Reasoning with quantifiers

In the semantics of natural language, quantification may have received more attention than any other subject, and one of the main topics in psychological studies on deductive reasoning is syllogistic inference, which is just a restricted form of reasoning with quantifiers. But thus far the semantical and psychological enterprises have remained disconnected. This paper aims to show how our understanding of syllogistic reasoning may benefit from semantical research on quantification. I present a very simple logic that pivots on the monotonicity properties of quantified statements--properties that are known to be crucial not only to quantification but to a much wider range of semantical phenomena. This logic is shown to account for the experimental evidence available in the literature as well as for the data from a new experiment with cardinal quantifiers ("at least n" and "at most n"), which cannot be explained by any other theory of syllogistic reasoning.

[1]  G. Boolos.  On ‘syllogistic inference’ , 1984, Cognition.

[2]  Victor Sanchez,et al.  Studies on Natural Logic and Categorial Grammar , 1991 .

[3]  Dov M. Gabbay,et al.  Handbook of Philosophical Logic , 2002 .

[4]  G. Gigerenzer,et al.  Domain-specific reasoning: Social contracts, cheating, and perspective change , 1992, Cognition.

[5]  L. Cosmides,et al.  The Adapted mind : evolutionary psychology and the generation of culture , 1992 .

[6]  N. Chater,et al.  The Probability Heuristics Model of Syllogistic Reasoning , 1999, Cognitive Psychology.

[7]  Makoto Kanazawa.  Weak vs. strong readings of donkey sentences and monotonicity inference in a dynamic setting , 1994 .

[8]  Göran Sundholm,et al.  Systems of Deduction , 1983 .

[9]  Shalom Lappin,et al.  当代语义理论指南 = The Handbook of Contemporary Semantic Theory , 2015 .

[10]  Marilyn Ford,et al.  Two modes of mental representation and problem solution in syllogistic reasoning , 1995, Cognition.

[11]  Laurence R. Horn.  A Natural History of Negation , 1989 .

[12]  Mandy Harvey,et al.  Proceedings from Semantics and Linguistic Theory IV , 1994 .

[13]  Jack Kaminsky,et al.  Reference And Generality , 1962 .

[14]  Stephen E. Newstead,et al.  Drawing inferences from quantified statements: a study of the square of opposition , 1983 .

[15]  N. Chater,et al.  The probabilistic approach to human reasoning , 2001, Trends in Cognitive Sciences.

[16]  Philip N. Johnson-Laird,et al.  Reasoning by model: The case of multiple quantification. , 1989 .

[17]  S. Levinson,et al.  Language Acquisition and Conceptual Development , 2001 .

[18]  Symmetry and Transitivity Assumptions about a Nonspecified Logical Relation , 1977 .

[19]  L. Rips.  The Psychology of Proof: Deductive Reasoning in Human Thinking , 1994 .

[20]  William A. Ladusaw.  Polarity sensitivity as inherent scope relations , 1980 .

[21]  L. Cosmides.  The logic of social exchange: Has natural selection shaped how humans reason? Studies with the Wason selection task , 1989, Cognition.

[22]  K. Gilhooly,et al.  Lines of thinking : reflections on the psychology of thought , 1990 .

[23]  L. Cosmides,et al.  Cognitive adaptations for social exchange. , 1992 .

[24]  B. Geurts.  Quantifying Kids , 2003 .

[25]  B. Geurts.  Presuppositions and Pronouns , 1999 .

[26]  Louis S. Dickstein,et al.  The effect of figure on syllogistic reasoning , 1978 .

[27]  Jonathan Evans,et al.  Human Reasoning: The Psychology Of Deduction , 1993 .

[28]  K. Drozd.  Language acquisition and conceptual development: Children's weak interpretations of universally quantified questions , 2001 .

[29]  Louis S. Dickstein,et al.  Conversion and possibility in syllogistic reasoning , 1981 .

[30]  Brian J. Reiser,et al.  Some Empirical Justification for a Theory of Natural Propositional Logic , 1984 .

[31]  Carol L. Smith.  Quantifiers and Question Answering in Young Children. , 1980 .

[32]  Carol L. Smith.  Children's understanding of natural language hierarchies , 1979 .

[33]  Victor Manual Sánchez Valencia,et al.  Studies on natural logic and categorial grammar , 1991 .

[34]  Bart Geurts,et al.  Donkey Business , 2002 .

[35]  P. Johnson-Laird,et al.  The psychology of syllogisms , 1978, Cognitive Psychology.

[36]  Rocky Ross,et al.  Mental models , 2004, SIGA.

[37]  J. Barwise,et al.  Generalized quantifiers and natural language , 1981 .

[38]  David R. Dowty.  The Role of Negative Polarity and Concord Marking in Natural Language Reasoning , 1994 .

[39]  Bernard Harrison,et al.  Reference and Generality , 1979 .