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More Logic. The arenas of Arles Van Gogh. Discrete Structures (CS 173) Madhusudan Parthasarathy. Promoting Undergraduate Research in Engineering ( P.U.R.E.). Promoting Undergraduate Research in Engineering (P.U.R.E.). Fall 2013 Information Session - PowerPoint PPT Presentation

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More Logic Discrete Structures (CS 173)Madhusudan ParthasarathyThe arenas of ArlesVan Gogh

1Promoting Undergraduate Research in Engineering (P.U.R.E.)Spring 2010 Information SessionUndergraduate Advising Office Program Director

Slides are borrowed and adapted from fall 2008(PURE CommitteeHKN, Alpha ChapterUniversity of Illinois at Urbana-ChampaignAugust 30, 2008)

Visit http://pure.engr.illinois.edu

Promoting Undergraduate Research in Engineering (P.U.R.E.)Fall 2013 Information Session

Wednesday, September 4th from 7pm to 8pmat 1404 Siebel CenterFood will be provided!https://wiki.engr.illinois.edu/display/PURE/Home)

The PUREResearch Program is an interdisciplinary program in the College of Engineering pairing freshman and sophomore undergraduates with research mentors(graduate students). The general goal of the program is to encourage underclassmen to explore research at an early stage in their academic career.

2Brief ReviewPropositional logicAND, OR, T/F, implies, etc.Equivalence and truth tablesManipulating propositionsThe satisfiability problem (SAT)Applications of SAT solvers: model checking

Predicate logicPredicate logic (first-order logic)QuantifiersBinding and scopebindingscopeSimilar to local variables in programs:

int f(x) { int y; y := x+2; }Manipulating quantifiersManipulating quantifiersQuantifiers with two variablesProving universal statementsApproach to proving universal statementsProving universal statementsProving universal statementsProving universal statementsApplications of first-order logic Programming models:Imperative programming (C, )Functional programming (Haskell, Ocaml, )Object-oriented programming (Java, C++, ...) Logic programming (Prolog, Datalog, )

Declaratively state what you want in logic; program will compute it.

Prolog: Rules of the form p(X, Y) ifq(X) and r(Y), etc. Question: p(Obama, president)? Take home messagesPropositions with for all and there exists can be encoded with quantifiers

Remember rules for negation and equivalence of quantifiers

Universal proofs are solved byStating suppositionExpanding definitionsManipulating expressions to reach claimStating that the claim has been shownTo doMini-HW 1 due tomorrow, Wed, at 11:45pm on MoodleReading quiz due tomorrow night at 1:00am

Next class:Strategies for proving and disproving different types of claims


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