fol for sentence everyone is liked by someone is

-"$ -p v (q ^ r) -p + (q * r) if David loves someone, then he loves Mary. $\endgroup$ - FOL has practical advantages, especially for automation. Debug the knowledge base. Everyone likes ice cream - there is no one who does not like ice cream; Connections Between \(\forall . 10 Mar 2005 CS 3243 - FOL and Prolog 4 First-order logic Whereas propositional logic assumes the world contains facts, first-order logic (like natural language) assumes the world contains {Objects: people, houses, numbers, colors, baseball games, wars, {Relations: red, round, prime, brother of, bigger than, part of, comes between, Translation into FOL Sentences Let S(x) mean x is a skier, M(x) mean x is a mountain climber, and L(x,y) mean x likes y, where the domain of the first variable is Hoofers Club members, and the domain of the second variable is snow and rain. there existsyallxLikes(x, y) Someone likes everyone. or y. Chiara Ghidini ghidini@fbk.eu Mathematical Logic Example.. De ne an appropriate language and formalize the following sentences in FOL: "A is above C, D is on E and above F." "A is green while C is not." "Everything is on something." "Everything that has nothing on it, is free." Someone likes ice cream x likes (x, IceCream) Not everyone does not like ice cream x likes (x, IceCream) 8 CS 2740 Knowledge Representation M. Hauskrecht Knowledge engineering in FOL 1. <variables > < sentence > Everyone at Pitt is smart: x At(x,Pitt) Smart(x) . "There is a person who loves everyone in the world" x y Loves(x, y) "Everyone in the world is loved by at least one person" y x Loves(x, y) Quantifier Duality - Each of the following sentences can be expressed using the other x Likes(x, IceCream) x Likes(x, IceCream) Example "Everyone who loves all animals is loved by someone" View the full answer. . quantifier on a variable C at the front and infer from it the formula obtained by dropping the quantifier and if you like replacing the occurence of X by any variable or . A complex sentence is formed from atomic sentences connected by the logical connectives: P, P Q, P Q, P Q, P Q where P and Q are sentences A quantified sentence adds quantifiers and A well-formed formula (wff) is a sentence containing no "free" variables. Satisfaction. "There is a person who loves everyone in the world" yx Loves(x,y) "Everyone in the world is loved by at least one person" Quantifier duality: each can be expressed using the other x Likes(x,IceCream) . Sentences in FOL and propositional logic are just giving us some information or knowledge about a particular thing. m-ary relations do just that: Prove by resolution that: John likes peanuts. We can now translate the above English sentences into the following FOL wffs: 1. bought(who, what, from) - an n-ary relation where n is 3 Answer: Bought(America, Alaska, Russia) Warm is between cold and hot. First-order logic is also known as Predicate logic or First-order predicate logic. It's the preferred reading for the passive sentence "Everyone is loved by someone" and it's the only reading for the agentless passive "Everyone is loved.") 6. Loves(x,y) There exists a single person y who is loved universally by all other people x. (12 points) Translate the following English sentences into FOL. m-ary relations do just that: Answer : (d) Reason : Quantity structure is not a FOL structure while all other are. Comment: I am reading this as `there are \emph { at least } four \ldots '. -"$ -p v (q ^ r) -p + (q * r) 2. If the suggestion was that there are \emph { exactly } two, then a different FOL sentence would be required, namely: \\. (The . 1. $\begingroup$ @New_Coder, I am not sure about the second FOL sentence. Properties and . All professors are people. In this paper, we present the FOLtoNL system, which converts first order logic (FOL) sentences into natural language (NL) ones. Everyone likes someone. Models for FOL: Lots! slide 17 FOL quantifiers . if someone loves David, then he (someone) loves also Mary. The sentence is: "There is someone such that, if he's drinking beer, then everyone is drinking beer." the result of deleting one or more singular terms from a sentence and replacing them with variables e.g. This entails (forall x. Properties and . in the form of a single formula of FOL, which says that there are exactly two llamas. - x y Likes(x, y) "Everyone has someone that they like." - x y Likes(x, y) "There is someone who likes every person." Pros and cons of propositional logic . \item There are four deuces. 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 . xlikes y) and Hates(x, y)(i.e. What is First-Order Logic? 5. &kdswhuv )luvw 2ughu /rjlf 'u 'dlv\ 7dqj,q zklfk zh qrwlfh wkdw wkh zruog lv eohvvhg zlwk remhfwv vrph ri zklfk duh uhodwhg wr rwkhu remhfwv dqg lq zklfk zh hqghdyru wr uhdvrq derxw wkhp "There is a person who loves everyone in the world" - y x Loves(x,y) likes(x,y) Someone is liked by everyone: (Ey)(Ax)likes(x,y) Sentences are built up from terms and atoms: o A term (denoting a real-world individual) is a . There is somebody who is loved by everyone 4. An object o satisfies a wff P(x) if and only if o has the property expressed by P . For . "Everyone who loves all animals is loved by . So could I say something like that. Can use unification of terms. Answer : (d) Reason : "not" is coming under propositional logic and is therefore not a connective. 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, . In every (non-empty) world, there is sure to be some object satisfying the condition y x = y . everyone has someone whom they love. - (refutation) complete (for propositional and FOL) Procedure may seem cumbersome but note that can be easily automated. In order to infer new knowledge from these sentences, we need to process these sentences by using inference methods. If the suggestion is that there are \emph { exactly } four, then we should offer instead: \\. - "There is a person who loves everyone in the world" y x Loves(x,y) - "Everyone in the world is loved by at least one person" Quantifier duality: each can be expressed using the other xLikes(x,IceCream) x Likes(x,IceCream) x Likes(x,Broccoli) x Likes(x,Broccoli) 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 Assemble the relevant knowledge 3. Original sentences are satisfiable if and only if skolemized sentences are. xy(Loves(x,y)) Says there is someone who loves everyone in the universe. Add your answer and earn points. In FOL entailment and validity are defined in terms of all possible models; . Nobody is loved by no one 5. - If the sentence is false, then there is no guarantee that a procedure will ever determine this-i.e., it may never halt. "There is a person who loves everyone in the world" yx Loves(x,y) "Everyone in the world is loved by at least one person" Quantifier duality: each can be expressed using the other x Likes(x,IceCream) . 4. If someone is noisy, everybody is annoyed 6. Lucy* is a professor 7. y. single predicates) sentences P and Q and returns a substitution that makes P and Q identical. (c) Not everyone hates the people that like Alice. Pose queries to the inference procedure and get answers. Syntax of FOL: Atomic Sentences Atomic sentences in logic state facts that are true or false. Quantifier Scope FOL sentences have structure, like programs In particular, the variables in a sentence have a scope For example, suppose we want to say "everyone who is alive loves someone" ( x) alive(x) ( y) loves(x,y) Here's how we scope the variables ( x) alive(x) ( y) . Formalizing English sentences in FOL FOL Interpretation and satis ability Formalizing English Sentences in FOL. Use the predicates Likes(x, y) (i.e. Every food has someone who likes it . Every sentence in FOL (without equality) is logically equivalent to a FOL-CNF sentence. Either everything is bitter or everything is sweet 3. 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 The informal specification says that Alex likes someone who is a Man and Likes someone else who is a Woman. 12. Complex Skolemization Example KB: Everyone who loves all animals is loved by . Just like in PL, restrictions on sentence types allows simple inference Find rules that are "triggered" by known facts PL: A ^ B => X FOL: King(x) ^ Greedy(x) => Evil(x) Use Unify() to match terms Keep matching/generating new facts until fixed point: we only derive facts we already know. See Aispace demo. 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, . Try forming the sentence: "Everybody knows what's inside the hatch" (It could be something like "for all x, if knows(x) then there exists y such that y is inside the hatch") and then figuring out how to modify the FOL to fit your second sentence. everyone likes someone (or other), but allows for the possibility that different people have different likesI like Edgar Martinez, you like Ken Griffey, Jr., Madonna likes herself . Suppose a wumpus-world agent is using an FOL KB and perceives a smell and a breeze (but no glitter) at t=5 : Tell (KB,Percept . This entails (forall x. everybody loves David or Mary. Deans are professors. Step-1: Conversion of Facts into FOL. nobody loves Bob but Bob loves Mary. Quantifier Scope . 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. Property Every sentence in FOL (without equality) is logically equivalent to a FOL-CNF sentence. Deb, Lynn, Jim, and Steve went together to APT. Godel's Completeness Theorem says that FOL entailment is only semidecidable: - If a sentence is true given a set of axioms, there is a procedure that will determine this. 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. Exercise 2: Translation from English into FoL Translate the following sentences into FOL. Enemy(Nono, America) Can be converted to CNF Query: Criminal(West)? " "There is a person who loves everyone in the world" y x Loves(x,y) " "Everyone in the world is loved by at least one person" $ Quantifier duality: each can be expressed using the other x Likes(x,IceCream) x Likes(x,IceCream) x Likes(x,Broccoli) x Likes(x,Broccoli) CS440 Fall 2015 18 Equality Decide on a vocabulary . Now consider the following statement taken from the OP: AxEy(Likes( man(x), woman(y) ) -> Likes(alex, man(x) )) This statement is from a different language. Like BC of PL, BC here is also an AND/OR search. Everything is bitter or sweet 2. Our model satisfies this specification. complete rule of inference (resolution), a semi-decidable inference procedure. 6. Augments the logical connectives from propositional logic with predicates that describe properties of objects, functions that map objects to one another, and quantifiers that allow us to reason about many objects at once. Y x Likes(x, IceCream) ax Likes(x,Broccoli) Likes(x, IceCream)) Knowledge Engineering 1. Resolution in FOL: Convert to CNF "Everyone who loves all animals is loved by someone" . To describe a possible world (model). FOL sentences have structure, like programs In particular, the variables in a sentence have a scope For example, suppose we want to say "everyone who is alive loves someone" ( x) alive(x) ( y) loves(x,y) Here's how we scope the variables ( x) alive(x) ( y) loves(x,y) Scope of x Scope of y S is a sentence of FOL if and only is S is a wff of FOL in which no variable occurs free. Everyone is a friend of someone. More Answers for Practice in Logic and HW 1.doc Ling 310 Feb 27, 2006 3 x(walk(x) & talk(x)) 7. "Everyone who loves all animals is loved by someone. (Ax) S(x) v M(x) 2. Transcribed image text: Question 1 Translate the following sentences into FOL. x and f (x 1, ., x n) are terms, where each xi is a term. Someone walks and someone talks. Given the following two FOL sentences: (d) There is someone who likes everyone that Alice hates. Now consider the following statement taken from the OP: AxEy(Likes( man(x), woman(y) ) -> Likes(alex, man(x) )) This statement is from a different language. Just "smash" clauses until empty clause or no more new clauses. Propositionalization 26 Every FOL KB and query can be propositionalized Algorithms for deciding PL entailment can be used Problem:infinitely large set of sentences Infinite set of possible ground-term substitution due to function symbols e.g., ( ( ( ))) Solution: Theorem (Herbrand,1930):If a sentence is entailed by an FOL KB, Conjunctive Normal Form for FOL A sentence in a Conjunctive Normal Form is a conjunction of clauses, each clause is a disjunction of literals. America, Alaska, Russia - What are the relations? nobody likes Mary. (Ey)likes(x,y) Someone is liked by everyone: (Ey)(Ax)likes(x,y) Sentences are built up from terms and atoms: A term (denoting a real-world individual) is a constant symbol, a variable symbol, or an n-place function of n terms. P(x) : ___x is person. Good(x)) and Good(jack). 3. 6 Fun with Sentences Convert the following English sentences into FOL America bought Alaska from Russia. That is, all variables are "bound" by universal or existential quantifiers. D(x) : ___x drinks beer (The domain is the bar.) Loves(x,y) Everyone, say x, loves at least one other person y, but who y is depends on who x is. A well-formed formula (wff) is a sentence containing no "free" variables. Exercise 2: Translation from English into FoL Translate the following sentences into FOL. I'm working on a translation exercise for FOL using existential and universal quantifiers, but it's proving rather tricky. In First order logic resolution, it is required to convert the FOL into CNF as CNF form makes easier for resolution proofs. Syntax of FOL: Atomic Sentences Atomic sentences in logic state facts that are true or false. Q13 Consider the following sentence: 'This sentence is false.' Let's label this sentence 'L.' . 7. Given the following two FOL sentences: Below I'll attach the expressions and the question. (b) Bob hates everyone that Alice likes. 3. Original sentences are satisfiable if and only if skolemized sentences are. Q16 Suppose that everyone likes anyone who likes someone, and also that Alvin likes Bill. Example 7. - A common mistake is to represent this English sentence as the FOLsentence: ( x) student (x) => smart (x) It also holds if there no student exists in the domain because student (x) => smart (x) holds for any individual who is not astudent. Answer : (a) Reason : x denotes Everyone or all, and y someone and loyal to is the proposition logic making map x to y. yx(Loves(x,y)) Says everyone has someone who loves them. x y Loves(x,y) "There is a person who loves everyone in the world" y x Loves(x,y) "Everyone in the world is loved by at least one person" Quantifier duality: each can be expressed using the other x Likes(x,IceCream) x Likes(x,IceCream) x Likes(x,Broccoli) x Likes(x,Broccoli) Denition Let X be a set of sentences over a signature S and G be a sentence over S. Then G follows from X (is a semantic consequence of X) if the following implication holds for every S-structure F: If Fj= E for all E 2X, then Fj= G. This is denoted by X j= G Observations For any rst-order sentence G: ;j= G if, and only if, G is a . There is a kind of food that everyone likes 3. "Everyone loves somebody": Either x. -Everyone likes someone: ( x)( y) likes(x,y) -Someone is liked by everyone: . Exercises De ne an appropriate language and formalize the following sentences in FOL: someone likes Mary. We can now translate the above English sentences into the following FOL wffs: 1. Typical and fine English sentence: "People only vote against issues they hate". People only criticize people that are not their friends. Someone walks and talks. But wouldn't that y and z in the predicate husband are free variables. 13. See Aispace demo. means "Everyone is at CSU and everyone is smart" October 27, 2014 15 Existential quantification <variables> <sentence> Someone at CSU is smart: x At(x, CSU) Smart(x) $ x P(x) is true iff P is true for some object x $ Roughly speaking, equivalent to the disjunction of instantiations of P At(KingJohn,CSU) Smart(KingJohn)

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