Logic has played an important role in the development of Artificial Intelligence (AI). In turn, thinking about applications in AI has led to the development of many new and interesting logical systems. See the Stanford Encyclopedia of Philosophy entry Logic and Artificial Intelligence for an interesting discussion about the relationship between (philosophical) logic and AI. This course will introduce and critically examine a number of different logical frameworks that have been developed with applications to AI in mind.

Broadly speaking, the goal of this course is to critically examine different logical frameworks that can be used to reason about rational agents interacting (with the environment and each other) over time. We will discuss the main research themes and the technical and conceptual issues that arise here. The primary objective is to understand the complex phenomena that arise when rational agents interact and how to incorporate these phenomena into formal models. Studying rational agents involves many different aspects including (but not limited to) action, knowledge, belief, desires, and revision. This course covers all these ingredients towards the goal of understanding how these things work together.

Specific topics that will be introduced during the semester include (a detailed schedule is provided below):

1. Logics of knowledge and belief (including probabilistic models);
2. Information dynamics and belief revision (including non-monotonic consequence relations);
3. Logics of time, action and agency;
4. Preference logics and preference change;
5. Logical models of intentions (time permitting);
6. Group phenomena and issues of social choice (time permitting); and
7. Logics for reasoning about games (time permitting).

In fact, not all parts of this story have been developed within one single discipline. The course will also bring together several research programs: from philosophy, computer science, logic, and game theory, and try to see their various contributions in one coherent manner.

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Related Courses
For more information about the topics we will discuss this semester, you can consult the webpages of the following related courses that I have taught:

• Rational Agency and Intelligent Interaction, Advanced undergraduate/graduate seminar co-taught with Johan van Benthem and Yoav Shoham at Stanford University.
• Logics of Rational Agency, Short course taught at the North American Summer School for Logic, Language and Information (NASSLLI 2010). Also, see the earlier version taught at the European Summer School for Logic, Language and Information (ESSLLI 2009).
• CAPUT Logic, Language and Information: Social Software, Seminar for Masters of Logic students at the Institute for Logic, Language and Information.

The course will be self-contained, but it will be useful to familiarize yourself with some general topics in modal logic throughout the semester. (I will introduce any general topics that we need during the semester.) The following books are good resources.

• A recent book introducing the basics of some of the logical systems we will discuss this semester.
  • [MLOM] Johan van Benthem (2010). Modal Logic for Open Minds, CSLI Publications.
• A modern introduction to modal logic aimed at researchers.
  • Patrick Blackburn and Johan van Benthem (2007). Modal Logic: A Semantic Introduction in: Handbook of Modal Logic, P. Blackburn, J. van Benthem and F. Wolter (editors), Elsevier, pgs. 1 - 84.
• Advanced textbook on modal logic.
  • Patrick Blackburn, Maarten de Rijke and Yde Venema (2001). Modal Logic, Cambridge University Press.

Below is a list of some general surveys and textbooks covering topics we will discuss during the semester. This is not a complete list of all relevant material, but a reasonably large sampling. Consult the schedule for the specific papers and excerpts from the books below that we will discuss in class.

Broad Discussions of Logics of Rational Agency

• Johan van Benthem (2007). "Logic, Rational Agency, and Intelligent Interaction," in C. Glymour, W. Wei & D. Westerståhl (eds.), Logic, Methodology and Philosophy of Science XIII, College Publications. (PDF)
• Y. Shoham (2009). "Logical Theories of Intention and the Database Perspective," Journal of Philosophical Logic, 38(6): 633-648. (PDF)
• W. van der Hoek and M. Wooldridge (2003). "Towards a logic of rational agency," Logic Journal of the IGPL, 11(2): 133-157. (PDF)

Logics of Knowledge and Belief

• R. Fagin, J. Halpern, Y. Moses and M. Vardi (1995). Reasoning About Knowledge , The MIT Press.
• [MAS] Yoav Shoham and Kevin Leyton-Brown (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge University Press. (Especially Chapters 13 and 14.)
• P. Vandershraaf and G. Sillari, Common Knowledge, Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward Zalta (editor).

Belief Revision and Non-Monotonic Logics

• A.P. Pedersen & H. Arló-Costa (2011). "Belief Revision." In L. Horsten and R. Pettigrew, editors, Continuum Companion to Philosophical Logic. Continuum Press, 2011. (Paper: PDF)
• Hans Rott (2001). Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning, Oxford University Press.
• David Makinson (2005). Bridges from Classical to Nonmonotonic Logic, College Publications.
• Robert Stalnaker (2009). "Iterated Belief Revision," Erkenntnis, 70(2): 189 - 209.

Dynamic Logics of Knowledge and Beliefs

• [LOGDYN] Johan van Benthem (2011). Logical Dynamics of Information and Interaction, Cambridge University Press. (This will be available only in September, I will hand out versions of his chapters as needed.)
• Eric Pacuit (2011). "Logics of Informational Attitudes and Informative Actions", in Logic and Philosophy Today, J. van Benthem and A. Gupta (eds.), College Publications (PDF)
• H. van Ditmarsch, W. van der Hoek and B. Kooi, Dynamic Epistemic Logic, Synthese Library, Volume 337, Springer.

Preference Logic and Preference Change

• Sven Ove Hansson and Till Grüne-Yanoff, "Preferences", The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.).
• Till Grüne-Yanoff and Sven Ove Hansson, Editors (2009). Preference Change Approaches from Philosophy, Economics and Psychology, Theory and Decision Library A: Volume 42, Springer.
• F. Liu (2011). Reasoning about Preference Dynamics, Synthese Library, Vol. 354, Springer-Verlag.

Logics for Actions, Abilities and Intention

• Krister Segerberg, John-Jules Meyer, and Marcus Kracht, "The Logic of Action", The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), Edward N. Zalta (ed.).

Logics for Games

• Johan van Benthem, Eric Pacuit and Olivier Roy (2011). "Games and Interaction: the Logical Perspective," Games, 2(1): 52 - 86. (PDF)

Please consult this schedule regularly throughout the semester as meeting times and readings may change.

Date	Lecture	Notes/Readings
8/29	Introductory Remarks: Logics of Rational Agency	Chapter 1 of [LOGDYN]
8/31	A Primer on Epistemic Logic	Introductory Notes on Modal Logic Chapter 12 of [MLOM] Sections 13.1 - 13.3 [MAS]
9/5	No Class: Labor Day
9/7	A Primer on Epistemic Logic, continued	Introductory Notes on Modal Logic
9/12	Logics of Knowledge and Belief	EP, Logics of Informational Attitudes and Informative Actions, Sections 1 & 2. J. Halpern, Should Knowledge Entail Belief?, Journal of Philosophical Logic Problem Set 1 (Due Monday, 9/19 )
9/14	Knowledge, Belief and Unawareness	EP, Logics of Informational Attitudes and Informative Actions, Sections 1 & 2 E. Dekel, B. Lipman and A. Rustichini, Standard State-Space Models Preclude Unawareness, Econometrica (1998)
9/19	Common Knowledge	M. Chwe Chapter 1 of Rational Ritual SEP Article on Common Knowledge (Sections 1, 2 and 3.1) Video by Steven Pinker touching on issues of common knowledge
9/21	Common Knowledge: Agreeing to Disagree	R. Aumann, Agreeing to Disagree, Annals of Statistics D. Samet, Agreeing to disagree: the non-probabilistic case
9/26	Lectures 8 & 9 Handout	D. Samet, Agreeing to disagree: the non-probabilistic case
9/28	Lectures 8 & 9 Handout Proof of the main result	D. Monderer and D. Samet Approximating Common Knowledge with Common Belief, Games and Economic Behavior (Section 3). Problem Set 2 (Due Wednesday, 10/5 )
10/3	Introduction to Dynamic Logics of Information	J. van Benthem, Chapter 15 of [MLOM]
10/5	The Logic of Public Observation	H. van Ditmarsch, W. van der Hoek, B. Kooi, Playing cards with Hintikka
10/10	Dynamic Logics of Information Change	EP, Logics of Informational Attitudes and Informative Actions, (especially Section 3.1)
10/12	Dynamic logics of belief change	EP, Logics of Informational Attitudes and Informative Actions R. Stalnaker (2009). "Iterated Belief Revision," Erkenntnis, 70(2): 189 - 209.
10/17	Introduction to belief revision, part 1 Guest Lecturer: Paul Pedersen	A.P. Pedersen & H. Arló-Costa (2011). Belief Revision. In L. Horsten and R. Pettigrew, editors, Continuum Companion to Philosophical Logic.
10/19	Introduction to belief revision, part 2 Guest Lecturer: Paul Pedersen	A.P. Pedersen & H. Arló-Costa (2011). Belief Revision. In L. Horsten and R. Pettigrew, editors, Continuum Companion to Philosophical Logic.
10/24	Grove's Representation Theorem, I (see Grove's paper for more information)	A. Grove, Two Modellings for Theory Change, Journal of Philosophical Logic, 17, pp. 157 - 170, 1988 Problem set 3 (midterm)
10/26	Grove's Representation Theorem, II (see Grove's paper for more information)	A. Grove, Two Modellings for Theory Change, Journal of Philosophical Logic, 17, pp. 157 - 170, 1988
10/31	Non-monotonic reasoning	A. Antonelli, Non-monotonic logic, Stanford Encyclopedia of Philosophy J. Horty, Skepticism and floating conclusions, Artificial Intelligence, 135: 55–72, 2002.
11/2	Belief revision and the Ramsey test	P. Gardenfors (1986). Belief revisions and the Ramsey test for conditionals, The Philosophical Review, 95:1, pp. 81 - 93. H. Leitgib (2007). Beliefs in Conditionals Vs. Conditional Beliefs, Topoi, 26:1, pp. 115 - 132.
11/7	Logics of Time and Agency	Y. Venema, Temporal Logic, Chapter 10, L Goble (editor), The Blackwell Guide to Philosophical Logic, Blackwell Publishers, 2001, pp 203 - 223. G. Governatori and A. Rotolo, On the axiomatization of Elgesem's logic of agency and ability. Journal of Philosophical Logic, 34, 4, pp. 403-431, 2005.
11/9	Logics of Abilities and Logics of Action	M. Brown, On the Logic of Ability, Journal of Philosophical Logic, 17, p. 1 - 26, 1988. J. van Benthem et al., Chapter 6: Propositional Dynamic Logic, Logic in Action Open Course Project P. Balbiani, Propositional Dynamic Logic, Stanford Encyclopedia of Philosophy, 2007
11/14	Introduction to STIT Logic	J. Horty and N. Belnap The deliberative STIT: a study of action, omission, ability, and obligation, Journal of Philosophical Logic, vol. 24 (1995), pp. 583 - 644. P. Balbiani, A. Herzig and N. Troquard, Alternative Axiomatics and Complexity of Deliberative STIT Theories, Journal of Philosophical Logic, 37:4, pp. 387 - 406, 2008.
11/16	Group action and logics of preference	Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences, Journal of Philosophical Logic, 38:1, 2009. M. Pauly A Modal Logic for Coalitional Power in Games, Journal of Logic and Computation, 12:1, pp. 149-166, 2002. Problem set 4
11/21	Preference lifting	Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences, Journal of Philosophical Logic, 38:1, 2009. Y. Kannai and B. Peleg, A Note on the Extension of an Order on a Set to the Power Set, Journal of Economic Theory, Vol. 32, pg. 172 - 175, 1984.
11/23	No Class: Thanksgiving
11/28	Know-how, abilities, plans and logics of intention	Y. Shoham (2009). Logical Theories of Intention and the Database Perspective, J. Philosophical Logic 38(6), pgs. 633-648 Section 14.4: Yoav Shoham and Kevin Leyton-Brown, Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge University Press, 2009 Problem set 5
11/30	Logics for reasoning about games	Johan van Benthem, Eric Pacuit and Olivier Roy, Games and Interaction: the Logical Perspective, Games, 2(1), 52 - 86
12/5	When are two games the same?/Common knowledge of rationality	J. Halpern, Substantive rationality and backward induction , Games and Economic Behavior 37, 2001, pp. 425-435.
12/7	Common knowledge of rationality and backward induction	J. Halpern, Substantive rationality and backward induction, Games and Economic Behavior 37, 2001, pp. 425-435. A. Baltag, S. Smets and J. Zvesper, Keep 'hoping' for rationality: a solution to the backward induction paradox, Synthese, Volume 169, Number 2, pgs. 301-333, 2009.

Students are required to attend all lectures and actively participate in the discussion. Final grades for the course will be calculated as follows:

1. (40%) Exercises: Exercises will be distributed periodically (Problem Set 1, Problem Set 2, Problem Set 4, Problem Set 5).
2. (20%) Midterm exam: Roughly half-way through the semester there will be a take-home midterm exam.
3. (40%) Final exam: The exam will be Tuesday, December 13, 5:30 PM - 8:30 PM in PH 125C.
   
   The final exam will contain question testing your comprehension of some of the basic material discussed during the course.
   
   The best way to prepare for the exam is to study the answers to the five problem sets (electronic copies of the solutions are no longer available.)
   
   Specific topics include:
   • Basic Modal Logic: semantics for modal logic, basic correspondence proofs (e.g., the T axiom is valid iff the frame is reflexive). See Introductory Notes on Modal Logic for details.
   • Basic dynamic epistemic/doxastic logic as discussed in Logics of Informational Attitudes and Informative Actions.
   • Basics of belief revision: see the introductory sections of Belief Revision.
   • Logics of time, action and ability: See the relevant lecture slides for the material here.
   • Preference logics: see the first 3 sections of Everything Else Being Equal: A Modal Logic for Ceteris Paribus Preferences.
   • Logics for reasoning about games: note that there will be 1-2 questions related to material on the last lectures on logics for reasoning about games and backward induction.