SOPhiA 2017
Salzburgiense Concilium Omnibus Philosophis Analyticis
Programme - Talk
Probabilistic Approaches to (Prototype) Concepts
(Affiliated Workshop, English)
he applicability of the classical, definitional view of meaning has long been disputed for common-sense concepts. Especially on the basic and superordinate level of abstraction we find many characteristic, though neither necessary nor sufficient, properties that contribute to the meaning of concepts -- prominent examples being 'can fly' for birds or 'having a peel' for fruit. In the 1970s, Eleanor Rosch and colleagues found that many natural categories are structured along an intersubjectively stable typicality gradient, which was repeatedly shown to influence many psychologically relevant variables (cf. Mervis&Rosch, 1981).
As a consequence, there has been intensive interdisciplinary research on probabilistic representations of concepts. Three general representation formats have been proposed:
(a) probabilistic attribute-value-structures (e.g. Barsalou, 1992, Schurz, 2012),
(b) probabilities in conceptual spaces (e.g. Gärdenfors, 2000), and
(c) association networks (e.g. de Deyne, Storms, 2008).
The workshop is thought of as a platform for presenting and comparing the different approaches and discuss current research projects.
References:
-- Barsalou, Lawrence W. (1992): Frames, Concepts, and Conceptual Fields. In: Kittay, E., Lehrer, A. (ed.): Frames, Fields, and Contrasts: Erlbaum, pp. 21-74.
-- Deyne, Simon de; Storms, Gert (2008): Word associations. Network and semantic properties. In: Behav Res 40 (1), pp. 213-231.
-- Gärdenfors, Peter (2000): Conceptual spaces. The geometry of thought. Cambridge, Mass: MIT Press.
-- Mervis, Carolyn B.; Rosch, Eleanor (1981): Categorization of Natural Objects. In: Annu. Rev. Psychol. 32 (1), pp. 89-115.
-- Schurz, Gerhard (2012): Prototypes and their Composition from an Evolutionary Point of View. In: Wolfram Hinzen, Edouard Machery und Markus Werning (Hg.): The Oxford Handbook of Compositionality: Oxford University Press, pp. 530-554.
Schedule.
09:00--09:50 Annika Schuster & Corina Strößner: Prototype Frames
10:00--10:50 Marta Sznajder: Reasoning with Conceptual Spaces: Towards a Bayesian Model
11:00--11:50 Peter Sutton: Prototypes as Bayesian Networks
12:00--12:50 Simon De Deyne: [TBA]
Abstracts.
Annika Schuster & Corina Strößner (Düsseldorf): Prototype Frames
For most common-sense concepts, no cognitively plausible classical definitions in terms of necessary and jointly sufficient conditions exist. It was argued (e.g. Rosch, Mervis 1975, Hampton 2006) that their meaning is instead constituted by their proximity to a prototype, which is commonly understood as a weighted aggregation of properties of the members of the category to which these concepts refer. The idea put forward in the talk is that prototype concepts are best explicated in terms of recursive attribute-value structures (frames, Barsalou 1992), which decompose properties into (functional) attributes to which values are assigned, allowing for an in-depth analysis of conceptual structure. Relations like structural invariants and constraints represent dependencies between different attributes and their values. There is evidence for the cognitive reality of frames (ibid., 25-27).
In prototype frames, weights are assigned to both attributes and values according to their contribution to the typicality gradient of the category. We propose to base the weights in prototype frames on subjective conditional probabilities as proposed in Schurz 2012. We also use them to quantify constraints, i.e. correlations between values of different attributes. Conditional probabilities reflect the structure of our evolutionary-shaped world, as fitness-contributing properties are found with high statistical probability. Our mind arguably makes use of the observed probability structure in reasoning (Schurz 2007), which makes prototype frames weighted by conditional probabilities a great candidate to explain the cognitive representation of common-sense categories.
Literature:
-- Barsalou, Lawrence W. (1992): Frames, Concepts, and Conceptual Fields. In: Kittay, E., Lehrer, A. (ed.): Frames, Fields, and Contrasts: Erlbaum, pp. 21-74.
-- Hampton, James A. (2006): Concepts as Prototypes. In: Psychology of Learning and Motivation (46), pp. 79?113.
-- Mervis, Carolyn B.; Rosch, Eleanor (1981): Categorization of Natural Objects. In: Annu. Rev. Psychol. 32 (1), pp. 89-115.
-- Schurz, Gerhard (2007): Human Conditional Reasoning Explained by Non-Monotonicity and Probability: An Evolutionary Account. In: Stella Vosniadou (ed.): Proceedings of EuroCogSci07, The European Cognitive Science Conference 2007: Erlbaum, pp. 628?633.
-- Schurz, Gerhard (2012): Prototypes and their Composition from an Evolutionary Point of View. In: Wolfram Hinzen, Edouard Machery und Markus Werning (ed.): The Oxford Handbook of Compositionality: Oxford University Press, pp. 530-554.
Marta Sznajde (Prague): Reasoning with Conceptual Spaces: Towards a Bayesian Model
While many to this day consider Carnapian inductive logic a failed endeavour, it is in fact the case that subsequent developments in Bayesian statistics can be seen as natural continuations of Carnap's program (Skyrms 1996)---a fact that renders it more relevant than it is commonly given credit for. My paper draws on those later developments, while adding a new thread linking Carnap's work with what came after him---this time in cognitive science.
In his Basic System of inductive logic (Carnap 1971, 1980), Carnap proposed to represent the meanings of the predicates used in the prediction setting as multi-dimensional attribute spaces. The predicates familiar from, e.g., his λ-continuum of inductive methods, were now represented as regions in an attribute space. However, Carnap himself did not put his attribute spaces to full use and did not develop a full theory of how the spaces influence degrees of belief.
My aim in this paper is to fill that gap. The additional motivation for the project comes from the fact that geometrical representations of concepts -- this time in the guise of conceptual spaces -- are now used in many applications, ranging from the study of perception to philosophy. At the same time, within the conceptual spaces (Gärdenfors 2000) framework, no model of making inductive predictions (or diachronic reasoning altogether) has been proposed so far.
I will start by introducing the Carnapian attribute spaces and showing how a general approach to modelling inductive reasoning directly on them can be founded on the statistical tools for prediction making in cases of value continuum (Blackwell-MacQueen rules (1973) and their Bayesian counterparts, the Ferguson (1973) distributions). I will then show how we can interpret predicates and observations on the conceptual space, and suggest a Bayesian model for inductive reasoning on conceptual spaces. The hypotheses considered by the agent become probability distributions on the space itself, with individual observations being modelled as its points.
Peter Sutton (Düsseldorf): Prototypes as Bayesian Networks
Bayesian networks are widely used as a means of representing knowledge and inference in psychology and cognitive science. This paper explores whether Bayesian networks can be used to represent of prototype structures. I argue that doing so has two benefits: (1) an account of typicality in terms of computing probabilities of conjunctions across the Bayesian net. For example, P(bird, flies) will be higher than P (bird, ¬flies). This also allows the computation of more subtle distinctions such as: P(bird, coastal_habitat, squawks) > P(bird, coastal_habitat, sings); (2) a means of composing intersective NN compounds that also accounts for challenges associated with such composition such as emergent properties that follows from Bayesian principles. For example, although living in a tank is improbable (i.e. atypical) for a pet and a for a fish, calculating P(lives_in_tank | pet, fish) can be high given that e.g., P(lives_in_house | fish) and P(lives_in_lake | pet) are both very low. Finally, building on recent work by Taylor and Sutton, I discuss whether Bayesian networks can also be used as a means of defining how diagnostic an attribute is as a function of path distance, namely, I will discuss whether, as a rule of thumb, features 'higher up' in a Bayesian network are more diagnostic than those 'lower down'.
Organisation: Annika Schuster & Corina Strößner (HHU Düsseldorf).
Chair: Annika Schuster & Corina Strößner
Time: 09:00-13:00, 13 September 2017 (Wednesday)
Location: SR 1.005
Simon De Deyne
(University of Adelaide, Australia)
Annika Schuster
(HHU Düsseldorf, Germany)
Annika Schuster (M.A.) studied philosophy and linguistic at the University of Düsseldorf, where she is now a research fellow at the institute of theoretical philosophy. Since 2016, she is working on her dissertation on prototype frames in the research group CRC991 ''The structure of representations in language, cognition and science'' under supervision of Gerhard Schurz.
Corina Strößner
(HHU Düsseldorf, Germany)
Dr. Corina Strößner studied Philosophy and Linguistics in Rostock. She received her PhD from the University of the Saarland with a study on statistical and non-statistical semantics of normality statements. As a Post Doc her research interests shifted to the study of concepts and conceptual change. Since 2016, she is research fellow at the DCLPS and works on the subproject ''Frame representations of prototype concepts and prototype-based reasoning'' within the CRC 991: The Structure of Representations in Language, Cognition, and Science.
Peter Sutton
(HHU Düsseldorf, Germany)
Doctorate from King's College London: Vagueness, communication and semantic information (2013), supervised by Shalom Lappin. 2014-present, postdoctoral researcher at HHU Düsseldorf at the Institute of Language and Information. Fields of interest: Probabilistic semantics and pragmatics, vagueness, the philosophy of information, the mass/count distinction, applications of information theory in linguistics.
Marta Sznajder
(Czech Academy of Sciences, Czech Republic)
Marta Sznajder is a postdoctoral researcher at the Czech Academy of Sciences. Her doctoral project, completed in 2017, concerned the links between Carnapian inductive logic and the theory of conceptual spaces. She continues to work on inductive logic, with the focus on concept formation and theory change.
