fol for sentence everyone is liked by someone is
Sentences in FOL: Atomic sentences: . How to pick which pair of literals, one from each sentence, 1.All dogs don't like cats No dog likes cats 2.Not all dogs bark There is a dog that doesn't bark 3.All dogs sleep There is no dog that doesn't sleep 4.There is a dog that talks Not all dogs can't talk Notational differences Different symbolsfor and, or, not, implies, . Identify the problem/task you want to solve 2. allxthere existsyLikes(x, y) Someone is liked by everyone. 1.Everything is bitter or sweet 2.Either everything is bitter or everything is sweet 3.There is somebody who is loved by everyone 4.Nobody is loved by no one 5.If someone is noisy, everybody is annoyed 1 America, Alaska, Russia - What are the relations? p =BFy"!bQnH&dQy9G+~%4 First-order logicalso known as predicate logic, quantificational logic, and first-order predicate calculusis a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a . Our model satisfies this specification. yx(Loves(x,y)) Says everyone has someone who loves them.
Morphology is even richer in other languages like Finnish, Russian,
In FOL entailment and validity are defined in terms of all possible models; . All professors are people. Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? This defines a, Example: KB = All cats like fish, cats eat everything they We can enumerate the models for a given KB vocabulary: For each number of domain elements n from 1 to 1 For each k-ary predicatePk in the vocabulary For each possible k-ary relation onn objects For each constant symbol C in the vocabulary For each choice of referent for C from n objects::: Computing entailment by enumerating models is not going to be easy! one trying to prove, From the sentence "Heads I win, tails you lose," prove that "I win.". "There is a person who loves everyone in the world" - y x Loves(x,y) 2. sentences and wffs a term (denoting a real-world individual) is a constant symbol, avariable symbol, or an n-place function of n terms. Complex Skolemization Example KB: Everyone who loves all animals is loved by . (Ax) S(x) v M(x) 2. D. What meaning distinctions are being made? A variable can never be replaced by a term containing that variable. "if-then rules." I'm working on a translation exercise for FOL using existential and universal quantifiers, but it's proving rather tricky. If the suggestion was that there are \emph { exactly } two, then a different FOL sentence would be required, namely: \\. \item There are four deuces. All professors consider the dean a friend or don't know him. . But the FOL sentence merely says that if someone has a father and a mother, then the father is the husband of the mother. We can now translate the above English sentences into the following FOL wffs: 1. - x y Likes(x, y) "Everyone has someone that they like." possibilities): B | GodExists (i.e., anything implies that God exists), or any other algorithm that produces sentences from sentences
In FOL entailment and validity are defined in terms of all possible models; . truth value of G --> H is F, if T assigned to G and F assigned to H; T
D(x) : ___x drinks beer (The domain is the bar.) everybody loves David or Mary. o o o Resolution Proof Converting FOL sentences to CNF Original sentence: Anyone who likes all animals is loved by someone: x [ y Animal(y) Likes(x, y)] [ y Loves(y, x)] 1. Why implication rather than conjunction while translating universal quantifiers? Of course, there is a tradeoff between expressiveness and
we would have to potentially try every inference rule in every Another example of a type of inconsistency that can creep in: Above is all fine. A common mistake is to represent this English sentence as the FOL sentence: (Ex) cs170-student(x) => smart(x) But consider what happens when there is a person who is NOT a cs170-student. not practical for automated inference because the "branching predicate symbol "siblings" might be assigned the set {
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