Reasoning about relations.

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. (a) The structure of mental models is iconic as far as possible. (b) The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. (c) Individuals tend to construct only a single, typical model. (d) They spontaneously develop their own strategies for relational reasoning. (e) Regardless of strategy, the difficulty of an inference depends on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle.

[1]  D. Spalding.  The Principles of Psychology , 1873, Nature.

[2]  J. Mctaggart,et al.  The nature of existence , .

[3]  Judgment and Reasoning in the Child , 1928, Nature.

[4]  C. Hartshorne,et al.  Collected Papers of Charles Sanders Peirce , 1935, Nature.

[5]  C. Peirce,et al.  Collected Papers of Charles Sanders Peirce , 1936, Nature.

[6]  R. Thouless.  Experimental Psychology , 1939, Nature.

[7]  Z. Harris,et al.  Foundations of language , 1941 .

[8]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[9]  I. Hunter,et al.  The solving of three-term series problems. , 1957, British journal of psychology.

[10]  J. Piaget.  Judgement and Reasoning in the Child , 1962 .

[11]  Martha Kneale,et al.  The development of logic , 1963 .

[12]  S. Handel,et al.  Social reasoning and spatial paralogic. , 1965, Journal of personality and social psychology.

[13]  Nicholas Rescher,et al.  The Logic of Decision and Action , 1967 .

[14]  Janellen Huttenlocher,et al.  Constructing spatial images: A strategy in reasoning. , 1968 .

[15]  R. Hursthouse.  THE LOGIC OF DECISION AND ACTION , 1969 .

[16]  D. J. WOOD.  Approach to the Study of Human Reasoning , 1969, Nature.

[17]  Herbert H. Clark,et al.  Linguistic processes in deductive reasoning. , 1969 .

[18]  E. Leeuwenberg.  Quantitative specification of information in sequential patterns. , 1969, Psychological review.

[19]  R. Shepard,et al.  Mental Rotation of Three-Dimensional Objects , 1971, Science.

[20]  P. Johnson-Laird.  The three-term series problem ☆ , 1972 .

[21]  D. Wood,et al.  A Preliminary Study of Distinctive Features in Problem Solving , 1973 .

[22]  J. Barclay.  The role of comprehension in remembering sentences , 1973 .

[23]  R. Shepard,et al.  Transformational studies of the internal representation of three-dimensional objects. , 1974 .

[24]  S. Haviland,et al.  ‘This man's father is my father's son’: a study of the acquisition of English kin terms , 1974, Journal of Child Language.

[25]  D. Godden,et al.  An Investigation of the Relationships between Problem Solving Strategies, Representation and Memory , 1974 .

[26]  T. Trabasso,et al.  Comparatives, logical structures, and encoding in a transitive inference task. , 1974 .

[27]  G. R. Potts,et al.  The internal representation of a three-term series problem , 1975 .

[28]  B. Fellows,et al.  'Perceptual' strategies in the solving of three term series problems. , 1975 .

[29]  J. Winkelman.  Semantic representation of Kinship systems , 1975 .

[30]  P. Shaver,et al.  Converging evidence for the functional significance of imagery in problem solving , 1975, Cognition.

[31]  G. Miller,et al.  Language and Perception , 1976 .

[32]  C. Riley.  The representation of comparative relations and the transitive inference task , 1976 .

[33]  Mark A. Sabol,et al.  Constructive Processes in Simple Linear-Order Problems. , 1976 .

[34]  John R. Anderson.  Arguments concerning representations for mental imagery. , 1978 .

[35]  J. Ormrod.  Cognitive processes in the solution of three-term series problems. , 1979, The American journal of psychology.

[36]  Richmond H. Thomason,et al.  Formal Philosophy; Selected Papers , 1979 .

[37]  R. Sternberg.  Representation and Process in Linear Syllogistic Reasoning. , 1980 .

[38]  Lola L. Lopes,et al.  Kin search: Answering questions about relations among relatives. , 1980 .

[39]  R. Sternberg,et al.  An Aptitude-Strategy Interaction in Linear Syllogistic Reasoning. , 1980 .

[40]  E. Shoben,et al.  Componential reasoning in kinship. , 1980 .

[41]  B. Fischhoff,et al.  Journal of Experimental Psychology: Human Learning and Memory , 1980 .

[42]  G. Claxton.  Cognitive psychology: New directions , 1980 .

[43]  R. Jeffrey.  Formal Logic: Its Scope and Limits , 1981 .

[44]  Z. Pylyshyn.  The imagery debate: Analogue media versus tacit knowledge. , 1981 .

[45]  L. Breslow.  Reevaluation of the Literature on the Development of Transitive Inferences. , 1981 .

[46]  Mark Steedman,et al.  Reference to past time , 1982 .

[47]  R. Sternberg.  Advances in the psychology of human intelligence , 1982 .

[48]  E. Hunt,et al.  Individual differences in secondary task performance , 1982, Memory & cognition.

[49]  P. Johnson-Laird,et al.  Spatial Descriptions and Referential Continuity , 1982 .

[50]  Mark Steedman.  Speech, Place, and Action , 1982 .

[51]  R. Shepard,et al.  Mental Images and Their Transformations , 1982 .

[52]  D. Egan,et al.  Differences in mental representations spontaneously adopted for reasoning , 1982, Memory & cognition.

[53]  John F. Sowa,et al.  Conceptual Structures: Information Processing in Mind and Machine , 1983 .

[54]  P. Johnson-Laird,et al.  Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness , 1985 .

[55]  R. Weale.  Vision. A Computational Investigation Into the Human Representation and Processing of Visual Information. David Marr , 1983 .

[56]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[57]  Göran Hagert,et al.  Modeling Mental Models: Experiments in Cognitive Modeling of Spatial Reasoning , 1984, ECAI.

[58]  S Ohlsson,et al.  Induced strategy shifts in spatial reasoning. , 1984, Acta psychologica.

[59]  C. Brainerd,et al.  Do children have to remember to reason? A fuzzy-trace theory of transitivity development , 1984 .

[60]  G. Halford.  Can young children integrate premises in transitivity and serial order tasks? , 1984, Cognitive Psychology.

[61]  S. Carey.  Conceptual Change in Childhood , 1985 .

[62]  C. Clement,et al.  Logical reasoning, world knowledge, and mental imagery: Interconnections in cognitive processes , 1986, Memory & cognition.

[63]  J. Bain,et al.  Information-Processing Demands of Transitive Inference , 1986 .

[64]  P. Pollard,et al.  Response bias in relational reasoning , 1986 .

[65]  J. Richardson.  The role of mental imagery in models of transitive inference , 1987 .

[66]  E. Hunt,et al.  Individual Differences in Attention. , 1989 .

[67]  K. Springer,et al.  Children's awareness of the biological implications of kinship. , 1992, Child development.

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

[69]  J. Barwise.  Everyday reasoning and logical inference , 1993 .

[70]  G. Halford.  Children's Understanding: The Development of Mental Models , 1993 .

[71]  P. Johnson-Laird,et al.  PSYCHOLOGICAL SCIENCE Research Article HOW DIAGRAMS CAN IMPROVE REASONING , 2022 .

[72]  P. Wenderoth.  On the relationship between the psychology of visual perception and the neurophysiology of vision , 1994 .

[73]  L. Rips.  The Psychology of Proof , 1994 .

[74]  Nick Chater,et al.  A rational analysis of the selection task as optimal data selection. , 1994 .

[75]  Sun-Joo Shin,et al.  Peirce and the logical status of diagrams , 1994 .

[76]  K. Springer.  Acquiring a naive theory of kinship through inference. , 1995, Child development.

[77]  Jon Oberlander,et al.  A Cognitive Theory of Graphical and Linguistic Reasoning: Logic and Implementation , 1995, Cogn. Sci..

[78]  Graeme S. Halford,et al.  Modeling the development of reasoning strategies: The roles of analogy, knowledge, and capacity , 1995 .

[79]  M. Knauff,et al.  Preferred mental models in qualitative spatial reasoning: A cognitive assessment of Allen's calculus , 1995 .

[80]  P. Johnson-Laird,et al.  Development of syllogistic reasoning. , 1995, The American journal of psychology.

[81]  A. Vandierendonck.  Evidence for Mental-model-based Reasoning: A Comparison of Reasoning with Time and Space Concepts , 1996 .

[82]  Arthur C. Graesser,et al.  Models of Understanding Text , 1996 .

[83]  Explaining preferred mental models in Allen inferences with a metrical model of imagery , 1996 .

[84]  Keith Stenning.  The Cognitive Impact of Diagrams , 1996 .

[85]  Jane Oakhill,et al.  The mental models theory language of comprehension , 1996 .

[86]  P. Johnson-Laird,et al.  Mental models and temporal reasoning , 1996, Cognition.

[87]  A. Clark,et al.  Philosophy and Cognitive Science , 1996 .

[88]  S. Sloman.  The empirical case for two systems of reasoning. , 1996 .

[89]  M. Carreiras,et al.  Reasoning about relations: Spatial and nonspatial problems , 1997 .

[90]  John E. Hummel,et al.  Distributed representations of structure: A theory of analogical access and mapping. , 1997 .

[91]  K. C. Klauer.  Working Memory Involvement in Propositional and Spatial Reasoning , 1997 .

[92]  S. Phillips,et al.  Processing capacity defined by relational complexity: implications for comparative, developmental, and cognitive psychology. , 1998, The Behavioral and brain sciences.

[93]  S. Phillips,et al.  Relational complexity metric is effective when assessments are based on actual cognitive processes , 1998 .

[94]  Göran Rossholm,et al.  Languages of Art , 1998 .

[95]  Philip N. Johnson-Laird,et al.  A Model Theory of Modal Reasoning , 1998, Cogn. Sci..

[96]  Philip N. Johnson-Laird,et al.  The Effect of an Irrelevant Premise on Temporal and Spatial Reasoning , 1998, Kognitionswissenschaft.

[97]  Lyn D. English,et al.  Children's Reasoning in Solving Relational Problems of Deduction , 1998 .

[98]  P. Johnson-Laird,et al.  Strategies in syllogistic reasoning , 1999, Cogn. Sci..

[99]  Maria Sonino Legrenzi,et al.  Naive probability: a mental model theory of extensional reasoning. , 1999, Psychological review.

[100]  K. Sijtsma,et al.  An Ordinal Scale for Transitive Reasoning by Means of a Deductive Strategy , 1999 .

[101]  K. Holyoak,et al.  A System for Relational Reasoning in Human Prefrontal Cortex , 1999 .

[102]  L. Barsalou,et al.  Whither structured representation? , 1999, Behavioral and Brain Sciences.

[103]  Jonathan Evans,et al.  Reasoning about necessity and possibility : a test of the mental model theory of deduction , 1999 .

[104]  G. d'Ydewalle,et al.  Deductive Reasoning and Strategies , 1999 .

[105]  O. Wilhelm,et al.  Effects of directionality in deductive reasoning: I. The comprehension of single relational premises. , 2000, Journal of experimental psychology. Learning, memory, and cognition.

[106]  P. Johnson-Laird,et al.  Strategies in temporal reasoning , 2000 .

[107]  A. Markman,et al.  Extending the classical view of representation , 2000, Trends in Cognitive Sciences.

[108]  P N Johnson-Laird,et al.  Illusions in reasoning about consistency. , 2000, Science.

[109]  A. Vandierendonck,et al.  Model construction and elaboration in spatial linear syllogisms , 2000 .

[110]  M. Roberts.  Strategies in relational inference , 2000 .

[111]  Philip N. Johnson-Laird,et al.  Naive causality: a mental model theory of causal meaning and reasoning1 , 2001, Cogn. Sci..

[112]  Gerhard Strube,et al.  Spatial Reasoning: No Need for Visual Information , 2001, COSIT.

[113]  E John,et al.  A Process Model of Human Transitive Inference , 2001 .

[114]  G. d'Ydewalle,et al.  The processing of negations in conditional reasoning: A meta-analytic case study in mental model and/or mental logic theory , 2001 .

[115]  Merideth Leigh Gattis,et al.  Spatial schemas and abstract thought , 2001 .

[116]  David L. Davidson,et al.  The Logical Form of Action Sentences , 2001 .

[117]  Jean-Baptiste Van der Henst.  Mental model theory versus the inference rule approach in relational reasoning , 2002 .

[118]  Z. Pylyshyn.  Mental imagery: In search of a theory , 2002, Behavioral and Brain Sciences.

[119]  Mark T. Keane,et al.  Conditionals: a theory of meaning, pragmatics, and inference. , 2002, Psychological review.

[120]  Sun-Joo Shin.  The Iconic Logic of Peirce's Graphs , 2002 .

[121]  Graeme S. Halford,et al.  Cognitive complexity of suppositional reasoning: An application of the relational complexity metric to the knight-knave task , 2002 .

[122]  Philip N. Johnson-Laird,et al.  Strategies in sentential reasoning , 2002, Cogn. Sci..

[123]  Jean-Baptiste Van der Henst,et al.  When is a conclusion worth deriving? A relevance-based analysis of indeterminate relational problems , 2002 .

[124]  P. Johnson-Laird,et al.  Visual imagery can impede reasoning , 2002, Memory & cognition.

[125]  Philip N. Johnson-Laird,et al.  Peirce, logic diagrams, and the elementary operations of reasoning , 2002 .

[126]  G. Halford,et al.  A cognitive complexity metric applied to cognitive development , 2002, Cognitive Psychology.

[127]  M. Oaksford.  Contrast classes and matching bias as explanations of the effects of negation on conditional reasoning , 2002 .

[128]  P. Johnson-Laird,et al.  Reasoning, Models, and Images: Behavioral Measures and Cortical Activity , 2003, Journal of Cognitive Neuroscience.

[129]  A. Vandierendonck,et al.  Is model construction open to strategic decisions? An exploration in the field of linear reasoning , 2003 .

[130]  W. Schroyens,et al.  In Search of Counter-Examples: Deductive Rationality in Human Reasoning , 2003, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[131]  T. Ormerod,et al.  On the generation and evaluation of inferences from single premises , 2003, Memory & cognition.

[132]  Werner Kuhn,et al.  Spatial Information Theory. Foundations of Geographic Information Science , 2003, Lecture Notes in Computer Science.

[133]  P. Johnson-Laird,et al.  Counterexamples in sentential reasoning , 2003, Memory & cognition.

[134]  K. Holyoak,et al.  A symbolic-connectionist theory of relational inference and generalization. , 2003, Psychological review.

[135]  Jonathan Evans.  In two minds: dual-process accounts of reasoning , 2003, Trends in Cognitive Sciences.

[136]  P. Johnson-Laird,et al.  Co-reference and reasoning , 2004, Memory & cognition.

[137]  P. Johnson-Laird,et al.  Does everyone love everyone? The psychology of iterative reasoning , 2004 .

[138]  Georg Jahn,et al.  Reasoning About Consistency with Spatial Mental Models: Hidden and Obvious Indeterminacy in Spatial Descriptions , 2004, Spatial Cognition.

[139]  Randall R. Dipert,et al.  Reflections on iconicity, representation, and resemblance: Peirce's theory of signs, goodman on resemblance, and modern philosophies of language and mind , 1996, Synthese.

[140]  John E. Hummel,et al.  Varieties of sameness: the impact of relational complexity on perceptual comparisons , 2004, Cogn. Sci..

[141]  P. Johnson-Laird,et al.  Reasoning from inconsistency to consistency. , 2004, Psychological review.

[142]  J. Bain,et al.  PSYCHOLOGICAL SCIENCE Research Article How Many Variables Can Humans Process? , 2022 .

[143]  P. Johnson-Laird,et al.  Naïve deontics: A theory of meaning, representation, and reasoning , 2005, Cognitive Psychology.

[144]  Geoffrey P. Goodwin,et al.  Reasoning about the Relations between Relations , 2006, Quarterly journal of experimental psychology.

[145]  G. d'Ydewalle,et al.  The mental models theory of reasoning: refinements and extensions , 2007 .