Subject: Logic and Reasoning

Scientific Area:

Scientific, Cultural, Social and Ethical Formation

80 Hours

Number of ECTS:

6 ECTS

Language:

Portuguese

# Overall objectives:

1 - Introduction to the problematic of formal (logical) systems and their main associated concepts.
2 - Introduction to numerical and non-numeric reasoning techniques.
3 - Knowledge of different formal decision-making methods.
4 - Introduction to Social Choice
5 - Introduction to epistemology.

# Syllabus:

1 - Propositional Logic and Deductive Reasoning: Formal Systems: Introduction. Syntax. Semantic Theory and Evidence. Propositional Logic. Syntax: Alphabet. Connectives. Formulas. Semantics: Interpretation. Truth tables. Equivalent formulas. Substitution rules. Tautologies - Contradictions and Contingencies. Proof Theory: syllogisms - Tableaux. Deductive Reasoning: The hidden logic: Sudoku Puzzles and Logic. The logic in scientific demonstrations.
2 - Deductive Reasoning not: not monotonous Inference: Induction, Abduction, Analogy, Numerical Models.
3 - Decision Theory: Decision under ignorance. Decision under Risk: Probability - Utility
4 - Social Choice: Concepts, origins. Aggregation of basic judgment. Aggregation rules. Fair Allocation.
5 - Theory of Knowledge: Knowledge: Definitions - Sources of Knowledge. The Justification of Knowledge: Foundationalism versus Coherentism

# Literature/Sources:

Hamilton, A.G. , 1988 , Logic for Mathematicians , Cambridge University Press
Pigozzi, Gabriela , 2021 , Belief Merging and Judgment Aggregation , The Stanford Encyclopedia of Philosophy (Spring 2021 Edition)
Resnik, M. D. , 1987 , Choices: An introduction to Decision Theory , University of Minnesota Press
Lehrer, Keith , 1990 , Theory of Knowledge , Routledge
Brachman, Ronald & Levesque, Hector , 2004 , Knowledge Representation and Reasoning , Morgan Kaufmann Publishers

# Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Theoretical classes, problem solving, home work, individual presentations. 1st test: Propositional Logic and deductive reasoning. (1/3 of the final grade) 2nd test: Decision Theory and Social Choice. (1/3 of final grade) Group work on Non-Deductive Reasoning and Knowledge. (1/3 of the final grade)