1. Set theory
Content covered:
- basic notions of (naïve) set theory
- sets, elements, relations between and operations on sets
- relations and their properties
- functions and their properties
- examples of informal proofs
- counterexamples
- direct, indirect proofs
- inductive proofs
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2. Propositional logic
Content covered:
- syntax & semantics of propositional logic;
- truth-tables
- tautologies vs. contradictions vs. contingencies
- logical equivalence
- translations from natural language into propositional logic
- semantic meaning vs. pragmatic enrichment
- argument schemas & logical validity.
Material
3. Natural deduction
Content covered:
- semantic vs. syntactic approach to logical inference
- derivations and derivation rules
- soundness & completeness
- natural deduction system
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4. Predicate logic
Content covered:
- formulas of predicate logic
- predicate letters, variables & individual constants
- domain of quantification
- quantifier scope and binding
- atomic sentences
- predicate-logical meaning of natural language sentences
- semantics of predicate logic
- model, domain and interpretation function
- assignment and valuation functions
- validity
- predicate logic with identity
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4. Modal logic
Content covered:
- language of modal logic
- (pointed) modal models
- truth in pointed models
- belief and knowledge models
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5. Probability theory
Content covered:
- basics of probability theory
- axiomatic definition & interpretation
- joint distributions
- marginalization
- conditional probability
- Bayes rule
- stochastic independence
- random variables & expected values
Material:
Content covered:
- information content / surprisal
- entropy (joint, conditional, cross)
- Kullback-Leibler divergence
- mutual information
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