Mathematical Foundations of Computational Linguistics I:
Set Theory, Algebra and Logic

(http://www.coli.uni-saarland.de/~saurer/lehre/mg1/mg1-engl.html)

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Lecture with exercise session
B.Sc. Computational Linguistics
Instructor: Werner Saurer, Stefan Thater


Lec Mon 14-16, Wed 13-14; Building C 72, Seminar Room
Ex: Wed 16-18; Building C 72, Seminar Room
First lecture: Wed 22 Oct 2014, 13h


Content of course

This course - the first of a 2-semester sequence - introduces set theory, ordering relations, some algebra (groups, lattices) as well as propositional logic and first order predicate logic with identity. The emphasis will be on logic. Each of the two logics will be investigated from four aspects: formal syntax, formal (model-theoretic) semantics, proof theory and application to natural language (formalisation, "informal semantics"). The aim of the course is to make the student familiar with basic logical skills such as formalizing natural language sentences, construction of formal proofs within a natural deduction system and semantic evaluation of (sets of) formulas (truth table method, determining truth conditions of formulas).

Prerequisites

None. The language of instruction is German and set theory.

Position in degree programs

Obligatory course for the  B.Sc. in Computational Linguistics (CL), and CL as a minor for M.A. students. There will be a midterm and a final exam, 45 min each. The course carries 8 credit points.(For further details regarding course requirements, in particular registration for the exams, see German version.)

Text books

Partee, B., A. ter Meulen, R.Wall, Mathematical Methods in Linguistics. Kluwer 1990.
Leblanc, H., W. Wisdom, Deductive Logic. Allyn and Bacon, 1976.
Thomason, R., Symbolic Logic. Macmillan, 1970.

Exercise session

Wed 16-18; first meeting: 29 October 2014


Lecture plan (approximate)

Weeks 1 and 2 Basic concepts of set theory
Weeks 3 and 4 Basic concepts of ordering relations and algebraic structures (groups, lattices)
Weeks 5 - 8 Propositional logic: Formalisation, syntax and semantics
Week 8 Midterm exam on material of the first half of the course; sample exam
Weeks 9 and 10 Propositional logic: Proof theory (Natural Deduction)
Weeks 11 - 13 Predicate logic: Formalisation, syntax, proof theory (Natural Deduction)
Weeks 14 and 15 Predicate Logic: formal (model-theoretic) semantics
Week 16 Final exam on material of the second half of the course; sample exam


Course mechanics (in German only)


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