Learning objectives
By the end of this week you can:
- 1 Decide whether an argument form is valid using a truth table.
- 2 Apply the rules of inference (modus ponens, modus tollens, hypothetical syllogism, …).
- 3 Build a step-by-step argument, naming the rule used at each step.
- 4 Use rules of inference with quantifiers (universal instantiation and generalization).
- 5 Spot common fallacies: affirming the conclusion and denying the hypothesis.
★ the wow moment
A program that reasons: forward chaining in 20 lines of Python.
Give the computer facts and if-then rules, and it keeps applying modus ponens until nothing new appears. This is the engine behind expert systems, Prolog and the rule engines that approve your bank transactions.
Topics
- Arguments and validity
- Rules of inference for propositional logic
- Resolution
- Fallacies
- Rules of inference for quantified statements
Before class
- Skim Rosen 1.6 (20 minutes is enough; we go through it together).
- Bring paper and a pen: part of every lecture is solving by hand.
In industry
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Type checkers
Compilers infer types with inference rules; a type error is a failed proof.
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Rule engines
Fraud detection and insurance systems chain thousands of if-then rules with modus ponens.
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AI reasoning
Neuro-symbolic systems check a language model's step-by-step reasoning against formal inference rules.
Lab 5: A Tiny Inference Engine
Implement forward chaining with modus ponens, then use it to answer questions from a rule base.
due Fri, Oct 30 · 23:59 · 100 points · opens in week 6
Go deeper
- forall x: Calgary, an open logic textbook · natural deduction chapters
- Book of Proof (Richard Hammack) · Chapter 2, logic
- Hacettepe BBM 205 slides · rules of inference slides
Tags:inferencemodus ponensmodus tollensresolutionfallacyargument