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**Doctoral course by Val Tannen** | **Doctoral course by Val Tannen** | ||
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+ | Lecture notes 1 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/ln1.pdf|(pdf)]] | ||
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+ | Homework 1 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/hw1.pdf|(pdf)]] | ||
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+ | Lecture notes 2 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/ln2.pdf|(pdf)]] | ||
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+ | Lecture notes 3 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/ln3.pdf|(pdf)]] | ||
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+ | Lecture notes 4 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/ln4.pdf|(pdf)]] | ||
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+ | Homework 2 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/hw2.pdf|(pdf)]] | ||
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+ | Lecture notes 5 (revised) [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/ln5rev.pdf|(pdf)]] | ||
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+ | Lecture notes 6 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/ln6.pdf|(pdf)]] | ||
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+ | Lecture notes 7 [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/ln7.pdf|(pdf)]] | ||
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+ | //Course Materials// | ||
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+ | "Models for Incomplete and Probabilistic Information" Green and Tannen [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/GreenTannen06.pdf|(pdf)]] | ||
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+ | Old lecture notes on computability [[http://www.cis.upenn.edu/~val/LogicProbEPFL2011files/compNotes.pdf|(pdf)]] | ||
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+ | "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// | //Syllabus// | ||
- | -Introduction | + | *Introduction |
- | -Truth, proof, and computation: some basic results about first-order logic | + | *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. | + | *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). | ||
- | -Part I: Probability of Logic | + | For 0-1 laws, I will consult |
- | -Random graphs and random structures | + | *"Elements of Finite Model Theory", Libkin, Springer 2004. |
- | -0-1 laws | + | *"The Strange Logic of Random Graphs", Spencer, Springer 2001. |
- | -Queries on probabilistic databases | + | |
- | -Part II: Logic of Probability | + | For the logic of independence in Bayesian and Markov networks I will follow selected sections from: |
- | -Pearl-Paz logics for reasoning about probabilistic (in)dependence | + | *"Probabilistic Graphical Models", Koller, Friedman, MIT Press 2009. |
- | -Reasoning about independence in Bayesian and Markov networks; the Hammersley-Clifford theorem | + | |
- | -Reasoning about independence in relational graphical models (PRMs and RMNs) | + | |
- | My lecture notes on Computability |