Mathematical Logic
(https://www.coli.uni-saarland.de/~saurer/lehre/ml/math-logic.html)
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Lecture with Exercise Session.
B.Sc., M.Sc. LS&T and LCT
Instructor: Werner Saurer
Lecture: Tue 12:15 - 13:45, online
Exercise Session: Mon 12:15 – 13:45, online
First meeting: Mon 19.04.2021 (lecture)
Content
The course will be offered
this summer semester and will be taught– for the time being anyway – online,
using MS Teams. A team “Mathematical Logic” has been installed to which you can
add yourself by using the code rt23vjy. (To log on to MS Teams you have to use
your university user id, e.g. abcd001, followed by @uni-saarland.de. You will
also need your password for this user id.) – The first meeting of this course
will take place on Monday, April 19, 12:15 pm. You will see that I have
added some course material for the lectures and exercise sessions. More will be
added later, as needed. I will provide notes for each lecture and exercise
session, and I will closely follow these lecture notes in my presentation.
Please get a hard copy of the lecture notes and have them with you during the
lectures. In addition the course notes will be visible on screen during the
lectures. The registration deadline for the final exam is July 12, 2021.
If you are interested in
this course, you can add yourself to the team for this course with the code
rt23vjy.
Mathematical logic is one of the
most important formal tools in computational linguistics, especially - but not
only - for semantics. In this intermediate to advanced course in logic we will
be largely concerned with metalogical results such as
correctness and completeness of logical calculi. We will consider axiom systems
for propositional and first order predicate logic and prove that these systems
are semantically correct and complete.
Prerequisites
Mathematical Foundations I or good
working knowledge of first order predicate logic.
Text book (available in the library)
R. H. Thomason, Symbolic Logic.
An Introduction. Macmillan 1970 [T]
·
Position in degree programs
The course carries 6 credit points
(M.Sc.: specialization course in linguistics/computational linguistics). There
will be a written exam (90 min) at the end of the semester. The dates for registration
and exam will be announced in time.
Exercise session
There will be a separate exercise
session (2h). The beginning will be announced in the first lecture meeting.
· Course Schedule
<>Lecture 1
Introduction, (uninterpreted) formal systems, an
axiom system, informal semantics
Reading: [T] Chapters I and II
Lecture 2
Natural deduction (conditional logic and full propositional logic)
Reading: [T] Chapters III and IV
Lecture 3
Metatheory of propostional logic: syntax; the system
Hs, various metatheorems on Hs (M1-M7); significance
of the deduction theorem
Reading: [T] Chapter V
Lecture 4
Proof of the deduction theorem; further metatheorems
and definitions; metatheorems and their relation to
the rules of natural deduction
Reading: [T] Chapter V
Lecture 5
Replacement and substitution; admissible and derived rules; consistency
Reading: [T] Chapter V
Lecture 6
Semantics for the system Hs. Important semantic definitions and metatheorems. Truth table method, consistency trees,
semantic tableaux
Reading: [T] Chapter VI
Lecture 7
Correctness and completeness of Hs (1)
Reading: [T] Chapter VII
<>
Lecture 8
Correctness and Completeness of Hs (2); Introduction to predicate logic
Reading: [T] Chapters VII and VIII
Lecture 9
The system Sp= (natural deduction). The axiom system Hp= (proof theory)
Reading: [T] Chapters IX and X
Lecture 10
Semantics of Hp=
Reading: [T] Chapter XI
Lecture 11
Correctness and Completeness of Hp= (1)
Reading: [T] Chapter XII
Lecture 12
Completeness of Hp= (2), adequacy results of Hp=, closing remarks
Reading: [T] Chapter XII
Office hours
Wed
14-15, Building C 72, Room 1.06, Tel. 302-4177
E-mail 
Werner Saurer