Minds and Machines
Department of Philosophy
Carnegie Mellon University
Pittsburgh, USA
Center for Adaptive Behavior and Cognition
Max Planck Institute for Human Development
Berlin, Germany
Rational Choice
Carnegie Mellon University
80-305
Fall 2012
This course will cover selected topics in rational choice theory, which informally is the analysis of how to make a correct decision in a given context. The course offers an introduction to the main normative theories of rational choice: von Neumann-Morgenstern theory of expected utility, Anscombe-Aumann's account and Savage's theory of choice under uncertainty. The course also includes an introduction to the main descriptive accounts of decision making used in Psychology and Economics. Possible topics may include, and are not limited to: a review of the main theories of non-expected utility and related issues in the psychology of judgment and decision making (especially recent advances extending Rank Dependent Utility and Prospect theory from risk to uncertainty), game-theoretic problems of conflict and coordination, the role of heuristics in choice behavior and strategic reasoning, as well as recent theories that abandon the Bayesian assumption that the decision maker's beliefs can always be represented by a unique probability distribution. This course will stress the role that formal methods can play in the analysis of decisions and alternative applications of decision theory to issues in philosophy and social science.
Modal Logic
Carnegie Mellon University
80-315 (80-615)
Fall 2012
This course is an introduction to first-order modal logic. After a thorough grounding in propositional normal modal logic, which covers rudimentary modal model theory (invariance results, the relationship between modal and first-order logic, the finite model property, and notions of modal model equivalence), soundness, completeness, and basic decidability results, several interpretations and applications of normal modal logics are considered. Modal languages are simple languages for talking about relational structures, with several applications appearing in philosophy, computer science, and linguistics. Some examples the course may touch upon include temporal and epistemic logics, multi-agent systems, finite parse trees, labeled transition systems, among others. In the last part of the course we will consider extensions of the Kripke models to interpret first-order modal languages, and close with the more general still Scott-Montague models of "classical" modal logic and extend those to first-order modal languages.
Logic & AI
Carnegie Mellon University
80-314
Spring 2013
An introduction to several formalisms used in knowledge representation and reasoning (KRR). The first half of the course covers the theoretical foundations of KRR: first-order logic, the principles for creating knowledge bases, propositional and first-order resolution, horn logics, description logics for reasoning about individuals and categories, inheritance, `non-monotonic' reasoning and defaults, principles of belief revision, representing and reasoning about actions, and planning. After this review, we will then look at a formalism for multiple epistemic agents and actions in some depth, and consider the trade-off between expressiveness and tractability. Finally, we shall introduce probabilistic methods for knowledge representation and reasoning under conditions of uncertainty.
The Nature of Mathematical Reasoning
Carnegie Mellon University
80-1010
Spring 2013
If asked to describe the study of mathematics, most people are likely to describe some specific mathematical theory – like calculus or algebra. In fact, the bulk of your mathematical upbringing was probably spent learning to perform different sorts of calculations according to different sorts of rules. But underneath the technical details lies the fascinating world of mathematical reasoning. In this course, our aim is to gain an understanding of contemporary mathematical reasoning and to see the simple elegance that abstract reasoning can bring to seemingly counter-intuitive problems. We will approach this project with the aid of examples found in the history and philosophy of mathematics, which will help us to better understand how the modern theory of mathematical reasoning has developed. In addition, we will consider several problems that seem to defy any intuitive solution, but which have compelling and in some cases simple solutions when put into mathematical form. These cases will highlight the value of approaching a problem in a carefully considered, mathematical manner.
My research addresses a range of issues in epistemology, broadly construed to include topics in philosophical logic and the philosophy of science, computational logic and artificial intelligence, normative and descriptive decision theory, imprecise probability theory, modal belief revision and, recently, formal models of heuristic rationality.
Recent highlights:
- Coherence and Confirmation Through Causation (with
Richard Scheines ) - Formal Epistemology
- Demystifying Dilation (with
Arthur Paul Pedersen )
Articles
new: "Is There a Logic of Information?"
2013: "Coherence and Confirmation Through Causation" (with
2013: "Character Matching and the Locke Pocket of Belief,"
2013: "Models, Models, and Models,"
2012: "Objective Bayesian Calibration and the Problem of Non-convex Evidence,"
2012: "Belief Contraction Through Safe Formulas" (with
2012: "Why the Hardest Logic Puzzle Ever Cannot be Solved in Less Than Three Questions" (with 
2012: "Formal Epistemology," in
2012: "Explaining the Limits of Olsson's Impossibility Result,"
2012: "Modeling of Phenomena and Dynamic Logic of Phenomena"
(with
2011: "NO revision and NO contraction" (with
2011: "Evidential Probability and Objective Bayesian Epistemology"
(with
[Amazon UK]
2011: "Focused Correlation, Confirmation, and the Jigsaw Puzzle of Variable Evidence"
(with
2011: “Causation, Association, and Confirmation"
(with
2011: "Editorial,"
2010: “Robustness of Evidential Probability"
(with
2010: “AGM Belief Revision in Monotone Modal Logics,"
2009: "Focused Correlation and Confirmation,”
2009 : "A Good Year for Imprecise Probabilities," in Vincent F. Hendricks (ed.)
2009: "Logical Relations in a Statistical Problem"
(with
2009: "Review of Formal Philosophy
(Automatic Press, 2005),"
2008: "Methodological Naturalism and Epistemic Internalism"
(with
2008: “Possible Semantics for a Common Framework for Probabilistic Logic”
(with
2008: "Applied Logic without Psychologism,"
2007: "Conditionals and Consequences" (with
2007: "Two Puzzles Concerning Measures of Uncertainty and the Positive Boolean Connectives,"
13th Portuguese Conference on Artificial Intelligence (
2007: "A Review of the Lottery Paradox,"
in William Harper and Gregory Wheeler (eds.)
2007: “Humanists and Scientists,”
2006: "Rational Acceptance and Conjunctive/Disjunctive Absorption,"
2006: Reprint of "On the Structure of Rational Acceptance," in Wiebe van der Hoek (ed.),
2005: "On the Structure of Rational Acceptance: Comments on Hawthorne and Bovens,"
2005: “Review of Hans Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning
(Oxford: Clarendon Press, 2001),"
2005: "The Paradoxes of Rational Acceptance and the Logic of Belief," in Lorenzo Magnani and Riccardo Dossena (eds.)
2004: "Epistemology and Artificial Intelligence" (with
2004: "An Implementation of Statistical Default Logic" (with
2004: "A Resource Bounded Default Logic,"
in James Delgrande and Torsten Schaub (eds.) Proceedings of the 10th International
Workshop on Non-Monotonic Reasoning (
—— An abstract of “A Resource Bounded Default Logic," in
2003: "A Note on Epistemology and Logical Artificial Intelligence,"
in Claudio Delrieux and Javier Legris (eds.) Proceedings of the Third International
Workshop on Computational Models of Scientific Reasoning and Applications
(CMSRA-III), Buenos Aires, Argentina, 207-22, 2003. (w/
—— An expanded version appears in
2002: "Statistical Defaults and Paraconsistency,"
2002: "Kinds of Inconsistency,"
in Walter A. Carnielli, Marcelo E. Coniglio, Italia Loffredo D'Ottaviano (eds.)
2000: "Error Statistics and Duhem's Problem,"
Monograph
2011: Probabilistic Logics and Probabilistic Networks
The Synthese Library, Springer.
Available from Amazon: UK or
US.
- Reviewed by Jan Sprenger in Metascience.
Edited Books
new: Horacio: Commemorative Essays on Horacio Arló-Costa
2013: New Challenges to Philosophy of Science
Available from Amazon: UK or US
2007: Probability and Inference: Essays in Honour of Henry E. Kyburg, Jr.
London: College Publications, 2007.
Available from Amazon: UK or
US.
Special Journal Issues
2012: "Special issue Commemorating Henry E. Kyburg, Jr.,"
2009: “Special issue on Combining Probability and Logic”,
2007: “Special issue on Formal and Computational Epistemology,”
Recent Projects
Deutscher Akademischer Austausch Dienst / German Academic Exchange Service (DAAD): The Puzzle of Heuristic Rationality, with Konstantinos Katsikopoulos The Max Planck Institute for Human Development, Berlin (2012).
European Science Foundation (ESF), LogiCCC Program: Dialogical Foundations of Semantics, (DiFoS), associate partner, (2009-2011).
European Science Foundation (ESF): Philosophy of Science in a European Perspective (PSE), formal methods group & steering committee, (2008-2013).
The Leverhulme Trust: Probabilistic Logics and Probabilistic Networks PROGICNET. co-PI, (2006-2008).
Collaborators
- Marco Alberti (New University of Lisbon)
- Pedro Barahona (New University of Lisbon)
- Carlos Damásio (New University of Lisbon)
- Rolf Haenni (Bern)
- Konstantinos Katsikopoulos (Max Planck Institute for Human Development)
- Boris Kovalerchuk (Central Washington University)
- Viktoriia Kozyreva, (Ufa State Aviation Technical University)
- Henry E. Kyburg, Jr.* (Rochester)
- Arthur Paul Pedersen (Max Planck Institute for Human Development)
- Luís Moniz Pereira (New University of Lisbon)
- Leonid Perlovsky (Harvard)
- Jan-Willem Romeijn (Groningen)
- Richard Scheines (Carnegie Mellon)
- Maximillian Schlosshauer (Copenhagen)
- Choh Man Teng (Institute for Human and Machine Cognition)
- Jon Williamson (Kent)
Co-editors
- Hanne Andersen (Aarhus)
- Horacio Arló-Costa* (Carnegie Mellon)
- Fabio Cozman (São Paulo)
- Dennis Dieks (Utrecht)
- Wenceslao González (Coruña)
- William Harper (Western Ontario)
- Jeffery Helzner (Columbia)
- Vincent Hendricks (Copenhagen)
- Arthur Paul Pedersen (Max Planck Institute for Human Development)
- Marcel Weber (Geneva)
Erdös Number
- 4.
Media
- Three gods: The Hardest Logic Puzzle Ever
- New Scientist, December 22, 2012
- by Richard Webb
- The World Science Festival
- Architects of the Mind:
- Douglas Fields
- Murray Shanahan
- Gregory Wheeler
- New York City
- May 31, 2013
Editorial Positions
- Minds and Machines, Editor-in-Chief
- Synthese, Editorial Board
- The Philosophy of Science in a European Perspective Book Series, Editorial Board
Academic Weblogs
- Choice & Inference, Formal Epistemology
- Certain Doubts, Epistemology
LaTeX Resources
Data sets
Credits
- Photo by Isabel Kronenberger
