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- | ====== Logic and Probability ====== | + | ====== EPFL Fall 2011: Logic and Probability ====== |
**Doctoral course by Val Tannen** | **Doctoral course by Val Tannen** | ||
- | Thank you, Viktor! | + | Lecture notes 1 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/ln1.pdf|(pdf)]] |
+ | |||
+ | //Course Materials// | ||
+ | |||
+ | Old lecture notes on computability [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/compNotes.pdf|(pdf)]] | ||
+ | |||
+ | "On the Unusual Effectiveness of Logic in Computer Science" Halpern, Harper, Immerman, Kolaitis, Vardi, and Vianu" [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/UnusualEffectiveness.pdf|(pdf)]] | ||
+ | |||
+ | //Syllabus// | ||
+ | |||
+ | *Introduction | ||
+ | *Truth, proof, and computation: some basic results about first-order logic | ||
+ | *A bit of the story of how Mathematical Logic (and Electronic Technology) gave birth to Computer Science. | ||
+ | |||
+ | *Part I: Probability of Logic | ||
+ | *Random graphs and random structures | ||
+ | *0-1 laws | ||
+ | *Queries on probabilistic databases | ||
+ | |||
+ | *Part II: Logic of Probability | ||
+ | *Pearl-Paz logics for reasoning about probabilistic (in)dependence | ||
+ | *Reasoning about independence in Bayesian and Markov networks; the Hammersley-Clifford theorem | ||
+ | *Reasoning about independence in relational graphical models (PRMs and RMNs) | ||
+ | |||
+ | //Some useful books// | ||
+ | |||
+ | I will rely on basic results about computability and complexity that | ||
+ | are (usually) covered in a Computer Science undergraduate curriculum. | ||
+ | If you need to freshen up on these topics, I can recommend: | ||
+ | |||
+ | "Introduction to the Theory of Computation", Sipser, PWS 1997. | ||
+ | |||
+ | "Introduction to Automata Theory, Languages, and Computability", | ||
+ | Hopcroft, Motwani, and Ullman, 2nd edition, Addison-Wesley 2001. | ||
+ | |||
+ | "Computational Complexity", Papadimitriou, Addison-Wesley 1994. | ||
+ | |||
+ | "Computational Complexity: A Modern Approach", Arora and Barak, | ||
+ | Cambridge University Press 2009. | ||
+ | |||
+ | I have also made available my own notes on computability (see above). | ||
+ | |||
+ | |||
+ | There many textbooks on logic but let me recommend my favorites: | ||
+ | |||
+ | "Logic for Computer Science", J. Gallier, | ||
+ | (Wiley 1986), out of print but available [[http://www.cis.upenn.edu/~jean/gbooks/logic.html|here]] | ||
+ | with the latest revisions. | ||
+ | |||
+ | |||
+ | "A mathematical introduction to logic", H. B. Enderton, | ||
+ | Harcourt/Academic Press, 1972 and 2000. | ||
+ | |||
+ | "Introduction to mathematical logic", E. Mendelson, | ||
+ | various publishers, 1964, 1979, 1987, and 1997. | ||
+ | |||
+ | "Computability and logic", G. Boolos and R. Jeffrey, | ||
+ | Cambridge Univ.~Press, 1974 and 1980. | ||
+ | |||
+ | The complete classification of the prefix fragments of FOL | ||
+ | from the point of view of the decidability of satisfiability | ||
+ | is in: | ||
+ | |||
+ | "The Classical Decision Problem", Boerger, Graedel, and Gurevich, Springer 1997. | ||
+ | |||
+ | The story of how mathematical logic gave birth to computer | ||
+ | science is told best in: | ||
+ | |||
+ | "Engines of Logic: Mathematicians and the Origins of the Computer", | ||
+ | Davis, 2nd edition, Norton 2001. | ||
+ | |||
+ | There are many, many textbooks that offer an introduction to probabilities | ||
+ | I prefer those that do a good job on discrete probability spaces. Some examples: | ||
+ | |||
+ | "Probability and Random Processes", Grimmett, Stirzaker, Oxford U. Press 2001. | ||
+ | |||
+ | "Probability: Theory and Examples", Durrett, Thomson (Brooks/Cole) 2005. | ||
+ | |||
+ | There is also a brief introduction to probability | ||
+ | in chapter 2 of Koller-Friedman (mentioned below). | ||
+ | |||
+ | For 0-1 laws, I will consult | ||
+ | |||
+ | "Elements of Finite Model Theory", Libkin, Springer 2004, | ||
+ | |||
+ | and | ||
+ | |||
+ | "The Strange Logic of Random Graphs", Spencer, Springer 2001. | ||
+ | |||
+ | |||
+ | For the logic of independence in Bayesian and Markov networks I will follow | ||
+ | selected sections from: | ||
+ | |||
+ | "Probabilistic Graphical Models", Koller, Friedman, MIT Press 2009. | ||
+ | |||