Course manual

Important

• Email: logische.methoden@uu.nl
• New course: active development
• Material: logicalmethods.ai
• Exams: only endterm

What is logic?

Science of valid inference

Given that Ada is either on the Philosopher’s Walk or in the study, and she’s not in the study, she therefore must be on the Philosopher’s Walk.

• Inference indicator
• Premise indicator
• Conclusion

Validity = premises support conclusion

• Deductive validity = necessitation
• Inductive validity = probability raising
• Fallacy = reasoning mistake

Logical systems

Components

• Syntax = model of language
• Semantics = model of meaning
• Proof theory = model of stepwise inference

Mathematical models

• abstraction
• idealization
• assumptions

Artificial intelligence

AI=study+replication of intelligence

• Foundations
• Methodology
• Tool

Foundations

• Inference is intelligence
• Know your enemy!
• Gödel and Turing

Methodology

• Logic-based/symbolic AI
• Expert systems: KB + Inference engine

Plato.ai

• Knowledge base: $$Featherless(x)\land Biped(x)\Rightarrow Human(x)$$
• Inference engine: $$Featherless(c),Biped(c)\vdash Human(c)$$
• Hard to build and maintain

Subsymbolic AI

Statistics + machine learning

Thinking, fast and slow

• System 1: fast, automatic, intuitive, unconscious, associative, ...
• System 2: slow, deliberate, conscious, logical, calculating, ...

Logic and AI

• Subsymbolic AI = system 1
• Symbolic AI = system 2