Ch 8 FOL Flashcards
What are the advantages of propositional language and being declarative?
Its semantics is based on a truth relation between sentences and possible worlds, and deals with partial information through disjunction and negation.
It also holds compositionality.
What do procedural languages lack?
The ability to derive facts from other facts without a domain specific procedure derived by the programmer’s knowledge.
They cannot deal well with partial information
How is the declarative nature of propositional logic contrasted against procedural languages?
knowledge and inference are separate and inference is entirely domain independent
What is the drawback or limfac of PL?
It lacks the expressive power to CONCISELY describe an objects with many objects. It has to write a separate rule for every breeze and pit separately.
What is the cost paid for going to FOL from PL and why?
The cost is enumerating, while possible, is astronomically long and impossible in practice due to models and interpretations.
Describe universal quantification. What connective is usually used, what is the common error and what does it mean?
For all…same as conjunction of instances of P.
∀x P is true in a model m iff P is true with x being EACH possible object in the mode
(At(KingJohn,Berkeley) ⇒ Smart(KingJohn)) ∧ (At(Richard,Berkeley) ⇒ Smart(Richard))
∧ (At(Berkeley,Berkeley) ⇒ Smart(Berkeley))
∧ …
USES => common error is AND
∀x At(x,Berkeley)∧Smart(x)
means “Everyone is at Berkeley and everyone is smart”
Describe existential quantification. What connective is usually used, what is the common error and what does it mean?
∃x P istrueinamodelmiffP istruewithxbeing
some possible object in the model
Roughly speaking, equivalent to the disjunction of instantiations of P
(At(KingJohn,Stanford)∧Smart(KingJohn)) ∨ (At(Richard,Stanford)∧Smart(Richard))
∨ (At(Stanford,Stanford)∧Smart(Stanford))
Typically uses AND, common mistake is =>
∃x At(x,Stanford) ⇒ Smart(x)
is true if there is anyone who is not at Stanford!
