key projects. (Palmer et al 2002, Fillmore et al 2001, Gildea and Jurafsky 2002) Given the increas- ing reliance to these databases, it may appear that the terms meaning and semantic are not being used glibly and that the theoretical foundations of these databases were sound. Even the most cursory analysis shows that this is not so. Consider the distinction made by the originators of WordNet between a constructive vs. differential lex- icon: In a differential theory of the lexicon, meanings can be represented by any symbols that enable a theo- rist to distinguish among them; In a constructive theory of the lexicon, the representation should “contain suffi- cient information to support an accurate construction of the concept (by either a person or a machine)” (Miller et al 1990). Today’s dictionaries and all of today’s lexi- cal databases are differential: the intension of synsets of WordNet are just sufficient so that someone who already knows English can distinguish among synsets, while the thematic roles used in VerbNet and FrameNet are noto- riously difficult to define: primitive terms such as Agent, For example, recall the well-known observaton that children, when probed indirectly for the meaning of uncle at one stage (T1), thinks it means “friendly middle aged men”, and when probed at a later stage (T2), thinks it refers to a “parent’s sibling” (Keil 1989). The standard explanation is the child at T1 does not have the kinship framework that the child at T2 has. In this UT model, T1 and T2 are two possible states T ∗ of the TAD (all else held constant). In L, the word uncle is mapped to an element of the set G(T 1) when T ∗ = T 1, and then mapped to an element of the set G(T 2) when T ∗ = T 2. This theory acquisition device (TAD) has an initial state T ∗ (t = 0), and a set of possible states it may as- sume. The theory of the initial state of TAD, we will call Universal Theory (UT), analogous to Universal Gram- mar (Chomsky 1981). UT constrains the set of possible states that the TAD can be in. The TAD state may evolve to improve on the generative model, given either observations in the domain or by mental fiat.