In this two volume festschrift, contributors explore the theoretical developments (Volume I) and applications (Volume II) in traditional cognitive psychology domains, and model other areas of human performance that benefit from rigorous mathematical approaches. It brings together former classmates, students and colleagues of Dr. James T. Townsend, a pioneering researcher in the field since the early 1960s, to provide a current overview of mathematical modeling in psychology. Townsend’s research critically emphasized a need for rigor in the practice of cognitive modeling, and for providing mathematical definition and structure to ill-defined psychological topics. The research captured demonstrates how the interplay of theory and application, bridged by rigorous mathematics, can move cognitive modeling forward.
1. Introduction Leslie M. Blaha and Joseph W. Houpt 2. High-Probability Logic and Inheritance Donald Bamber 3. Stochastic Orders of Variability Hans Colonius 4. Subset System: Mathematical Abstraction of Object and Context Jun Zhang and Yitong Sun 5. Uniqueness of a Multinomial Processing Tree Constructed by Knowing Which Pairs of Processes are Ordered Richard Schweickert and Hye Joo Han 6. Simple Factorial Tweezers for Detecting Delicate Serial and Parallel Processes Mario Fifi´c 7. Identifying Spatiotemporal Information Joseph S. Lappin 8. Models of Intertemporal Choice Junyi Dai and Jerome R. Busemeyer 9. Variations on the Theme of Independence: Tasks and Effects of Stroop, Garner, and Townsend Daniel Algom 10. Modeling Interactive Dimensions in a Component Comparison Task using General Recognition Theory Robin D. Thomas, Noah H. Silbert, Emily Grossman and Shawn Ell 11. Symmetry Provides a Turing-type Test for 3D Vision Zygmunt Pizlo 12. Cognitive Psychometrics William H. Batchelder