Modelling Scientific Problem Solving by DOP

Modeling Scientific Problem Solving by DOP Rens Bod (rens@science.uva.nl) Institute for Logic, Language and Computation University of Amsterdam, and School of Computing, University of Leeds Plantage Muidergracht 24, 1018 TV Amsterdam, NL Abstract This paper deals with the problem of derivational redundancy in science, i.e. the problem that there can be extremely many different explanatory derivations for a phenomenon, while students and experts tend to come up with only one derivation. Given the remarkable agreement among humans in deriving phenomena, we need to have a story of how to select from the space of possible derivations of a phenomenon the derivation that humans come up with. In this paper we argue that the problem of derivational redundancy can be solved by a notion of shortest derivation , by which we mean the derivation that can be constructed by the fewest (and therefore largest) partial derivations of previously derived phenomena that function as exemplars . We show how a model of exemplar-based reasoning, known as DOP, can be used to select the shortest derivation. We evaluate DOP on a corpus of phenomena from classical and fluid mechanics that were derived by fourth-year physics students, showing that the shortest derivation closely corresponds to the derivations that humans construct. Keywords: Problem Solving; Exemplar-Based Reasoning; Derivational Redundancy; Case-Based Reasoning; Data - Oriented Parsing; Philosophy of Science; Physics. 1 Introduction This paper deals with the problem of derivational redundancy, i.e. the problem that there can be extremely many different explanatory derivations for a phenomenon while students and experts tend to come up with only one and the same derivation for a phenomenon. Given this remarkable agreement among students, we need to have a story of why humans focus on one derivation and not on others. In this paper we shall argue that the problem of derivational redundancy can be solved by a notion of shortest derivation . By the shortest derivation of a phenomenon we mean the derivation that can be constructed by the fewest (and therefore largest) partial derivations of previously derived phenomena that function as exemplars . The idea that natural phenomena can be explained by modeling them on exemplars is usually attributed to Thomas Kuhn in his account on “normal science” (Kuhn 1970). Kuhn urges that exemplars are concrete problem solutions that students encounter from the start of their scientific education (ibid. p. 187) and that scientists solve puzzles by modeling them on previous puzzle- solutions (ibid. p. 189). Instead of explaining a phenomenon from scratch, Kuhn contends that scientists try to match the new phenomenon to one or more previous phenomena-plus-explanations. In similar vein, Philip Kitcher argues that new phenomena are derived by using the same patterns of derivations ( argument patterns ) as used in previously explained phenomena: Science advances our understanding of nature by showing us how to derive descriptions of many phenomena, using the same patterns of derivation again and again (Kitcher 1989, p. 432). Different from Kuhn, Kitcher proposes a rather concrete account of explanation, known as the unificationist view , which he still links to Kuhn's view by interpreting exemplars as derivations (ibid. pp. 437-8). Yet, we will argue in section 3 that Kitcher’s account does not solve the problem of derivational redundancy. Thomas Nickles relates Kuhn's view to Case-Based Reasoning (Nickles 2003, p. 161). Case-Based Reasoning (CBR) is an artificial intelligence technique that stands in contrast to rule-based problem solving. Instead of solving each new problem from scratch, CBR stores previous problem-solutions in memory as cases. When CBR begins to solve a new problem, it retrieves from memory a case whose problem is similar to the problem being solved. It then adapts the example's solution and thereby solves the problem. CBR has been instantiated in many different ways and has been used in various applications such as reasoning, learning, perception and understanding (cf. Carbonell 1986; Falkenhainer et al. 1989; Kolodner 1993; Veloso and Carbonell 1993; VanLehn 1998). However, none of these instantiations specifically addresses the problem of massive derivational redundancy. An instantiation of CBR that does address the problem of derivational redundancy, albeit in a different domain, is Data-Oriented Parsing (DOP). DOP is a natural language processing technique that provides an alternative to rule-based language processing. It analyzes new sentences by modeling them on analysis-trees of previous sentences (Bod 1998; Scha et al. 1999; Collins and Duffy 2002). DOP operates by decomposing the given trees into “subtrees” and recomposing those pieces to build new trees. When a sentence has more than one possible analysis or interpretation -- which is the typical case in natural language -- DOP selects the analysis-tree that is constructed by the “shortest derivation”, which is the tree consisting of the fewest (and therefore largest) subtrees from previous trees (Bod 2000). DOP has been highly successful in solving syntactic and semantic redundancy (“ambiguity”) in natural language understanding (see Manning and Schutze 1999; Bod et al. 2003). In Scha et al. (1999) it is shown how DOP can be defined as an instantiation of CBR. In the current paper we argue that DOP can also be used for solving derivational redundancy in physics. The DOP approach may be particularly suitable to tackle the redundancy problem because of the analogy between explanatory derivations in physics and tree structures in linguistics and logic. If we can convert explanatory derivations into trees, we can directly apply the DOP approach to the redundancy problem. That is, when a phenomenon has more than one derivation tree, DOP proposes to select the tree that can be constructed by the fewest subtrees from trees of previously derived phenomena.