Phil 301 : Symbolic Logic <wmi

Class Times: Tuesdays and Thursdays, 11.30am-l pmLocation: McDonnell Hall, 162

Course Website: http://wvvvv.artsci.vvustl.edu/-gnissell/Phin0l-F1 1 .html

Instructor: Professor Gillian RussellOffice hours: Thursdays 2.30-3.30pm or by appointment

Office Location: 209 Wilson HallEmail: grussell - at - vvustl - dot - edu

Teaching Assistant: Justin TaylorOffice Hours: Mondays and Wednesdays 1 lam-noon.

Location of office hours: Justin Taylor's office in the Danforth University CenterEmail: wjtaylor - at - go - dot - vvustl - dot - edu

This course continues on where Phil 100: An introduction to Logic and Criticial Analysis leaves off. It is recommended forstudents who have already taken that course, or for students who have a strong background in mathematics. It is intended to helpbridge the gap between Phil 100 and Phil 403: Mathematical Logic. To that end will we gradually introduce more metatheoreticalresults and more challenging proof methods, with a particular focus on proof by induction.

In the first half of the course we will be studying some features of truth-functional and first-order classical logics, and in particularwe'll investigate the model theory for first-order logic in much greater depth than in Phil 100. After the midterm, we'll go on tostudy three different styles of proof: tableaux, axiomatic, and natural deduction. We will study completeness results for thesesystems.

_>ooks

The textbook for this course is David Bostock's Intermediate Louie, published by Oxford (Clarendon). It is the only text you needto buy and there has only been one edition. Second hand copies are fine.

Readings, Topics and Homework AssignmentsTuesday 30th AugustTruth-functions and truth-functors.Reading: Pages 3-24 of Bostock.

Thursday 1st SeptemberSemantics for truth-functional languages.Reading: Pages 24-30 of Bostock. No homework this week.

Tuesday 6th SeptemberPrinciples of entailment (thinning, cut, etc.)Reading: Pages 30-37 of Bostock.

hursday 8th SeptemberNormal forms (DNF, PNF, etc.)Pages 37-45 of Bostock.Exercises (1): 2.1.1,2.2.1,2.3.1, 2.4.1(a), (c), (e), (g), (i), 2.4.2. Due Friday 9th September. It hCfc5pw Vr

Tuesday 13th September

Expressive adequacey. Pages 45-48.

Thursday 15th SeptemberMathematical Induction.Reading: Pages 48-56 of Bostock.Exercises (2): 2.5.1,2.5.3, 2.6.1 Due Friday 16th September.

Tuesday 22nd September

Expressive adequacey II.Reading: Pages 56-62 of Bostock.

Thursday 24th September

Duality and truth-value analysis.Reading: Pages 62-69 of Bostock.Exercises (3): 2.7.1,2.8.1 ,2.8.2,2.8.3. Due Friday 25th September.

Tuesday 27th SeptemberThe language of first order logic.Reading: Pages 70-81 of Bostock.

Thursday 29th SeptemberModel theory for first order logic.Reading: Pages 81-96 of Bostock.Exercises (4): 2.9.1,2.9.2, 2.10.1, 2.11.1 Due Friday 30th September.

Tuesday 4th OctoberMore principles of entailment.Reading: Pages 96-108 of Bostock.

Thursday 6th OctoberPrenex normal form.Reading: Pages 109-115 of Bostock.

Exercises (5): 3.3.1,3.3.4,3.5.1 Due Friday 7th October.

Tuesday 11th OctoberDecision procedures for monadic predicate formulas. Pages 115-126 of Bostock.

Thursday 13th OctoberMidterm Preparation - your homework this week is to prepare for the exam.

Tuesday 18th OctoberMIDTERM EXAMINATION (IN CLASS)

Thursday 20th October

No Class No Homework due. Professor Russell's office hours will be on Wednesday at 2.30pm this week.

Tuesday 25th October

Proofs and Counterexamples. Pages 131-138 of Bostock.

Thursday 27th Octobermantle tableaux I - proofs with truth-functors,jading: Pages 141-147 of Bostock. No homework this week.

Tuesday 1st NovemberSemantic Tableaux II - proofs with quantifiersReading: Pages 149-165 of Bostock

Thursday 3rd NovemberNo Class. Professor Russell's office hours will be on Wednesday at 2.30pm this week.

Exercises (6): 3.6.3, 3.7.1, 3.7.2 Due Friday 4th November.

Tuesday 8th November

Semantic tableaux III - Soundness and Completeness.Readings: pages 164 - 189 of Bostock.

Thursday 10th NovemberAxtiomatic proofs I - proofs and the deduction theorem.Reading: Pages 190 - 208 of Bostock. No homework this week.

Tuesday 15th Novemberrvxiomatic proofs II - Laws of negation. Truth-functional completeness.Reading: Pages 208 - 220 of Bostock.

Thursday 17th NovemberNO CLASS. Professor Russell's office hours will be on Wednesday at 2.30pm this week.

Tuesday 22nd NovemberAxiomatic proofs III - Axioms for the quantifiers. Alternative axiomatisations.Reading: Pages 220 - 238 of Bostock.

Thurday 24th NovemberTHANKSGIVING BREAK . NO HOMEWORK THIS WEEK.

Tuesday 29th NovemberNatural deduction I - rules for the truth-functors.Reading: Pages 239 - 254 of Bostock.

Thursday 1st DecemberNatural deduction II - rules for the quantifiers. Alternative proof styles...eading: Pages 254-272.

Homework exercises (7): 4.1.2,4.2.1,4.4.1 (a), (e) and (k) and 4.4.2(a), (b) and (c) Due Friday 2nd December.

Tuesday 6th DecemberScheduled catch up class (in case any of these topics take more time than planned.)

Thursday 8th DecemberReview class for final examination (Monday 19th December l-3pm in usual room.)

Homework Exercises (8): 5.3.1,. 1,5.4.1 Due Friday 9th December.

• Homework exercises are listed on the syllabus, with their due dates (always a Friday.) They are to be completed on paperand turned in to the appropriate drawer of the "turn-in" filing cabinent in the philosophy department office (2nd floor ofWilson Hall, opposite Professor Russell's office.)

• Homework is due by 3.30pm on the date listed. Please be considerate of the office staff; the office closes at 4pm and we tryto discourage students from knocking on the door at 4.01pm.

You may handwrite your homework (in fact, this is often faster and less prone to unfortunate typing errors) but you shouldalways turn in neat, legible work, clearly marked with your name (you should not put your student number on your work.)Do not turn in "rough" work, or work with lots of crossings-out.

• Solutions to the problem sets will be given out in class.

> Any homework set received after the solutions have been given out will receive a grade of zero.

Assessment50% of the arade for this course will come from the homework exercises completed during the semester. 25% will come from thein-class midterm exam on October 18th and 25% from the final exam, which will be held during the official exam period, onMonday 19th December, lpm-3pm, in our usual room. If you decide to take this course, you will need to make sure that you arestill on campus for the exams.

For students taking the course pass/fail, the minimum letter grade required for a pass will be a D, which can be obtained with anoverall percentage grade of 50%.

Academic IntegrityIt is very important that you understand the rules for collaboration on this course. You may work with other studeiwork out solutions to the exercises in your take-home problem sets; in fact, this is encouraged. However, each stULup his or her solutions to the exercises alone. You may not do it with another student looking over your shoulder to co_You may not write your homework from notes which another student has made, nor may you make notes on another student swritten solutions. You may not lend or copy digital or paper homework solutions - at any stage of completion.

Collaboration is, of course, completely forbidden during the midterm and final examinations.

Sometimes it is unclear whether a hypothetical case of collaboration is permissible according to these rules, or whether it counts asmisconduct, but it is your duty to ensure that ALL your collaborations are clearly permissible. One good way to do this is not towrite anything down on paper whilst investigating problems with other students: use a chalk board or white board to work outideas, (or, if you use paper, dispose of the written solutions before you separate to write up your individual homeworks alone.)

Students suspected of plagiarism or any other form of academic dishonesty or misconduct will be reported to the academic integrityofficer for Arts and Sciences (currently Dean Killen), so that the incident may be handled in a consistent, fair manner, and so thatsubstantiated charges of misconduct may be noted in students' records.

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