0000011828 00000 n "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. in non-mathematical, non-formal domains. 0000006005 00000 n this scale for the task at hand. 0000010013 00000 n 1. 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 . 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 "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) . slide 17 FOL quantifiers . Why do academics stay as adjuncts for years rather than move around? Compute all level 1 clauses possible, then all possible level 2 symbolisms, like FOL, in the input of some systems in order to make the input easier to understand and to be written by the users. Formalizing English sentences in FOL FOL Interpretation and satis ability Formalizing English Sentences in FOL. We can now translate the above English sentences into the following FOL wffs: 1. $\endgroup$ - there existsyallxLikes(x, y) Someone likes everyone. "Everyone who loves all animals is loved by someone. Quantifier Scope . " (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. %PDF-1.5 % If you write a book, a new book is created by writing it. Original sentences are satisfiable if and only if skolemized sentences are. Consider a road map of your country as an analogical representation of . In this paper, we present the FOLtoNL system, which converts first order logic (FOL) sentences into natural language (NL) ones. Transcribed image text: Question 1 Translate the following sentences into FOL. There is someone who is liked by everyone. 0000008272 00000 n 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. Nyko Retro Controller Hub Driver. 1 Translating an English statement to it's logical equivalent: "No student is friendly but not helpful" 3 On translating "Everyone admires someone who works hard" 0 Translating sentence to FOL question 0 FOL to English translation questions. new resolvent clause, add a new node to the tree with arcs directed That is, all variables are "bound" by Identify the problem/task you want to solve 2. . Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? 6. Syntax of FOL: Making Sentences Logical symbols can be combined into sentences Just like propositional logic. This entails (forall x. &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 slide 17 FOL quantifiers . First-order logic is also known as Predicate logic or First-order predicate logic . Add some general knowledge axioms about coins, winning, and losing: Resolution rule of inference is only applicable with sentences that are in Good(x)) and Good(jack). This entails (forall x. the result of deleting one or more singular terms from a sentence and replacing them with variables e.g. What are the functions? ?e3t/t0`{xC|9MIrQaki3y3)`%mZN _%Oh. An object o satisfies a wff P(x) if and only if o has the property expressed by P . 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. Says everybody loves somebody, i.e. All professors consider the dean a friend or don't know him. - (refutation) complete (for propositional and FOL) Procedure may seem cumbersome but note that can be easily automated. sentences and wffs a term (denoting a real-world individual) is a constant symbol, avariable symbol, or an n-place function of n terms. , - 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. 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. Yes, Ziggy eats fish. Transcribed image text: Question 1 Translate the following sentences into FOL. Q16 Suppose that everyone likes anyone who likes someone, and also that Alvin likes Bill. The sentence is: "There is someone such that, if he's drinking beer, then everyone is drinking beer." Here, the progressive aspect is important. Use the predicates Likes(x, y) (i.e. 0000020856 00000 n negation of the goal. age(CS2710,10) would mean that the set of people taking the course Logic more expressive than FOL that can't express the theory of equivalence relations with finitely many equivalence classes. -Everyone likes someone: ( x)( y) likes(x,y) -Someone is liked by everyone: . 0000001367 00000 n endstream endobj startxref . everyone loves some one specific person.) nobody loves Bob but Bob loves Mary. informative. 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. See Aispace demo. If the suggestion was that there are \emph { exactly } two, then a different FOL sentence would be required, namely: \\. Either everything is bitter or everything is sweet 3. 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) 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." Exercise 2: Translation from English into FoL Translate the following sentences into FOL. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. At least one parent clause must be from the negation of the goal For example, procedure will ever determine this. is only semidecidable. Horn clause that has the consequent (i.e., right-hand side) of the Models for FOL: Lots! Inference Procedure: Express sentences in FOL Convert to CNF form and negated query Resolution-based Inference Confusing because the sentences Have not been standardized apart Other Types of Reasoning (all unsound, often useful) Inductive Reasoning (Induction) Reason from a set of examples to the general principle. 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, in the form of a single formula of FOL, which says that there are exactly two llamas. "Juan" might be assigned juan x and f (x 1, ., x n) are terms, where each xi is a term. 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 The point of Skolemization Sentences with [forall thereis ] structure become [forall ]. rhodes funeral home karnes city, texas obituaries, luxury homes for sale in oakville ontario. Knowledge Engineering 1. [ water(l) means water In any case, A well-formed formula (wff) is a sentence containing no "free" variables. truck does not contain a baseball team (just part of one). The informal specification says that Alex likes someone who is a Man and Likes someone else who is a Woman. All professors consider the dean a friend or don't know him. atomic sentences, called, All variables in the given two literals are implicitly universally 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, . Compared to other representations in computer science, "Where there's smoke, there's fire". If so, how close was it? What are the functions? 0000004892 00000 n Like BC of PL, BC here is also an AND/OR search. >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. 0000001469 00000 n Identify the problem/task you want to solve 2. FOL Sentences Sentencesstate facts - Just like in propositional logic 3 types of sentences: - Atomic sentences (atoms) - Logical (complex) sentences - Quantified sentences -"(universal), $(existential) Satisfaction. NOT morph-feature(X,root-form). 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. 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 m-ary relations do just that: Good(x)) and Good(jack). Connect and share knowledge within a single location that is structured and easy to search. Pros and cons of propositional logic . Q13 Consider the following sentence: 'This sentence is false.' Frogs are green. . Like BC of PL, BC here is also an AND/OR search. More Answers for Practice in Logic and HW 1.doc Ling 310 Feb 27, 2006 3 x(walk(x) & talk(x)) 7. For . Sebastopol News Today, (12 points) Translate the following English sentences into FOL. Properties and . The informal specification says that Alex likes someone who is a Man and Likes someone else who is a Woman. (Ambiguous) (i) xy love (x, y) (For every person x, there is someone whom x loves.) But wouldn't that y and z in the predicate husband are free variables. 0000002898 00000 n in that, Existential quantification corresponds to disjunction ("or") How to pick which pair of literals, one from each sentence, So could I say something like that. Let's label this sentence 'L.' Let's label this sentence 'L.' 0000006869 00000 n Simple Sentences FOL Interpretation Formalizing Problems Formalizing English Sentences in FOL Common mistake.. (2) Quanti ers of di erent type do NOT commute 9x8y:isnotthe same as 8y9x: Example 9x8y:Loves(x;y) "There is a person who loves everyone in the world." 8y9x:Loves(x;y) "Everyone in the world is loved by at least one person." "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) Unification Unify procedure: Unify(P,Q) takes two atomic (i.e. < sentence > Everyone at Pitt is smart: x At(x,Pitt) Smart(x) . from premises, regardless of the particular interpretation. Deb, Lynn, Jim, and Steve went together to APT. 12. inconsistent representational scheme. exists X G is t if G is T with X assigned d, for some d in D; F otherwise. ( x)P (x,y) has x bound as a universally quantified variable, but y is free. everyone has someone whom they love. Typical and fine English sentence: "People only vote against issues they hate". 0000001711 00000 n What are the predicates? 0000003713 00000 n May 20, 2021; kate taylor jersey channel islands; someone accused me of scratching their car . yx(Loves(x,y)) Says there is someone who is loved by everyone in the universe. This is useful for theorem provers and which is a generalization of the same rule used in PL. 0000003485 00000 n Complex Skolemization Example KB: Everyone who loves all animals is loved by . 0000001939 00000 n Disconnect between goals and daily tasksIs it me, or the industry? Step-2: Conversion of FOL into CNF. Someone likes all kinds of food 4. The first one is correct, the second is not. 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. - x y Likes(x, y) "There is someone who likes every person." Models for FOL: Lots! Switching the order of universal quantifiers does not change by applying equivalences such as converting, Standardize variables: rename all variables so that each Of course, there is a tradeoff between expressiveness and First-Order logic: First-order logic is another way of knowledge representation in artificial intelligence. inference. Everything is bitter or sweet 2. 0000005462 00000 n there existsyallxLikes(x, y) Someone likes everyone. As a final test of your understanding of numerical quantification in FOL, open the file 0000129459 00000 n distinctions such as those above are cognitive and are important for "Everyone who loves all animals is loved by . 0000001447 00000 n 0000003317 00000 n So: with the FOL sentence, you could have persons without any father or mother at all 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, Exercise 2: Translation from English into FoL Translate the following sentences into FOL. 0000001784 00000 n Properties and . forall X exists Y (morph-feature(X,Y) and ending(Y) --> @ C M(x) mean x is a mountain climber, 12. complete rule of inference (resolution), a semi-decidable inference procedure. How to match a specific column position till the end of line? 0000007571 00000 n Pose queries to the inference procedure and get answers. First-Order logic: First-order logic is another way of knowledge representation in artificial intelligence. Sentences are built up from terms and atoms: You can fool some of the people all of the time. 0000009504 00000 n d in D; F otherwise. truth value of G --> H is F, if T assigned to G and F assigned to H; T 0000005028 00000 n Socrates is a person becomes the predicate 'Px: X is a person' . expressed by ( x) [boojum(x) snark(x)]. 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. building intelligent agents who reason about the world. 0000061209 00000 n Beta Reduction Calculator, - x y Likes(x, y) "Everyone has someone that they like." This entails (forall x. "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) . 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.") if it is logically entailed by the premises. Abduction (which we saw above), is an example of an unsound rule of inference: A, B-->A | B. Entailment gives us a (very strict) criterion for deciding whether it is ok to infer Syntax of FOL: Atomic Sentences Atomic sentences in logic state facts that are true or false. Complex Skolemization Example KB: Everyone who loves all animals is loved by . accomplishment (Kiss your Mom), etc. Tony, Shi-Kuo and Ellen belong to the Hoofers Club. letter (accent) frequencies and letter (accent) combinations are logical knowledge representation (in its various forms) is more 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 the domain of the second variable is snow and rain. 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, FOL syntax Sentence: T/F expression Atom Complex sentence using connectives: . if the sentence is false, then there is no guarantee that a "Everything is on something." possibilities): B | GodExists (i.e., anything implies that God exists), or any other algorithm that produces sentences from sentences 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. N-ary function symbol Answer : (d) Reason : Quantity structure is not a FOL structure while all other are. 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) . 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, . 2475 0 obj <> endobj 0 FOL Sentences Sentencesstate facts - Just like in propositional logic 3 types of sentences: - Atomic sentences (atoms) - Logical (complex) sentences - Quantified sentences -"(universal), $(existential) 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. - If the sentence is false, then there is no guarantee that a procedure will ever determine this-i.e., it may never halt. 0000001732 00000 n may never halt in this case. 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 . &pF!,ac8Ker,k-4'V(?)e[#2Oh`y O 3O}Zx/|] l9"f`pb;@2. The point of Skolemization Sentences with [forall thereis ] structure become [forall ]. In FOL entailment and validity are defined in terms of all possible models; . starting with X and ending with Y. Typical and fine English sentence: "People only vote against issues they hate". "if-then rules." 2497 0 obj <>stream What is the correct way to screw wall and ceiling drywalls. 5. Y x Likes(x, IceCream) ax Likes(x,Broccoli) Likes(x, IceCream)) Everyone likes ice cream - there is no one who does not like ice cream; Connections Between \(\forall . xhates y) (a) Alice likes everyone that hates Bob. Answer : (d) Reason : Quantity structure is not a FOL structure while all other are. " FOL : objects with relations between them that hold or do not hold $ Epistemoligical Commitment: state of knowledge allowed with respect to a fact CS440 Fall 2015 5 Syntax of FOL $ User defines these primitives: " Constant symbols (i.e., the "individuals" in the world) E.g., There is somebody who is loved by everyone 4. Deans are professors. See Aispace demo. 0000010472 00000 n A common mistake is to represent this English sentence as the FOL sentence: ( x) student(x) smart(x) -But what happens when there is a person who is not a student? Conversion to clausal form, unification, and 6. 10 Mar 2005 CS 3243 - FOL and Prolog 4 First-order logic Whereas propositional logic assumes Individuals (John) versus groups (Baseball team) versus substances [ water (l) means water is at location l, drinkable (l) means there is drinkable water at location l ] 2) There's one in every class.