| What are the two components of Automated Reasoning? | Knowledge Base (KB): what we know about the world (a domain
of interest, e.g. number theory, medicine)
Inference Engine: how we think; used to answer queries and
derive implicit knowledge about the world (modeled domain) |
| What was the Initial proposal in early days of AI? | Deductive Logic
Top-down approach to logical thinking where conclusions are derived from general principles.
All dogs have ears; golden retrievers are dogs, therefore they have ears. |
| What is the weakness of Deductive Logic? | Deductive Logic fails in a domain like medical diagnosis (and others
such as: law, business, automobile repair, gardening, dating) due to:
Laziness
Theoretical ignorance
Practical ignorance |
| What are the Limits of Deduction Logic? | Deductive Logic is monotonic
Once we deduce something from a KB, we can never invalidate the
deduction by acquiring more knowledge |
| What is the Qualification Problem? | To deduce a conclusion without relying on assumptions by meeting all necessary preconditions.
e.g. must have two wings, must not be afraid of flying, must
have already learned how to fly, etc. |
| What are some solutions to monotonic logics? | Solution 1: Non-Monotonic Logics
Solution 2: Degree of Belief |
| What is Non-Monotonic Logics? | Equipping logic with the ability to jump into certain conclusions
Requires:
− Mechanisms for managing assumptions
− Criteria for deciding on which assumptions to assert and
retract, and when
Consistency-based approach:
• Assert as many assumptions as possible, as long as they do not lead
to a logical inconsistency |
| What is the problem with Non-Monotonic Logics? | They have contradicting extensions/conclusions! |
| How do you resolve the conflict for Non-Monotonic Logics? | Belief Revision in non-monotonic logics
Use the notion of a Degree of Belief and probabilistic reasoning |
| What is a Degree of Belief? | Instead of declaring facts (Deductive Logic) or assumptions (Non-monotonic Logics), assign a degree of belief to propositions |
| Degrees of belief assigned are.. | Interpreted as probabilites
Manipulated by the laws of probability |
| De Finetti‘s Theorem (1931): | Impossible to act rationally under uncertainty using degrees of
belief that violate axioms of probability. |
| What does Probability mean? What are the two approaches? | Objectivist (frequentist) approach
Subjectivist (Bayesian) approach |
| What is a Objectivitist (frequentist) approach? | Probabilities as
− inherent objective properties of objects
− real aspects of the universe
− view of probability based in the Law of Large Numbers
(prob. of event corresponds to relative frequency of over infinite
number of trials)
• Source of probability numbers: (only) experiments |
| What is an example of a frequentist approach? | Frequentist probability „a patient has cavity“
• Interpretation: Among 100 examined patients, we should detect
approximately 30 times a cavity |
| What is a Subjectivist (Bayesian) approach: | probability as
− quantifies subjective belief in the occurrence of an event
− reflects state of knowledge of an individual (person, agent)
• Allows any self-consistent ascription of prior probabilities to
propositions
• Insists on proper Bayesian updating as new evidence arrives |
| What is an example of a Subjectivist (Bayesian) approach? | Bayesian probability „a patient has cavity“
• Interpretation: With confidence 30% I believe that a particular
patient belongs to those people who have a cavity |
| Example of Degree of Belief | We see the bird on the right (E0)
• „this bird is normal“ since no evidence that
• something is wrong with this bird
→ derive „this bird can fly“
Then we see this bird from a new viewing angle (E1)
• Update based on E1
• Update belief of „this bird is normal“
→ Update belief of „this bird fly“ |
| Degree of Belief vs. Assumptions | Assumptions -
Either true or false
Decisions tend to follow naturally from the assumptions made
Pro: less information is needed
Con: Derived facts might turn out to be false later
Degree of Belief:
Continuous in interval , gives more information than assumptions
Decision-making: Decision Theory = Prob. Theory + Utility Theory
Con: more information is needed
Pro: degrees of belief do not imply any particular truth of the
underlying propositions, pitfalls can be avoided |
