
Schedule
Spring 2018
Lectures:
13:3015:15 in
Huygens 106109 on 6/02, 20/03, 03/04; Huygens 211/214 all other dates. Practica: 09:0010:45 in Snellius 313 and Snellius 412* * From March 23rd on the practica will be only in Snellius 313. 
Goal
This course gives an introduction to the field of mathematical logic by presenting the syntax and semantics of propositional logic and of the richer language of predicate logic. The goal is to describe and investigate the above logics by finitary methods, and to train students in formalizing specifications and in verifying properties of systems.
Description
Originally logic was used by the Greek Sophists to demonstrate the correctness of their argument in formal debates. The ambiguity of human languages asked for formulation of logic in a symbolic formal language.
Only towards the end of the 19th century logic has been formulated in the language of mathematics, and in particular of algebra, making it a useful tool to solve mathematical problems. In the same period the language used to prove theorems from mathematics begun suffering the same problems of natural language, showing many paradoxes. Logic was proposed as the foundational language of mathematics, but several limitation where soon discovered.
More recently logic has become the language of computer science, just as calculus is the language of many engineering discipline. In this course we will study propositional and predicate logic, their proof theory, their limitation, as well as some of their applications in computer science.
Literature
Schedule lectures
Nun  Date  Topic  Reading  Extra 
1a  6 Feb  Overview + history of logic  [V03]  
1b  The language of propositional logic (PL)  [HR04]:1.1, 1.3 
Ex. 1.1:12  
2a 
14 Feb 
Semantics
of propositional logic 
[HR04]:1.4.1 
Ex. 1.4: 13, 5 
2b 
Mathematical
induction 
[HR04]:1.4.2 
Ex.
1.4:79 

HOMEWORK 1 (deadline 2 March)  solution 

3a  20 Feb  Semantic entailment  [HR04]:Def. 1.34  
3b  Natural deduction (until rules for implication)  [HR04]:1.2.1 
Ex.
1.2:12 

4 
27 Feb 
Natural deduction (until rules for negation)  [HR04]:1.2.1  Ex.
1.2:12 
5a 
6 Mar 
Natural
deduction 
[HR04]:1.2 
Ex. 1.2:3,5 
5b  Soundness
and completeness of PL 
[HR04]:1.4.3, 1.4.4 
Ex. 1.4:12, 13,16,17  
HOMEWORK 2 (deadline 23 March)  solution 

13 Mar  No class  
6a  20 Mar  completeness of PL  [HR04]:1.4..4  Ex. 1.4:16,17 
6b  Semantic tableau
for propositional logic 
[Kup05] [BDKLM03] 
Ex. 1.2.2 

7  27 Mar  Validity and conjunctive normal form  [HR04]:1.5.12  Ex. 1.5:3,4, 7,9 
HOMEWORK 3 (deadline 10 Apr)  solution  
8a  3 Apr  Satisfiability and Horn formulas  [HR04]:1.5.3  Ex. 1.5:15 
8b  SAT solvers  [HR04]:1.6  Ex. 1.6:25  
9 
10 Apr  The
language of predicate
logic (PL) 
[HR04]:2.1,
2.2 
Ex. 2.1:1,3 2.2:3,4 
10 
17 Apr 
Natural deduction
for predicate logic 
[HR04]:2.3 
Ex. 2.3:3,7, 9,11,12 
HOMEWORK 4 (deadline 4 May)  solution  
11  24 Apr 
Semantics of
predicate logic 
[HR04]:2.4 
Ex. 2.4:1,5,6 
12a  1 May 
Undecidability of predicate logic (excluding proof of Theorem 2.22)  [HR04]:2.5  
12b 
Expressivity
of
predicate logic 
[HR04]:2.6 
Ex: 2.6: 1, 4, 5,
6, 8, 9 

13a  8 May  Expressivity of predicate logic  [HR04]:2.6  Ex: 2.6: 1, 4, 5, 6, 8, 9 
13a  Semantic
tableau
for predicate logic 
[Kup05] 
Ex. 2.3.9, 2.5.1 

HOMEWORK 5 (Deadline 25 May )  solution  
13  10 May  Final discussion 
Bibliography
[BDKLM03] J.F.A.K. van Benthem, H.P. van Ditmarsch, J. Ketting, J.S. Lodder, and W.P.M. MeyerViol. Logica voor informatica, derde editie Pearson Education, 2003.[HR04] Michael R. A. Huth and Mark D. Ryan. Logic in Computer Science: Modelling and Reasoning about Systems, Cambridge University Press, 2004.
[Kup05] Jan Kuper. Overview of proposition and predicate logic, notes 2005.
[V03] Moshe Vard.i A Brief History of Logic, 2003.
LaTeX and proofs
For writing natural deduction proofs in LaTeX you can use Paul Taylor's macro's voor proof boxes. Here is an example of a proof in natural deduction from the book in .tex en .pdf.Exam and homework information
 Examination is worth 70% of the final grade (with a minimum of 5.5). The remaining 30% is from the average grade of theof the 4 best out of the 5 homeworks.
 Write clearly your name and student number in your homework solution.
 Return your homework solution as a single pdf file by email to t.b.a..
 Name your pdf file containing the solution as HWxxNameSurname.pdf, where xx ranges from 1 to 5 and it is the number of homework.
 Solutions
sent after the deadline are not accepted.
 Grades of the homeworks will be published on blackboard.