Class notes
Intelligent systems lecture 2
- Course
- Institution
Intelligent systems lecture 2
[Show more]
Seller
Follow
nasrrr
Content preview
Lecture 24 nov 2022:Modelling schnapsen in propositional logics:
You can use logic for games in two ways; reasoning over models / states, or modeling strategies.
Reasoning over states in phase 2:
- ‘Would I be safe when playing the king of hearts.’
- f.e. -O10H ^ -OAsH ^ (OQH v OJH)
- The opponent does not have a higher card, but he does have a lower card of the same color
- Forgetful Schnapsen
- The way human play, up to now we have the assumption that perfect information in phase 2,
but:
- Normal players forget the cards that were played earlier
- I can remember Trumps (on good days)
- I can sometimes remember Asses (on good days)
- I can remember 10s on exceptional days
- We need to use logical reasoning to deal with this imperfect information
Modelling schnapsen cards:
- Use the representation of the cards of the practical assignments to give a numerical value to
each of the cards that’s in the game.
- This information can be modeled to propositions: If the card value is true it means that it exists
in the representation, if the color value is true it means that it’s black.
- In logic you want to evaluate the properties of a card given a deck.
- ‘Is a card entailed by KB w.r.t. PLayNoTrumpJackStrategy?
- We would have to pair all the propositions:
- FOR ALL x: PNTJS <-> J(x) ^ -Trump(x)
- This needs to be checked for each card, but it will work (huge kb)
- Pros:
- Propositional logic is declarative: you write out the properties that something should have
- Unlike in machine learning
- It allows partial/disjunctive/negated information
- Unlike most data structures and databases
- Compositional
- Meaning in propositional logic is context-independent
- In natural language humans can use the context that something was was said in to nd
the meaning
- Meaning does not depend on context and is always the same
- Cons:
- Propositional logic has very limited expressive power (unlike natural language), there are
very many things we cannot say in propositional logic
- Usage for Schnapsen is rather complicated (aka impossible)
Rule based reasoning:
An inference rule is a logical form consisting of a function which takes premises, analyzes their
syntax and returns a conclusion:
- Rules are often abbreviated as A -> B or A over B, this is not the same as ((A->B) ^ A) ->B
- Or with -> (written as ==>) (alpha ==> beta, alpha) over beta (models ponens)
Very speci c with propositional logic language, they are di erent to the object language to which
you model your domain.
- And elimination: form a conjunction any conjunct can be inferred: alpha ^ beta over alpha
- Logical equivalences can be used as rules: (alpha <==> beta) over ((alpha ==> beta ^ beta ==>
alpha)).
Searching for proofs: monotonicity, the set of entailed sentences can only increase as information
is added to the kb. The higher the input gets the higher the output gets. This can be applied to
logic. For any sentence alpha and beta: if KB |= alpha then KB ^ beta |= alpha
Forward chaining is data driven
Backward chaining is goal driven
fi ff fi
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller nasrrr. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.23. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
73918 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now