16 - Reasoning in Conceptual Spaces
Published online by Cambridge University Press: 05 June 2012
Summary
Three levels of modeling reasoning
Processes of reasoning have been at the heart of analysis in analytic philosophy, artificial intelligence (AI) and in the early development of cognitive science. In these traditions, reasoning has been modeled as operations on propositions that are expressed by symbolic structures. I will call this approach the symbolic paradigm.
The central tenet of the symbolic paradigm is that representing and processing information essentially consists of symbol manipulation according to explicit rules. For example, Pylyshyn (1984: 29) writes: “[T]o be in a certain representational state is to have a certain symbolic expression in some part of memory.” The symbols can be concatenated to form expressions in a language of thought (Fodor 1975), which is sometimes called Mentalese. The content of a sentence in Mentalese is a belief or a thought of an agent. The different beliefs in the cognitive states of a person are connected via their logical or inferential relations. Thus, the manipulations of symbols are performed without considering the semantic content of the symbols. In applications within AI, first-order logic has been the dominating inferential system (or some related programming version of it, such as Prolog). But in other areas more general forms of inference, like those provided by inductive logic or decision theory, have been utilized.
The symbols are used for modeling logical inferences and the expressions represent propositions, which stand in various logical relations to each other. Information processing involves above all computations of logical consequences.
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- ReasoningStudies of Human Inference and its Foundations, pp. 302 - 320Publisher: Cambridge University PressPrint publication year: 2008
References
C. Balkenius and P. Gärdenfors (1991): “Nonmonotonic inferences in neural networks,” in Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, , and , eds., Morgan Kaufmann, San Mateo, CA, 32–39.Google Scholar
, , , and (1974): “Comprehension and semantic flexibility,” Journal of Verbal Learning and Verbal Behavior 13, 471–481.CrossRefGoogle Scholar
L. W. Barsalou (1987): “The instability of graded structure: Implications for the nature of concepts,” in Concepts and Conceptual Development, , ed., Cambridge University Press, Cambridge, 101–140.Google Scholar
L. W. Barsalou (1992): “Flexibility, structure, and linguistic vagary in concepts: Manifestations of a compositional system of perceptual symbols,” in Theories of Memory, , , , and , eds., Lawrence Erlbaum Associates, Hillsdale, NJ, 29–89.Google Scholar
and (1969): Basic Color Terms: Their Universality and Evolution. University of California Press: Berkeley, CA.Google Scholar
(1983): Procedures for Learning Syntactic Structure: A Model and West with Artificial Grammars, doctoral dissertation, University of Michigan.Google Scholar
and (1996): “Unsupervised concept learning and value systematicity: A complex whole aids learning the parts,” Journal of Experimental Psychology: Learning, Memory and Cognition 22, 458–475.Google Scholar
(1994): The Role of Metaphor in Cognitive Semantics, Lund University Cognitive Studies 31, Lund.Google Scholar
R. Carnap (1971): “A basic system of inductive logic, Part 1,” in and , eds., Studies in Inductive Logics and Probability, Vol. 1, University of California Press, Berkeley, CA, 35–165.Google Scholar
(1998): Concepts: Where Cognitive Science Went Wrong, Clarendon Press, Oxford.CrossRefGoogle Scholar
, , and , eds. (1993): Handbook of Logic in Artificial Intelligence and Logic Programming, Volume III: Non-Monotonic and Uncertain Reasoning, Oxford University Press, Oxford.Google Scholar
and (1966): “Relation of cue to consequences in avoidance learning,” Psychonomic Science 4, 123–124.CrossRefGoogle Scholar
(1990a): “Induction, conceptual spaces and AI, ” Philosophy of Science 57, 78–95.CrossRefGoogle Scholar
(1990b): “Frameworks for properties: Possible worlds vs. conceptual spaces,” in Language, Knowledge and Intentionality, , , and , eds. (Acta Philosophica Fennica, 49), 383–407.Google Scholar
P. Gärdenfors (1992): “A geometric model of concept formation,” in Information Modelling and Knowledge Bases III, et al., eds., IOS Press, Amsterdam, 1–16.Google Scholar
P. Gärdenfors (1993): “Induction and the evolution of conceptual spaces,” in Charles S. Peirce and the Philosophy of Science, , ed., The University of Alabama Press, Tuscaloosa, 72–88.Google Scholar
P. Gärdenfors (1994): “Three levels of inductive inference,” in Logic, Methodology, and Philosophy of Science IX, , and , eds., Elsevier Science, Amsterdam, 427–449.Google Scholar
P. Gärdenfors (2004): “How to make the Semantic Web more semantic,” pp. 19–36 in Formal Ontology in Information Systems, ed. by and , IOS Press.Google Scholar
P. Gärdenfors (2007): “Representing actions and functional properties in conceptual spaces,” in Body, Language and Mind, and , eds., Benjamins, Amsterdam, 167–195.Google Scholar
and (1994): “Nonmonotonic inference based on expectations,” Artificial Intelligence 65, 197–245.CrossRefGoogle Scholar
and (2001): “Reasoning about categories in conceptual spaces,” Proceedings of IJCAI 2001, Morgan Kaufmann, Palo Alto, 385–392.Google Scholar
(2000): “Properties of inductive reasoning,” Psychonomic Bulletin and Review 7, 569–592.CrossRefGoogle Scholar
(1965): Aspects of Scientific Explanation, and Other Essays in the Philosophy of Science, Free Press, New York.Google Scholar
, , and (1986): Induction: Processes of Inference, Learning, and Discovery, MIT Press, Cambridge, MA.Google Scholar
and (2007): “Language structure: Psychological and social constraints,” Synthese 159, 99–130.CrossRefGoogle Scholar
(1993): Inductive Inference and Its Natural Ground: An Essay in Naturalistic Epistemology, MIT Press, Cambridge, MA.Google Scholar
W. Labov (1973): “The boundaries of words and their meanings,” in New Ways of Analyzing Variation in English, , ed., Georgetown University Press, Washington, DC, 340–373.Google Scholar
(1987): Women, Fire, and Dangerous Things, University of Chicago Press, Chicago.CrossRefGoogle Scholar
(1987): Foundations of Cognitive Grammar, Vol. 1, Stanford University Press, Stanford, CA.Google Scholar
W. T. Maddox (1992): “Perceptual and decisional separability,” in Multidimensional Models of Perception and Cognition, , ed., Lawrence Erlbaum Associates, Hillsdale, NJ, 147–180.Google Scholar
and (1991): “Floating conclusions and zombie paths: Two deep difficulties in the ‘directly skeptical’ approach to defeasible inheritance nets,” Artificial Intelligence 48, 199–209.CrossRefGoogle Scholar
and (1978): “Representation and recognition of the spatial organization of three-dimensional shapes,” Proceedings of the Royal Society in London, B 200, 269–294.CrossRefGoogle Scholar
R. D. Melara (1992): “The concept of perceptual similarity: From psychophysics to cognitive psychology,” in , editor, Psychophysical Approaches to Cognition, Elsevier, Amsterdam, 1992, 303–388.Google Scholar
and (1981): “Categorization of natural objects,” Annual Review of Psychology 32, 89–115.CrossRefGoogle Scholar
(1993): “Natural predicates and the topological structure of conceptual spaces,” Synthese 95, 219–240.CrossRefGoogle Scholar
and (1980): Human Inference: Strategies and Shortcomings of Social Judgement, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
, , , , and (1990): “Category-based induction,” Psychological Review 97, 185–200.CrossRefGoogle Scholar
S. E. Palmer (1978): “Fundamental aspects of cognitive representation,” in Cognition and Categorization, and , eds., Lawrence Erlbaum Associates, Hillsdale, NJ, 259–303.Google Scholar
C. S. Peirce (1932): Collected Pappers of Charles Sanders Peirce, volume II, Elements of Logic. and , eds., Harvard University Press, Cambridge, MA.Google Scholar
(1969): “Natural kinds,” in Ontological Relativity and Other Essays, Columbia University Press, New York, 114–138.Google Scholar
(2001): “Necessity and natural categories,” Psychological Bulletin 127, 827–852.CrossRefGoogle Scholar
(1975): “Cognitive representations of semantic categories,” Journal of Experimental Psychology: General 104, 192–233.CrossRefGoogle Scholar
E. Rosch (1978): “Prototype classification and logical classification: The two systems,” in New Trends in Cognitive Representation: Challenges to Piaget's Theory, , ed., Lawrence Erlbaum Associates, Hillsdale, NJ, 73–86.Google Scholar
(1982): “The concept of observation in science and philosophy,” Philosophy of Science 49, 485–525.CrossRefGoogle Scholar
, , , and (1988): “Combining prototypes: A selective modification model,” Cognitive Science 12, 485–527.CrossRefGoogle Scholar
(1988): “On the proper treatment of connectionism,” Behavioral and Brain Sciences 11, 1–23.Google Scholar
(1983): “From shapes and movements to objects and actions,” Synthese 54, 3–36.CrossRefGoogle Scholar
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