The interpretation of classically quantified sentences: A set-theoretic approach

Cognitive Science

Volumn 30, Issue 4, 2006, Pages 691-723

  Politzer, Guy ^a   Van der Henst, Jean Baptiste ^a   Delle Luche, Claire ^b   Noveck, Ira A ^a  

^a CNRS   (France)

^b UNIVERSITÉ LUMIÈRE LYON 2   (France)

Author keywords

Conversion; Human experimentation; Knowledge representation; Language understanding; Linguistics; Logic; Pragmatics; Psychology; Quantifiers; Representation; Semantics; Set diagrams

Indexed keywords

EID: 33748880973     PISSN: 03640213     EISSN: None     Source Type: Journal    
DOI: 10.1207/s15516709cog0000_75     Document Type: Article

References (55)

1. Begg, I., & Denny, J. P. (1969). Empirical reconciliation of atmosphere and conversion interpretations of syllogistic reasoning errors. Journal of Experimental Psychology, 81, 351-354.
2. Begg, I., & Harris, G. (1982). On the interpretation of syllogisms. Journal of Verbal Learning and Verbal Behavior, 21, 595-620.
3. Bochenski, I. M. (1970). A history of formal logic. New York: Chelsea Publishing Co.
4. Bott, L., & Noveck, I. A. (2004). Some utterances are underinformative: The onset and time course of scalar inferences. Journal of Memory and Language, 51, 437-457.
5. Brooks, P. J., & Braine, M. D. S. (1996). What do children know about the universal quantifiers all and each? Cognition, 60, 235-268.
6. Bucci, W. (1978). The interpretation of universal affirmative propositions. Cognition, 6, 55-77.
7. Carston, R. (2004). Relevance theory and the saying/implicating distinction. In L. R. Horn & G. Ward (Eds.), The handbook of pragmatics (pp. 633-656). Oxford, England: Blackwell.
8. Chierchia, G., & McConnell-Ginet, S. (2000). Meaning and grammar. An introduction to semantics. Cambridge, MA: MIT Press.
9. Drozd, K. F. (2001). Children's weak interpretations of universally quantified questions. In M. Bowerman & S. C. Levinson (Eds.), Language acquisition and conceptual development (pp. 340-376). Cambridge, England: Cambridge University Press.
10. Erickson, J. R. (1978). Research on syllogistic reasoning. In R. Revlin & R. E. Mayer (Eds.), Human reasoning (pp. 39-50). Washington, DC: Winston.
11. Euler, L. (1960). Lettres à une Princesse d'Allemagne sur divers sujets de physique et de philosophie [Letters to a princess of Germany on various subjects in physics and philosophy] (Vol. 11, A. Speiser, Ed.). Zurich: Orell Füssli. (Original work published 1768)
12. Evans, J. St. B. T., Handley, S. J., Harper, C. N. J., & Johnson-laird, P. N. (1999). Reasoning about necessity and possibility: A test of the mental model theory of deduction. Journal of Experimental Psychology: Learning, Memory, and Cognition, 25, 1495-1513.
13. Fisher, D. L. (1981). A three-factor model of syllogistic reasoning: The study of isolable stages. Memory and Cognition, 9, 496-514.
14. Gergonne, J. (1817). Essai de dialectique rationnelle. [Essay on rational dialectic]. Annales de Mathématiques Pures et Appliquées, 7, 189-228.
15. Grice, H. P. (1975). Logic and conversation. In P. Cole & J. L. Morgan (Eds.), Syntax and semantics: Vol 3. Speech acts (pp. 41-58). New York: Academic.
16. Griggs, R. A., & Warner, S. A. (1982). Processing artificial set inclusion relations: Educing the appropriate schema. Journal of Experimental Psychology: Learning, Memory and Cognition, 8, 51-65.
17. Gundel, J. K., & Fretheim, T. (2004). Topic and focus. In L. N. Horn & G. Ward (Eds.), The handbook of pragmatics (pp. 175-196). Oxford, England: Blackwell.
18. Hanlon, C. C. (1987). Acquisition of set-relational quantifiers in early childhood. Genetic, Social and General Psychology Monographs, 113, 215-264.
19. Horn, L. R. (1972). On the semantic properties of logical operators in English. Bloomington: Indiana University Linguistics Club.
20. Horn, L. R. (1989). A natural history of negation. Chicago: University of Chicago Press.
21. Johnson-Laird, P. N. (1970). The interpretation of quantified sentences. In G. B. Flores d'Arçais & W. J. M. Levelt (Eds.), Advances in psycholinguistics (pp. 347-372). Amsterdam: North-Holland.
22. Just, M. A. (1974). Comprehending quantified sentences: The relation between sentence-picture and semantic memory verification. Cognitive Psychology, 6, 216-236.
23. Leibniz, G. W. (1988). Opuscules et fragments inédits [Opuscula and unpublished fragments]. Hildesheim, Germany: Georg Olms Verlag. (Original work published 1903)
24. Levinson, S. C. (1983). Pragmatics. Cambridge, England: Cambridge University Press.
25. Levinson, S. C. (2000). Presumptive meanings. Cambridge, MA: MIT Press.
26. Meyer, D. E. (1970). On the representation and retrieval of stored semantic information. Cognitive Psychology, 1, 242-300.
27. Moxey, L. M., & Sanford, A. J. (1993). Communicating quantities. Hove, England: Lawrence Erlbaum Associates, Inc.
28. Moxey, L. M., & Sanford, A. J. (2000). Communicating quantities: A review of psycholinguistic evidence of how expressions determine perspectives. Applied Cognitive Psychology, 14, 237-255.
29. Neimark, E. D., & Chapman, R. H. (1975). Development of the comprehension of logical quantifiers. In R. J. Falmagne (Ed.), Reasoning: Representation and process in children and adults (pp. 135-151). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
30. Newell, A. (1981). Reasoning, problem solving and decision processes: The problem space as a fundamental category. In R. Nickerson (Ed.), Attention and performance (Vol. 8, pp. 693-718). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
31. Newstead, S. E. (1989). Interpretational errors in syllogistic reasoning. Journal of Memory and Language, 28, 78-91.
32. Newstead, S. E., & Griggs, R. A. (1983). Drawing inferences from quantified statements: A study of the square of opposition. Journal of Verbal Learning and Verbal Behavior 22, 535-546.
33. Noveck, I. A. (2001). When children are more logical than adults: Investigations of scalar implicature. Cognition, 78, 165-188.
34. Noveck, I. (2004). Pragmatic inferences related to logical terms. In I. A. Noveck & D. Sperber (Eds.), Experimental pragmatics (pp. 301-321). Basingstoke, England: Palgrave.
35. Noveck, I. A., & Posada, A. (2003). Characterizing the time course of an implicature: An evoked potentials study. Brain and Language, 85, 203-210.
36. Piaget, J., & Inhelder, B. (1964). The early growth of logic in the child: Classification and seriation. London: Routledge & Kegan Paul.
37. Politzer, G. (1990). Immediate deduction between quantified sentences. In K. J. Gilhooly, M. T. G. Keane, R. H. Logie, & G. Erdos (Eds.), Lines of thinking. Reflections on the psychology of thought (pp.85-97). London: Wiley.
38. Politzer, G. (1991). Comparison of deductive abilities across language. Journal of Cross-Cultural Psychology, 22, 389-402.
39. Politzer, G. (1997). Rationality and pragmatics. Current Psychology of Cognition/Cahiers de Psychologie Cognitive, 16, 190-195.
40. Politzer, G. (2004a). Reasoning, judgement and pragmatics. In I. N. Noveck & D. Sperber (Eds.), Experimental pragmatics (pp. 94-115). Basingstoke, England: Palgrave.
41. Politzer, G. (2004b). Some precursors of current theories of syllogistic reasoning. In K. Manktelow & M.-C. Chung (Eds.), Psychology of reasoning: Theoretical and historical perspectives (pp. 213-240). Hove, England: Psychology Press.
42. Politzer, G., & Macchi, L. (2000). Reasoning and pragmatics. Mind and Society, 1, 73-93.
43. Revlin, R., & Leirer, V. O. (1980). Understanding quantified categorical expressions. Memory & Cognition, 8, 447-458.
44. Scholz, H. (1961). Concise history of logic. New York: Philosophical Library. (Original work published 1931)
45. Smith, C.L. (1980). Quantifiers and question answering in young children. Journal of Experimental Child Psychology, 30, 191-205.
46. Sperber, D., & Wilson, D. (1995). Relevance: Communication and cognition (2nd ed.). London: Blackwell.
47. Stenning, K. (2002). Seeing reason: Image and language in learning to think. Oxford, England: Oxford University Press.
48. Stenning, K., & Cox, R. (1995). Attitudes to logical independence: Traits in quantifier interpretation. In J. D. Moore & J. F. Lehman (Eds.), Proceedings of the Seventeenth Conference of the Cognitive Science Society (pp. 742-747). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
49. Stenning, K., & Cox, R. (in press). Reconnecting interpretation to reasoning through individual differences. Quarterly Journal of Experimental Psychology.
50. Stenning, K., & Oberlander, J. (1995). A cognitive theory of graphical and linguistic reasoning: Logic and implementation. Cognitive Science, 19, 97-140.
51. Stenning, K., & Yule, P. (1997). Image and language in human reasoning: A syllogistic illustration. Cognitive Psychology, 34, 109-159.
52. Venn, J. (1971). Symbolic logic. Bronx, NY: Chelsea Pub. Co. (Original work published 1886)
53. Wason, P. C., & Johnson-Laird, P. N. (1972). Psychology of reasoning. Structure and content. London: Batsford.
54. Westerståhl, D. (2001). Quantifiers. In L. Goble (Ed.), The Blackwell guide to philosophical logic (pp. 437-460). Oxford, England: Blackwell.
55. Wetherick, N. E. (1993). Psychology and syllogistic reasoning: Further considerations. Philosophical Psychology, 6, 423-440.