2.0 VU Nonclassical logics (185.A95, SS 2018)
This course will be held in English.
The final meeting took
place Monday, June 25, 13.00 (sharp) - 15.00,
Seminar Room Gödel,
Favoritenstraße 9, ground floor.
Planned dates of meetings
(always Mondays 13.00-15.00)
April 8, April 23, April 30, May 14, May 28, June 4, June 18, June 25
Seminar Room Gödel
Favoritenstraße 9 / ground floor
At the meeting on May 28, we agreed to skip the topic "intuitionisitc logic" this year and rather to include at least some ideas and remarks on the following topics:
substructural logics, in particular linear logic and relevance logics, different forms of semantics, games and logic.
(If you have further suggestions drop an email to Chris Fermüller)
- short reminder on the main concepts
of classical first order logic
- informal classification and
overview over the vast area
of 'nonclassical logics' for orientation
- In the main part of the course we plan to cover the
following areas and topics:
- Modal logics (this will be our main topic):
- What are modal logics? What are they used for?
- Introduction into the general theory of modal logics:
syntax, (Kripke style) semantics,
proof systems, expressibility, 'correspondence theory',
relations between important modal logics, multi-modal logics, ...
- Epistemic logic(s) (for modelling multi-agent systems)
- Hints at other families of modal logics:
temporal logic, deontic logic, dynamic logic, provability logic, ...
- Constructive logic (intuitionistic logic):
- general motivation
- different semantics: Kripke/Beth style semantics,
Brouwer-Heyting-Kolmogorov interpretation, topological semantics
- different proof systems: Hilbert type, sequent system(s),
'natural deduction', ...
- dialogue games characterizing constuctive (and other) logics
- Selected topics on other types of logics, e.g.,:
- many valued logics, fuzzy logics
- game semantics, dialogue games
- dynamic epistemic logic
- relevance logic
Basic knowledge about classical propositional and first-order logic
as covered, e.g., in "Theoretische Informatik und Logik".
TEST YOURSELF whether you are fit for this course:
You should be able to prove without handwaving (and
preferably without consulting any book or notes)
that (forall x) (exists y) P(x,y) is a logical consequence of
(exists x) (forall y) P(y,x), and to (rigorously) show that
the converse does not hold.
In particular you should be able to present a formal definition
of the (logical) consequence relation and of a (formal)
model/interpretation of a classical first-order formula.
The course will take place in slightly blocked form on 8 or 9
Various course material - in particular copies of the lecture slides, including
the homework problems ('exercises') -
will be made available here (and/or in the lecture) to all participants.
- Slides, lecture 1 on 9/4/18: [PDF]
- Slides, lecture 2 on 23/4/18: [PDF]
- Slides, lecture 3 on 30/4/18: [PDF]
- Slides, lecture 4 on 14/5/18: [PDF]
- Slides, lecture 5 on 28/5/18: [PDF].
- Lecture 6 on 4/6/18:
Muddy children / Wise Men: [PDF, 3 pages]
slides 9 to 32 of ESSLI 2013 sildes, lecture 1(Wes Holliday)
See also `Simplifying the Surprise Exam' by Wes Holliday
Exercises for lecture 6: [PDF]
- Lecture 7 on 18/6/18:
You have received 3 handouts (Hilbert style axiom systems, classical and linear sequent calculi, sequent calculus for linear logic.)
We recommend to check the following entries
in the Stanford Encyclopedia of Philosophy
One of the exercises refers to:
Paradoxes of material implication, Wikipedia entry
Exercises for lecture 7: [PDF]
- Slides, lecture 8 on 25/6/18: [PDF].
I strongly recommend the use of LaTeX.
Useful style files are available from
Latex for Logicians.
For drawing graphs and automata - and thus also Kripke models -
the LaTeX package
VauCanSon-G should be useful. More options for automata/graph drawing
with LaTeX can be found at MET - Automata in LaTeX.
Also the TeX/LaTeX extension PGF/TikZ is well worth exploring.
Include the problem statement, its number
(`Exercise X: ... ') and your name
in the submitted solution files. Send corresponding
(uncompressed) PDF files via
email to Chris Fermüller
using "NCL exercises" as subject line.
The evaluation will be based on the amount and quality of
submitted solutions to the exercises (as assigned during the course).
Send COMMENTS/REQUESTS to Chris Fermüller
[ LVAs 185/2
| Abteilung 185/2
| Institut 185
| TU Wien
| Server home page