Logic and computational thinking
References
1. Johan van Benthem, Hans van Ditmarsch, Jan van Eijck, Jan Jaspars. Logic in Action, 2016.
http://www.logicinaction.org
2. Matthew J. van Cleave. Logic and Critical Thinking, 2016.
https://open.umn.edu/opentextbooks/textbooks/ introduction-to-logic-and-critical-thinking
Syllabus for week 3
• Chapter 1 (van Benthem, et al., 2016)
• Chapter 1, Sections 1.1 – 1.3; 1.6 – 1.7 (van Cleave, 2016)
• Exercises 1, 2, 3 and 5 (van Cleave, 2016)
Computational Thinking
• Thinking as Computation
o Flight -- study of birds vs. aerodynamics
o Nuclear energy conversion – study of the sun vs. nuclear physics
o Gravity – study of falling objects vs. theory of relativity
o -- study of cognition vs. computational thinking
• Aspects of computational thinking
o Abstraction
o Representation
o Algorithmics
o Decomposition
o Pattern recognition
Computation is a process that is defined in terms of an underlying model of computation and
computational thinking is the thought processes involved in formulating problems so their solutions can be
represented as computational steps and algorithms. – Alfred Aho
Logic
• Why study Formal Logic?
• Logic in the East – Buddhist and Islamic traditions
• Logic in the West, formulated explicit systems of reasoning in Greek Antiquity– Aristotle (300s BC)
• Logicism, where modern logic arrived from – Boole, Frege (late 1800s), Russell (early 1900s)
• The work of Persian logician Avicenna around 1000 AD was still taught in madrassa’s by 1900.
• Founder of Mohism – Mo Zi
• Indian Buddhist Logician – Dignaga
• Symbolic logic – G¨odel and Tarski (1930s)
• Computation and IT – Von Neumann and Turing (1940s)
• Classical logic – Idealist modelling and reasoning
• Non-classical logics
Notes made by Jessica Davids
, Propositions
• Propositions – claims, assumptions, justifications, observations, declarations, conclusions, ...
• ... contradictions, contingencies, tautologies
• ... and more tricky ones – counterfactuals, paradoxes
• Statements that can be either true or false
• But not: Exclamations, instructions, questions
Arguments
Built up from propositions and conclusion not always stated last in a natural language argument however
in a formal argument we always write the conclusion last
• Premises and Assumptions
• Conclusions
• Valid arguments : if all the premises are true and so is the conclusion
• Invalid arguments : when all the premises are true but the conclusion is false
• Sound arguments : one which is both valid and all the premises are true
• Necessary and sufficient conditions
Examples (valid arguments)
• “If everything is predetermined, then people are not free. People are free. Therefore everything is
not predetermined.”
• “If humans are mammals, then they are not cold-blooded. Humans are cold-blooded. Therefore
humans are not mammals.”
Arguments vs. explanations
• Arguments:
o The truth of the premises establishes the truth of the conclusion
o If all the premises are true, then so is the conclusion
o Reasoning proceeds from the premises to the conclusion
o Deductive inference
• Explanations:
o The explanation explains the truth of the observation
o Reasoning proceeds from the observation to the explanation
o Abductive inference
o Identify missing premises to validate an argument
Examples
• This graffiti was created with spray paint. Spray paint does not wash off easily. Therefore, this graffiti will not
wash off easily.
• This graffiti does not wash off easily. This could be because it was created with spray paint, which does not
wash off easily.
Notes made by Jessica Davids
