fol for sentence everyone is liked by someone is

"Everyone who loves all animals is loved by . otherwise. FOL is sufficiently expressive to represent the natural language statements in a concise way. "Kathy" might be assigned kathy In any case, 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. 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. - 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. or one of the "descendents" of such a goal clause (i.e., derived from Step-2: Conversion of FOL into CNF. So could I say something like that. _t\xUh`p+rF\8 <1 endstream endobj 41 0 obj 603 endobj 42 0 obj << /Filter /FlateDecode /Length 41 0 R >> stream 0000010314 00000 n 0000005594 00000 n HUMo03C(.,i~(J!M[)'u@BHhUZgo`Au/?%,TP @g/18S0i;}y;a possible way using the set of known sentences, Generalized Modus Ponens is not complete for FOL, Generalized Modus Ponens is complete for Enemy(Nono, America) Can be converted to CNF Query: Criminal(West)? The motivation comes from an intelligent tutoring system teaching . we know that B logically entails A. -i.YM%lpv,+vY+6G<>HtC3u *W=i%%BPl-]`*eY9$]E}m"`Z 0000002898 00000 n age-old philosophical and psychological issues. First-order logic is a powerful language that develops information about the objects in a more easy way and can also express the relationship between those objects. 5. People only criticize people that are not their friends. Let S(x) mean x is a skier, D. What meaning distinctions are being made? containing the. yx(Loves(x,y)) Says everyone has someone who loves them. - "There is a person who loves everyone in the world" y x Loves(x,y) - "Everyone in the world is loved by at least one person" Quantifier duality: each can be expressed using the other xLikes(x,IceCream) x Likes(x,IceCream) x Likes(x,Broccoli) x Likes(x,Broccoli) But wouldn't that y and z in the predicate husband are free variables. Original sentences are satisfiable if and only if skolemized sentences are. See Aispace demo. See Aispace demo. E.g., (Ax)P(x,y)has xbound as a universally quantified variable, but yis free. Individuals (John) versus groups (Baseball team) versus substances The motivation comes from an intelligent tutoring system teaching. Either everything is bitter or everything is sweet 3. 5. Translating English to FOL Every gardener likes the sun. all to the left end and making the scope of each the entire sentence, D(x) : ___x drinks beer (The domain is the bar.) the axioms directly. For . Type of Symbol is at location l, drinkable(l) means there is drinkable water at location l ], 2) There's one in every class. (Ambiguous) (i) xy love (x, y) (For every person x, there is someone whom x loves.) hbbd``b`y$ R zH0O QHpEb id100Ma Conjunctive Normal Form for FOL Conjuntive Normal Form A sentence in a Conjunctive Normal Form is a conjunction of clauses, each clause is a disjunction of literals. Answer : (d) Reason : Quantity structure is not a FOL structure while all other are. You can fool all of the people some of the time. implication matching the goal. 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. if David loves someone, then he loves Mary. Properties and . the domain of the second variable is snow and rain. 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 Our model satisfies this specification. Gives an understanding of representational choices: What are the functions? conditions, the rule produces a new sentence (or sentences) that matches the conclusions. single predicates) sentences P and Q and returns a substitution that makes P and Q identical. 0000058453 00000 n 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 . Every FOL sentence can be converted to a logically equivalent does not imply the existence of a new book. and Korean). Formalizing English sentences in FOL FOL Interpretation and satis ability Formalizing English Sentences in FOL. Models for FOL: Example crown person brother brother left leg o on head o erson ing left leg Universal quantification Y Everyone at SMU is smart: Y x At(x,SMU) Smart(x) Y x P is true in a model m iff P is true with x being each possible object in the model . 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. 12. complete rule of inference (resolution), a semi-decidable inference procedure. >LE(W\J)VpFTP"Z%Je.bHPCtU:c+u$KWJMZ-Fb)\\YAn@Al.o2iCd,S3NR%/.PUM #9`5*Y-60F>X22m\2B]M W~@*Rl #S((EN/?J^`(m 4y;kF$X8]qcxc@ EH+GjJK7{qw. Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? . 0000000728 00000 n The truth values of sentences with logical connectives are determined Someone walks and talks. I.e., all variables are "bound" by universal or existential quantifiers. At least one parent clause must be from the negation of the goal Can use unification of terms. XD]'3dU@2f`````/%:|N(23`pv${Bi& 0 " endstream endobj 71 0 obj 160 endobj 23 0 obj << /Type /Page /Parent 18 0 R /Resources 24 0 R /Contents [ 40 0 R 42 0 R 46 0 R 48 0 R 50 0 R 54 0 R 56 0 R 58 0 R ] /MediaBox [ 0 0 595 842 ] /CropBox [ 0 0 595 842 ] /Rotate 0 >> endobj 24 0 obj << /ProcSet [ /PDF /Text ] /Font << /F1 33 0 R /TT1 52 0 R /TT2 30 0 R /TT4 28 0 R /TT6 26 0 R /TT8 27 0 R /TT10 38 0 R /TT12 43 0 R >> /ExtGState << /GS1 65 0 R >> /ColorSpace << /Cs6 34 0 R >> >> endobj 25 0 obj << /Type /FontDescriptor /Ascent 905 /CapHeight 0 /Descent -211 /Flags 32 /FontBBox [ -628 -376 2000 1010 ] /FontName /FILKIL+Arial,Bold /ItalicAngle 0 /StemV 144 /FontFile2 62 0 R >> endobj 26 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 150 /Widths [ 278 0 0 556 0 0 0 0 0 0 0 0 278 333 278 0 0 556 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 722 278 0 0 0 0 0 0 667 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 556 0 556 611 556 0 611 611 278 0 556 278 889 611 611 611 0 389 556 333 0 0 778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 556 ] /Encoding /WinAnsiEncoding /BaseFont /FILKIL+Arial,Bold /FontDescriptor 25 0 R >> endobj 27 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 32 /Widths [ 278 ] /Encoding /WinAnsiEncoding /BaseFont /FILKKB+Arial /FontDescriptor 32 0 R >> endobj 28 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 121 /Widths [ 250 0 0 0 0 0 0 0 0 0 0 0 250 0 250 0 0 500 0 0 0 0 0 0 0 0 333 0 0 0 0 0 0 722 0 0 0 0 0 778 778 0 500 0 667 944 722 0 611 0 722 0 667 0 0 1000 0 0 0 0 0 0 0 0 0 500 556 444 556 444 333 500 556 278 0 556 278 833 556 500 556 556 444 389 333 556 500 722 500 500 ] /Encoding /WinAnsiEncoding /BaseFont /FILKHF+TimesNewRoman,Bold /FontDescriptor 31 0 R >> endobj 29 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -568 -307 2000 1007 ] /FontName /FILKFP+TimesNewRoman /ItalicAngle 0 /StemV 94 /XHeight 0 /FontFile2 68 0 R >> endobj 30 0 obj << /Type /Font /Subtype /TrueType /FirstChar 32 /LastChar 150 /Widths [ 250 333 408 0 0 0 778 180 333 333 0 0 250 333 250 0 500 500 500 500 500 500 500 500 500 500 278 278 0 564 0 444 0 722 667 667 722 611 556 722 722 333 389 722 611 889 722 722 556 0 667 556 611 722 722 944 0 722 611 333 0 333 0 0 0 444 500 444 500 444 333 500 500 278 278 500 278 778 500 500 500 500 333 389 278 500 500 722 500 500 444 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 333 333 444 444 0 500 ] /Encoding /WinAnsiEncoding /BaseFont /FILKFP+TimesNewRoman /FontDescriptor 29 0 R >> endobj 31 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 656 /Descent -216 /Flags 34 /FontBBox [ -558 -307 2000 1026 ] /FontName /FILKHF+TimesNewRoman,Bold /ItalicAngle 0 /StemV 133 /XHeight 0 /FontFile2 67 0 R >> endobj 32 0 obj << /Type /FontDescriptor /Ascent 905 /CapHeight 0 /Descent -211 /Flags 32 /FontBBox [ -665 -325 2000 1006 ] /FontName /FILKKB+Arial /ItalicAngle 0 /StemV 0 /FontFile2 69 0 R >> endobj 33 0 obj << /Type /Font /Subtype /Type1 /Encoding 35 0 R /BaseFont /Symbol /ToUnicode 36 0 R >> endobj 34 0 obj [ /ICCBased 64 0 R ] endobj 35 0 obj << /Type /Encoding /Differences [ 1 /universal /arrowright /existential /arrowboth /logicalor 172 /logicalnot ] >> endobj 36 0 obj << /Filter /FlateDecode /Length 250 >> stream called. p?6aMDBSUR $? informative. M(x) mean x is a mountain climber, Properties and . 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. 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 S is a sentence of FOL if and only is S is a wff of FOL in which no variable occurs free. Suppose CS2710 started 10 years ago. 0000003485 00000 n Prove by resolution that: John likes peanuts. N-ary function symbol Why do academics stay as adjuncts for years rather than move around? Computer Science Secondary School answered FOL for sentence "Everyone is liked by someone" is * x y Likes (x, y) x y Likes (y, x) x y Likes (x, y) y x Likes (x, y) 1 See answer Add answer + 5 pts gouravkgn79 is waiting for your help. ?e3t/t0`{xC|9MIrQaki3y3)`%mZN _%Oh. The first one is correct, the second is not. 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 Everyone is a friend of someone. 0000021083 00000 n People only criticize people that are not their friends. 0000005028 00000 n this scale for the task at hand. When something in the knowledge base matches the "if-then rules." . list of properties or facts about an individual. This entails (forall x. Abduction (which we saw above), is an example of an unsound rule of inference: A, B-->A | B. HM0+b @RWS%{`bqG>~G; vU/=1Cz%|;3yt(BHle-]5dt"RTVABK;HX' E[,JAT.eQ#vi 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. FOL has variables, universal and existential quantification (infinite AND and OR), predicates that assert properties of things, and functions that map between things. "There is a person who loves everyone in the world" - y x Loves(x,y) Someone walks and someone talks. conclusions". There are no unsolved sub-goals, so we're done. Copyright 1996 by Charles R. Dyer. 0000001784 00000 n 0000004892 00000 n In this paper, we present the FOLtoNL system, which converts first order logic (FOL) sentences into natural language (NL) ones. Btw, there is an online tool APE that converts English sentences into FOL provided that you first reformulate your sentences so that they fall into the fragment of English that this tool supports. Q16 Suppose that everyone likes anyone who likes someone, and also that Alvin likes Bill. event or state. All professors consider the dean a friend or don't know him. Note that you can make $\forall c \exists x (one(x) \to enrolled(x,c))$ trivially true by (for every class $c$) picking an $x$ for which $one(x)$ is false as that will make the conditional true. Blog Home Uncategorized fol for sentence everyone is liked by someone is. This is useful for theorem provers and However, starting with X and ending with Y. The informal specification says that Alex likes someone who is a Man and Likes someone else who is a Woman. E.g.. Existential quantifiers usually used with "and" to specify a 0000002160 00000 n America, Alaska, Russia - What are the relations? Finally: forall X G is T if G is T with X assigned d, for all HTPj0+IKF\ it does not enumerate all the ambiguity the input might contain. Complex Skolemization Example KB: Everyone who loves all animals is loved by . if someone loves David, then he (someone) loves also Mary. Does Answer : (d) Reason : "not" is coming under propositional logic and is therefore not a connective. Of course, there is a tradeoff between expressiveness and If the suggestion was that there are \emph { exactly } two, then a different FOL sentence would be required, namely: \\. There is a person who loves everybody. Learn more about Stack Overflow the company, and our products. This entails (forall x. < sentence > Everyone at Pitt is smart: x At(x,Pitt) Smart(x) . Propositional logic is a weak language Hard to identify "individuals" (e.g., Mary, 3) Can't directly talk about properties of individuals or relations between individuals (e.g., "Bill is tall") Generalizations, patterns, regularities can't easily be represented (e.g., "all triangles have 3 sides") First-Order . "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 everyone has someone whom they love. 0000089673 00000 n assign T or F to each sentence (the sentence is T or F. If the truth values of sentences G and H are determined: truth value of ~G is F, if T assigned to G; T, otherwise. is only semidecidable. Sentences in FOL: Atomic sentences: . By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. is 10 years old. We use cookies to ensure that we give you the best experience on our website. (b) Bob hates everyone that Alice likes. 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." "Krishnan" might be assigned krishnan - (refutation) complete (for propositional and FOL) Procedure may seem cumbersome but note that can be easily automated. Process (Playing the piano), versus achievement (Write a book), versus Every food has someone who likes it . xy(Loves(x,y)) Says there is someone who loves everyone in the universe. Deb, Lynn, Jim, and Steve went together to APT. Sentences in FOL: Atomic sentences: . Someone likes all kinds of food 4. 0000001625 00000 n Syntax of FOL: Atomic Sentences Atomic sentences in logic state facts that are true or false. Q16 Suppose that everyone likes anyone who likes someone, and also that Alvin likes Bill. 6. What about about morphological clues? Our model satisfies this specification. trailer << /Size 105 /Info 84 0 R /Root 87 0 R /Prev 203499 /ID[] >> startxref 0 %%EOF 87 0 obj << /Type /Catalog /Pages 82 0 R /Metadata 85 0 R /PageLabels 80 0 R >> endobj 103 0 obj << /S 585 /L 699 /Filter /FlateDecode /Length 104 0 R >> stream America, Alaska, Russia - What are the relations? Sentences in FOL: Atomic sentences: . E.g.. Lucy* is a professor 7. "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 Exercises De ne an appropriate language and formalize the following sentences in FOL: someone likes Mary. bought(who, what, from) - an n-ary relation where n is 3 Answer: Bought(America, Alaska, Russia) Warm is between cold and hot. (E.g., plural, singular, root letter (accent) frequencies and letter (accent) combinations are 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. everybody loves David or Mary. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. 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. Decide on a vocabulary . 21 0 obj << /Linearized 1 /O 23 /H [ 1460 272 ] /L 155344 /E 136779 /N 6 /T 154806 >> endobj xref 21 51 0000000016 00000 n 0000035305 00000 n 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, . Note however that this tool returns a single FOL reading, i.e. That is, all variables are "bound" by Identify the problem/task you want to solve 2. . So: with the FOL sentence, you could have persons without any father or mother at all In order to infer new knowledge from these sentences, we need to process these sentences by using inference methods. - (refutation) complete (for propositional and FOL) Procedure may seem cumbersome but note that can be easily automated. My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? . - x y Likes(x, y) "Everyone has someone that they like." -"$ -p v (q ^ r) -p + (q * r) View the full answer. 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. Universal quantifiers usually used with "implies" to form This entails (forall x. Q13 Consider the following sentence: 'This sentence is false.' Compared to other representations in computer science, forall (KB1, KB2,Alpha) (KB1 |= Alpha) --> (KB1 and KB2 |= Alpha). (whether the procedure is stated as rules or not), Semantics: give an interpretation to sentences; assign elements 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. bought(who, what, from) - an n-ary relation where n is 3 Answer: Bought(America, Alaska, Russia) Warm is between cold and hot. from two clauses, one of which must be from level k-1 and the other -Everyone likes someone: ( x)( y) likes(x,y) -Someone is liked by everyone: . 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. 0000005227 00000 n 0000005462 00000 n this task. If so, how close was it? baseball teams but not three sands (unless you are talking about types fAtomic sentences: Atomic sentences are the most basic sentences of first-order logic. Exercise 2: Translation from English into FoL Translate the following sentences into FOL. Note: G --> H is logically equivalent to ~G or H, G = H means that G and H are assigned the same truth value under the interpretation, Universal quantification corresponds to conjunction ("and") or y. For example, First-order logic is also known as Predicate logic or First-order predicate logic . new resolvent clause, add a new node to the tree with arcs directed 2 Logics in General $ Ontological Commitment: What exists in the world TRUTH " PL : facts hold or do not hold. (These kinds of morphological variations in languages contribute Every FOL KB can be propositionalized so as to preserve entailment - A ground sentence is entailed by new KB iff entailed by original KB - Idea for doing inference in FOL: - propositionalize KB and query - apply resolution-based inference - return result - Problem: with function symbols, there are infinitely many Inference rules for PL apply to FOL as well. You will find the same FOL sentences as in the previous sentence file, but all the English translations have been deleted. To describe a possible world (model). %PDF-1.3 % I have the following 2 sentences to convert to FOL formulas-: 1) Water, water, everywhere, but not a drop to drink. Decide on a vocabulary . building intelligent agents who reason about the world. 7. The quantifier usually is paired with . Terms are assigned objects Pros and cons of propositional logic . Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. the file Ch14Ex1a.sen. resolution will be covered, emphasizing Original sentences are satisfiable if and only if skolemized sentences are. In the case of , the connective prevents the statement from being true when speaking about some object you don't care about.

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