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• W2775974727 abstract "Componential Explanation in Philosophy, Cognitive Science and Computer Science Tibor Bosse (tbosse@cs.vu.nl), Catholijn M. Jonker 1 (C.Jonker@nici.ru.nl), Jan Treur 2 (treur@cs.vu.nl) Vrije Universiteit Amsterdam, Department of Artificial Intelligence De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands structured according to a number of aggregation levels. A central role is played by interlevel relations between properties at different levels of aggregation. For example, for a system S with property G that consists of two components A and B that have properties DP1 and DP2, respectively, the implication DP1 & DP2 & T G is an example of an interlevel relation expressing that S has property G in virtue of connectivity T and properties DP1 and DP2 of components A and B. Here the connectivity property T denotes a property that describes the connection or interaction between the components: transfers between the components. Compositional verification analyses properties of systems based on such interlevel relations. In this paper it is explored how the notion of compositional verification developed within Computer Science relates to the notion of componential explanation as developed within Philosophy and Cognitive Science (cf. Cummins, 1975, 1983; Clark, 1997; Davies, 2001), and how it can be used to obtain a formalisation of componential explanation in a more technical sense, opening doors to existing or new software tools to support the explanation process. First the notion of componential explanation is briefly described. Next compositional verification is summarised, and it is shown by a case study on the circulatory system, how the notions relate to each other. Abstract This paper shows how Componential Explanation as discussed within Cognitive Science and Philosophy of Science relates to Compositional Verification in Computer Science. It is shown how formal techniques and methods developed for Compositional Verification provide a formal basis and automated support for Componential Explanation. The role of formalised interlevel relations is shown to be crucial for formalisation of the analysis on which a componential explanation rests. A case study is used to illustrate the thoroughness of the approach. Introduction The notion of componential explanation plays a role in different disciplines such as Philosophy, Biology, Cognitive Science, Computer Science and AI. Roughly spoken, componential explanation describes how properties of a system that is organised according to a number of components, can be explained from properties of the components and their interactions. For componential explanation, Clark (1997) draws the analogy with modelling and analysis methods within AI, referring to, among others, Newell and Simon (1972) and Dennett (1978). 3 He also claims that componential explanation has a role to play in less classical AI areas such as connectionist approaches: in advanced connectionist work, complex tasks require highly structured multi-layer networks. 4 Clark (1997) gives suggestions, but does not address in more detail how to formalise componential explanation. This is the subject of the current paper. To this end methods developed originally in Computer Science are considered. The area within Computer Science in which properties of component-based systems are analysed in terms of properties of their components is called compositional verification; e.g., Roever et al. (1998, 2001), Jonker and Treur (2002). Formalisation and automation are important in the contributions to this area. The considered (software and hardware) systems are assumed to be hierarchically Componential Explanation in Philosophy Hempel (1959) and Nagel (1961) focus on functional explanations why certain items I (such as the heart) are present within an organised system S (e.g., a human being). They base the explanation on an attempted form of deduction, concluding that the item I is necessary in the context of the overall system S (for a certain function F). In this line of reasoning the existence of functional equivalents is problematic: why would another item I' with the same functional contribution F not be possible instead? The dilemma is that: • either functional equivalents exist, then the necessity of the existence of an item cannot be claimed deductively, • or the necessity of the existence of an item can be claimed deductively, but functional equivalents are not allowed. Currently at: Radboud Universiteit Nijmegen, Nijmegen Institute for Cognition and Information, The Netherlands. Part of this work was performed as part of a position at Utrecht University, Department of Philosophy, The Netherlands ‘Modular programming methods in classical AI lent themselves quite nicely to a componential form of explanation. In attempting to understand the success of such a program, it is often fruitful to isolate the various subroutines, modules, etc. and to display their role in dividing the target problem into a manageable series of subproblems.’ Clark, (1997, pp. 104-105) ‘In such cases it is possible to advance our understanding of how the system succeeds by asking after the roles of these gross components (layers and subnets).’ Clark, (1997, p. 105) Hempel (1959) takes the first horn of this dilemma, Nagel (1961) the second one. Hempel’s explanation does not provide a deductive argument. Nagel’s is deductive, but requires a premise excluding the existence of functional equivalents, which is problematic (since there are no laws to derive it). Cummins (1975) avoided this dilemma by a change of perspective. Instead of attempting to obtain a deduction concluding the existence of a certain item I, his deductive analysis A aims at concluding the systemic capacity C of the" @default.
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