• Think about how you solved this problem. You could treat it as a CSP with variables X1 and X2, and search through the set of candidate solutions, checking the constraints. • However, more likely, you just added the two equations, divided both sides by 2 to easily find out that X1 = 7. This is the power of logical inference, where we apply a set of truth-preserving rules to arrive at the answer. This is in contrast to what is called model checking (for reasons that will become clear), which tries to directly find assignments. • We'll see that logical inference allows you to perform very powerful manipulations in a very compact way. This allows us to vastly increase the representational power of our models. Course plan Search problems Constraint satisfaction problems Markov decision processes Markov networks Adversarial games Bayesian networks Reflex States Variables Logic "Low-level intelligence" "High-level intelligence" Machine learning CS221 4 • We are at the last stage of our journey through the AI topics of this course: logic. Before launching in, let's take a moment to reflect. Propositional logic Syntax Semantics formula models Inference rules CS221 26 [Warner, 1965] Privacy: Randomized response Do you have a sibling? Method: • Flip two coins. • If both heads: answer yes/no randomly • Otherwise: answer yes/no truthfully Analysis: 4 1 true-prob = 3 × (observed-prob − 8 ) CS221 136 Causality Goal: figure out the effect of a treatment on survival Data: For untreated patients, 80% survive For treated patients, 30% survive Does the treatment help? Sick people are more likely to undergo treatment... CS221 138 [Mykel Kochdorfer] Interpretability versus accuracy • For air-traffic control, threshold level of safety: probability 10−9 for a catastrophic failure (e.g., collision) per flight hour • Move from human designed rules to a numeric Q-value table? CS221 140 CS221 142 Societal and industrial impact Enormous potential for positive impact, use responsibly! CS221 144 Search problems Constraint satisfaction problems Markov decision processes Markov networks Adversarial games Bayesian networks Reflex States Variables Logic "Low-level intelligence" "High-level intelligence" Machine learning Please fill out course evaluations on Axess. Thanks for an exciting quarter! CS221 146.