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<title>Mathematical Logic via Foundational Algorithms</title>

CS 410/510 Mathematical Logic via Foundational Algorithms<br>
Winter term, 2011 <br>
CRN 44342 (CS 410) and 44343 (CS 510) <br>
Tuesday / Thursday 14:00-15:50<br>
Fourth Avenue Building (FAB), room 150.<br>
<p><!-- <table border="1"> --></p>
<table style="border-collapse: collapse" width="827" border="1" cellspacing="0" cellpadding="3" bgcolor="#e6e6cf">
	<tr>
		<th>Day</th>
		<th>Date</th>
		<th>Notes Topic</th>
		<th>Readings</th>
		<th>Exercises</th>
		<th>Problem sets</th>
		<th>Due Today</th>
	</tr>

	<tr><!--  ********* Week 1  Tuesday ************ -->
		<td>T1</td>
		<td>Jan 4</td>
		<!-- notes -->
		<td>Propositional Logic: definition, natural deduction proofs<br>
		MCECS <A HREF="http://web.cecs.pdx.edu/~sheard/course/CS457-557/Doc/MCECSInnovationProgram.pdf">Innovation Proposal</A> announcement.
		</td>
		<!-- reading -->
		<td>Read: HR 1.1-3 <a href="pdf/outline.pdf">outline.pdf</a> 1</td>
    <!-- exercise -->
		<td> <A HREF="Exercises/Ex1ForwardProof.html">Exercise 1</A>. Natural Deduction forward style Proofs.</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td>&nbsp;</td>
	</tr>
    <tr><!--  ********* Week 1  Thursday ************ -->
		<td>H1</td>
		<td>Jan 6</td>
		<!-- notes -->
		<td>Prop logic: truth, validity, satisfiability, tautology, soundness</td>
		<!-- reading -->
		<td>HR 1.4 <a href="pdf/outline.pdf">outline.pdf</a> 2</td>
    <!-- exercise -->
		<td><a href="Exercises/Ex2BackwardProof.html">Exercise 2</a>. Natural Deduction in HR style</td>
    <!-- Problem sets -->
		<td> <A HREF="Assignments/P1TautologyChecker.html">P1</A>. Write a tautology checker. </td>
		<!-- Due Today -->
		<td><A HREF="Exercises/Ex1ForwardProof.html">Exercise 1</A>.</td>
	</tr>

	<tr><!--  ********* Week 2  Tuesday ************ -->
		<td>T2</td>
		<td>Jan 11</td>
		<!-- notes -->
		<td>Prop logic: Tableau proof</td>
		<!-- reading -->
		<td><p>HR 1.4 - 1.6<br />
		  (Fitting Chapter 3) <a href="pdf/outline.pdf">outline.pdf</a> 3</p>
      </td>
    <!-- exercise -->
		<td><a href="Exercises/Ex3RefutationProof.html">Exercise 3</a>: Proofs in tableau style and L style</td>
    <!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td><a href="Exercises/Ex2BackwardProof.html">Exercise 2</a></td>
  </tr>
    <tr><!--  ********* Week 2  Thursday ************ -->
		<td>H2</td>
		<td>Jan 13</td>
		<!-- notes -->
		<td>Prop logic: completeness, deciding truth, normal forms,</td>
		<!-- reading -->
		<td>&nbsp; </td>
		<!-- exercise -->
		<td><A HREF="Exercises/Ex4Minisat.html">Exercise 4</A>. Using minisat to test tautologies.
		<A HREF="Assignments/MinisatOnWindows.html"><br />
		Installing MiniSat on Windows</A>. <br />
		<a href="Assignments/MinisatOnMac.html">Installing MiniSat on Mac</a></td>
  <!-- Problem sets -->
		<td><A HREF="Assignments/P2CNF.html">P2.</A> Write a toCNF function</td>
		<!-- Due Today -->
		<td><A HREF="Assignments/P1TautologyChecker.html">P1 - Tautology.</A> <a href="Exercises/Ex3RefutationProof.html">Exercise 3</a></td>
  </tr>



	<tr><!--  ********* Week 3  Tuesday ************ -->
		<td>T3</td>
		<td>Jan 18</td>
		<!-- notes -->
		<td> SAT solvers. Applications of SAT solvers. Representing and asking questions about finite sets.</td>
		<!-- reading -->
		<td><A HREF="lectures/FiniteSets.pdf">The FiniteSet module</A></td>
		<!-- exercise -->
		<td> <A HREF="Exercises/Ex5AlgebraOfSets.html">Exercise 5.</A> An algebra of sets.</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td><A HREF="Exercises/Ex4Minisat.html">Exercise 4</A></td>
  </tr>
    <tr><!--  ********* Week 3  Thursday ************ -->
		<td>H3</td>
		<td>Jan 20</td>
		<!-- notes -->
		<td>Applications of SAT solvers.</td>
		<!-- reading -->
		<td>&nbsp; </td>
		<!-- exercise -->
		<td>predicate logic word problems</td>
		<!-- Problem sets -->
		<td><A HREF="Assignments/P3Soduko.html">P3.</A> 4x4 Soduko Solver.<BR>
		    <A HREF="Code/Minisat.hs">Minisat library</A>.
		    <A HREF="Assignments/MinisatOnWindows.html">Installing MiniSat on Windows</A>. <a href="Assignments/MinisatOnMac.html">Installing MiniSat on Mac</a></td>
		<!-- Due Today -->
		<td><A HREF="Assignments/P2CNF.html">P2 - CNF.</A></td>
	</tr>




	<tr><!--  ********* Week 4  Tuesday ************ -->
		<td>T4</td>
		<td>Jan 25</td>
		<!-- notes -->
		<td>SAT solver internals</td>
		<!-- reading -->
		<td>HR 1.6, <a href="pdf/outline.pdf">outline.pdf</a> 6</td>
    <!-- exercise -->
		<td><a href="Exercises/Ex6CubicSolver.html">Exercise 6</a>: Reassembling the cubic solver (link coming soon)</td>
    <!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td><A HREF="Exercises/Ex5AlgebraOfSets.html">Exercise 5.</A></td>
	</tr>
    <tr><!--  ********* Week 4  Thursday ************ -->
		<td>H4</td>
		<td>Jan 27</td>
		<!-- notes -->
		<td>Predicate Logic: Introduction, Syntax, Substitution, Semantics</td>
		<!-- reading -->
		<td>HR 2.1 -- 2.4, <a
		href="pdf/outline.pdf">outline.pdf</a> 7 </td>
		<!-- exercise -->
		<td>&nbsp; </td>
		<!-- Problem sets -->
		<td><a href="pdf/outline.pdf">outline.pdf</a> 7.4  </td>
		<!-- Due Today -->
		<td><p><A HREF="Assignments/P3Soduko.html">P3 - Soduko Solver</A></p>
	    <p><a href="Exercises/Ex6CubicSolver.html">Exercise 6</a></p></td>
		<!-- Due Today --></td>
	</tr>




	<tr><!--  ********* Week 5 Tuesday ************ -->
		<td>T5</td>
		<td>Feb 1</td>
		<!-- notes -->
		<td>Tableau proofs; Herbrand models; Model existance theorem</td>
		<!-- reading -->
		<td><p>outline.pdf 8, <br />
		  (Fitting Chapter 5)
	  </p></td>
		<!-- exercise -->
		<td>&nbsp</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td>&nbsp;</td>
	</tr>
    <tr><!--  ********* Week 5  Thursday ************ -->
		<td>H5</td>
		<td>Feb 3</td>
		<!-- notes -->
		<td>NK, LK, and Tableau proof systems. Soundness and completeness.</td>
		<!-- reading -->
		<td>&nbsp</td>
		<!-- exercise -->
		<td><a href="Exercises/Ex7FOLProver.html">Exercise 7</a>: A prover for LK</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td><a href="pdf/outline.pdf">outline.pdf</a> 7.4  </td>
	</tr>




	<tr><!--  ********* Week 6  Tuesday ************ -->
		<td>T6</td>
		<td>Feb 8</td>
		<!-- notes -->
		<td>Automating proof systems, Skolem functions, unification</td>
		<!-- reading -->
		<td>&nbsp</td>
		<!-- exercise -->
		<td>&nbsp</td>
		<!-- Problem sets -->
		<td><a href="pdf/outline.pdf">outline.pdf</a> Problem Set 10.3: unification and tableau prover</td>
		<!-- Due Today -->
		<td>&nbsp;</td>
	</tr>
    <tr><!--  ********* Week 6  Thursday ************ -->
		<td>H6</td>
		<td>Feb 10</td>
		<!-- notes -->
		<td><A HREF="lectures/SMT.html">SMT provers</A>
	  </td>
		<!-- reading -->
		<td>&nbsp</td>
		<!-- exercise -->
		<td>&nbsp</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td>&nbsp;</td>
	</tr>

	<tr><!--  ********* Week 7  Tuesday ************ -->
		<td>T7</td>
		<td>Feb 15</td>
		<!-- notes -->
		<td>Path coverage using SMT</td>
		<!-- reading -->
		<td>&nbsp</td>
		<!-- exercise -->
		<td>&nbsp</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td><a href="pdf/outline.pdf">outline.pdf </a>10.3</td>
	</tr>
    <tr><!--  ********* Week 7  Thursday ************ -->
		<td>H7</td>
		<td>Feb 17</td>
		<!-- notes -->
		<td>&nbsp;</td>
    <!-- reading -->
		<td>&nbsp;</td>
    <!-- exercise -->
		<td>&nbsp;</td>
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td>&nbsp;</td>
	</tr>

		<tr><!--  ********* Week 8  Tuesday ************ -->
			<td>T8</td>
			<td>Feb 22</td>
			<!-- notes -->
			<td>Higher-order logics</td>
      <!-- reading -->
			<td>outline.pdf 11</td>
			<!-- exercise -->
			<td>&nbsp</td>
			<!-- Problem sets -->
			<td>&nbsp;</td>
			<!-- Due Today -->
			<td>&nbsp;</td>
		</tr>
	    <tr><!--  ********* Week 8  Thursday ************ -->
			<td>H8</td>
			<td>Feb 24</td>
			<!-- notes -->
			<td>Propositions as Types</td>
			<!-- reading -->
			<td>outline.pdf 12</td>
			<!-- exercise -->
			<td>Some <A HREF="Code/CurryHowardExamples.hs">examples</A> of Curry-Howard in Haskell</td>
		<!-- Problem sets -->
			<!-- Problem sets -->
			<td>&nbsp;</td>
			<!-- Due Today -->
			<td>&nbsp;</td>
	</tr>

	<tr><!--  ********* Week 9  Tuesday ************ -->
		<td>T9</td>
		<td>Mar 1</td>
		<!-- notes -->
		<td>Temporal Logic and model checking: Intro, Examples, NuSMV</td>
    <!-- reading -->
		<td>HR 3.1 -- 3.5</td>
  <!-- exercise -->
		<td>Download NuSMV (Mac ports for mac; <a href="http://nusmv.fbk.eu/">http://nusmv.fbk.eu/</a> for Linux and Windows)</td>
  <!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td>&nbsp;</td>
	</tr>
    <tr><!--  ********* Week 9  Thursday ************ -->
		<td>H9</td>
		<td>Mar 3</td>
		<!-- notes -->
		<td>Foundations: Process language; Kripke Models; Semantics; A Model checking algorithm</td>
		<!-- reading -->
		<td>HR 3.5 -- 3.7 (Clarke, Grumberg, and Peled 2, 3, 4)</td>
    <!-- exercise -->
		<td>&nbsp</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td>Share Experiences with NuSMV</td>
	</tr>

	<tr><!--  ********* Week 10  Tuesday ************ -->
		<td>T10</td>
		<td>Mar 8</td>
		<!-- notes -->
		<td>BDDs</td>
		<!-- reading -->
		<td>Chapter 6</td>
		<!-- exercise -->
		<td>&nbsp</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td>&nbsp;</td>
	</tr>
    <tr><!--  ********* Week 10  Thursday ************ -->
		<td>H10</td>
		<td>Mar 10</td>
		<!-- notes -->
		<td>&nbsp
		</td>
		<!-- reading -->
		<td>&nbsp</td>
		<!-- exercise -->
		<td>&nbsp</td>
		<!-- Problem sets -->
		<td>&nbsp;</td>
		<!-- Due Today -->
		<td>&nbsp;</td>
	</tr>


</table>
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