LEMUS LECTORIUM
LEMUS
A PROJECT FOR ECTS -
European Credit Transfer System
TEACHING SUBJECT CHART -- LOGIC
ECTS Code
Subject title: LOGIC
The Course Leader: Witold Marciszewski
Ordinary Professor, Habil. Dr.
Lectures: 2 hours every week, two semesters
Student outcomes assessment with:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(1) written partial exams
(2) written semester homeworks
(3) interactive seminars (within lectures)
(4) final spoken exam.
Exercises: 2 hours every week, two semesters
Written partial exams.
Full-time studies, First Year, Philosophy.
The goals of the course. Students should master:
~~~~~~~~~~~~~~~~~~~~~~~~
(1) first-order logic techniques of the algorithmic checking
of formal correctnes of inferences
(2) practical use of the theory of classes and relations
(3) the notions of consistency and algorithmic decidability
(4) the notions of algorithm, program, and their binary coding
(5) the use of normal and partial definitions
(6) applying the logic of questions in social research.
Preparatory Requirements
~~~~~~~~~~~~~~~~~~~~~~~~
versatility in the grammar of one's native language (as Polish)
at least basic knowledge of English
versatility in using the Web.
The set of key concepts
~~~~~~~~~~~~~~~~~~~~~~~
algorithm, analytic trees, automaton, class (set), computer, consequence,
consistency, counterexample, decidability, deduction, definition,
first-order logic, formalization, grammar, necessary condition, predicate
logic, program (software), propositional logic, question, relation,
satisfiability, semantics, sufficient condition, syntax, tautology, truth,
truth-functional operator.
Table of contents as divided into instructional four-hour-lecture units
~~~~~~~~~~~~~~~~~
1. Logical grammar compared with natural language grammars. Declarative,
normative and interrogative propositions. The structure of interrrogative
propositions, their underlying assumptions.
2. Propositional logic: truth-functional operators compared with connectives
of a natural language; the concepts of validity and tautology.
3. Propositional logic: algorithmic checking of validity: the "brute-force"
method, and the "intelligent" method of counterexample.
4. Propositional logic: applications to the testing of formal correctness
of deductive inferences. Necessary vs. sufficient condition.
5. Predicate logic: satisfiability, the system of analytic trees (semantic trees).
6. Predicate logic: the system of Borkowski/Słupecki inferential logic.
7. The comparison of inferential systems with axiomatic systems of
predicate logic. Predicate logic with identity and functions, its exemplary
applications in arithmetic.
8. Applications of predicate logic to the testing of formal correctness of
deductive inferences,
9. Applications of predicate logic to the testing of formal correctness of
deductive inferences. Continued with special regard to philosophical
reasonings.
10. Applications of predicate logic to the testing of formal correctness of
deductive inferences. Continued with special regard to reasonings in social
sciences.
11. The logical theory of classes and relations.
12. The logical theory of classes and relations. Compared with Boolean
algebra and predicate logic.
13. The logical theory of classes and relations. Continued with special
regard to applications in social sciences (e.g., the problem of the relation
of preference in game-theoretical model of social interactions).
14. Logical theory of definitions. Normal and partial definitions, their
applications esp. in social research.
The whole (maximal) number of hours: 56-60 for lectures, and 56-60 for
exercises.
Obligatory reading
~~~~~~~~~~~~~~~~~~
Witold Marciszewski: "Sztuka rozumowania w świetle logiki"
[The Art of Reasoning in the Light of Logic], Aleph, Warszawa [Warsaw,
Poland], 1994.
This Polish textbook is available at Web under the title
"Logika Współczesna w zastosowaniu do nauk społecznych".
Foreign students may use, instead, the respective parts of the books listed below
(as recommended to Polish readers), according to hints of their course leader.
Additional (recommended) reading
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Kazimierz Ajdukiewicz: "Logika pragmatyczna", PWN, Warszawa 1965.
English translation by Olgierd Wojtasiewicz: "Pragmatic Logic",
Reidel/PWN, Dordrecht/Warsaw 1965.
Witold Marciszewski (red.): "Mała encyklopedia logiki" [A Concise
Encyclopedia of Logic], Ossolineum, Wrocław etc. 1970, 1988.
Witold Marciszewski (red.): "Logika formalna. Zarys encyklopedyczny
z zastosowaniem do informatyki i lingwistyki" [Formal Logic. An Encyclopedic
Outline with Applications to Computer Science and Linguistics], PWN, Warszawa 1987.
English counterparts of the both Polish encyclopedias listed above are found
in the extensive English volume:
Witold Marciszewski (ed.): "Dictionary of Logic as Applied in the Study
of Language. Concepts, Methods, Theories", Martinus Nijhoff, The Hague etc. 1981.
Witold Marciszewski: "Logika z retorycznego punktu widzenia", UW, Warszawa 1991.
The English counterpart (by the same author):
"Logic from a Rhetorical Point of View", Walter de Gruyter, Berlin etc. 1994.
Alfred Tarski: "Wprowadzenie do logiki i do metodologii nauk dedukcyjnych",
Philomath, Warszawa 1994, 1996. Edited by Witold Marciszewski, translated by
Monika Sujczyńska from the fourth English edition "Introduction to Logic and
to the Methodology of Deductive Sciences", Oxford University Press 1994.
Methods of teaching
~~~~~~~~~~~~~~~~~~~
Students obtain course credits (a number of scores) for regular attending
lectures and exercises, and for successful activities as listed above in the
item "Student outcomes assessment". Students receive them after final
consultation and discussion with the course leader. The maximal amount of
scores equals 100%.
ECTS grades to record assessments
~~~~~~~~~~~
satisfactory (3)
51 - 60%
good (4)
75 - 84%
very good (5)
95 - 100%