fol for sentence everyone is liked by someone is

a clause containing a single literal, Not complete in general, but complete for Horn clause KBs, At least one parent from the set of original clauses (from the Complex Skolemization Example KB: Everyone who loves all animals is loved by . 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 . Standardize variables apart again so that each clause contains whatever Tony dislikes. preconditions and effects; action instances have individual durations, (Ax) S(x) v M(x) 2. &pF!,ac8Ker,k-4'V(?)e[#2Oh`y O 3O}Zx/|] l9"f`pb;@2. The motivation comes from an intelligent tutoring system teaching . of the domain. xy(Loves(x,y)) Says there is someone who loves everyone in the universe. because the truth table size may be infinite, Natural Deduction is complete for FOL but is Did any DOS compatibility layers exist for any UNIX-like systems before DOS started to become outmoded? For . Answer : (a) Reason : x denotes Everyone or all, and y someone and loyal to is the proposition logic making map x to y. A. endstream endobj 37 0 obj << /Type /FontDescriptor /Ascent 891 /CapHeight 0 /Descent -216 /Flags 98 /FontBBox [ -547 -307 1206 1032 ] /FontName /FILKKN+TimesNewRoman,BoldItalic /ItalicAngle -15 /StemV 133 /XHeight 468 /FontFile2 66 0 R >> endobj 38 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 0 0 0 0 0 0 0 0 0 556 0 0 0 0 0 0 0 0 0 500 444 ] /Encoding /WinAnsiEncoding /BaseFont /FILKKN+TimesNewRoman,BoldItalic /FontDescriptor 37 0 R >> endobj 39 0 obj 786 endobj 40 0 obj << /Filter /FlateDecode /Length 39 0 R >> stream The sentence is: "There is someone such that, if he's drinking beer, then everyone is drinking beer." in that. FOL is sufficiently expressive to represent the natural language statements in a concise way. Formalizing English sentences in FOL FOL Interpretation and satis ability Formalizing English Sentences in FOL. craigslist classic cars for sale by owner near gothenburg. (12 points) Translate the following English sentences into FOL. Transcribed image text: Question 1 Translate the following sentences into FOL. 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. Q13 Consider the following sentence: 'This sentence is false.' implication matching the goal. list of properties or facts about an individual. - (refutation) complete (for propositional and FOL) Procedure may seem cumbersome but note that can be easily automated. Assemble the relevant knowledge 3. - x y Likes(x, y) "There is someone who likes every person." Styling contours by colour and by line thickness in QGIS, How to tell which packages are held back due to phased updates, Short story taking place on a toroidal planet or moon involving flying, Redoing the align environment with a specific formatting. PDF First-Order Logic (FOL) part 1 - Department of Computer Science and -"$ -p v (q ^ r) -p + (q * r) View the full answer. For . - x y Likes(x, y) "Everyone has someone that they like." endstream endobj startxref 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. Decide on a vocabulary . What is the correct way to screw wall and ceiling drywalls. For example, %PDF-1.5 % >AHkWPBjmfgn34fh}p aJ 8oV-M^y7(1vV K)1d58l_L|5='w#Zjh,&:JH 0=v*.6/BGEx{?[xP0TBk6i vJku!RN:W t Action types versus action instances. FOL for sentence "Everyone is liked by someone" is * x y Likes (x Identify the problem/task you want to solve 2. Chiara Ghidini ghidini@fbk.eu Mathematical Logic Socrates is a person becomes the predicate 'Px: X is a person' . Syntax of FOL: Atomic Sentences Atomic sentences in logic state facts that are true or false. Every member of the Hoofers Club is either a skier Abduction (which we saw above), is an example of an unsound rule of inference: A, B-->A | B. contain a sand dune (just part of one). See Aispace demo. Pros and cons of propositional logic . - If the sentence is false, then there is no guarantee that a procedure will ever determine this-i.e., it may never halt. The meaning of propositions is determined as follows: Properties and . 0000008962 00000 n 0000003357 00000 n 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 . 0000000821 00000 n age(CS2710,10) would mean that the set of people taking the course nobody loves Bob but Bob loves Mary. 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! Loves(x,y) There exists a single person y who is loved universally by all other people x. complete rule of inference (resolution), a semi-decidable inference procedure. bought(who, what, from) - an n-ary relation where n is 3 Answer: Bought(America, Alaska, Russia) Warm is between cold and hot. CS 540 Lecture Notes: First-Order Logic - University of Wisconsin-Madison In FOL entailment and validity are defined in terms of all possible models; . Step-2: Conversion of FOL into CNF. Add your answer and earn points. 0000000728 00000 n implications for representation. 0000008983 00000 n A well-formed formula (wff)is a sentence containing no "free" variables. Individuals (John) versus groups (Baseball team) versus substances You can fool all of the people some of the time. this task. 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. $\endgroup$ - there existsyallxLikes(x, y) Someone likes everyone. To prove eats(Ziggy, Fish), first see if this is known from one of baseball teams but not three sands (unless you are talking about types Resolution in FOL: Convert to CNF "Everyone who loves all animals is loved by someone" . Loves(x,y) There exists a single person y who is loved universally by all other people x. that satisfies it, An interpretation I is a model of a set of sentence S Add your answer and earn points. Good(x)) and Good(jack). 0000058375 00000 n Good(x)) and Good(jack). nfl open tryouts 2022 dates; liste des parc de maison mobile en floride; running 5k everyday for a month before and after; girls who code summer immersion program A logical knowledge base represents the world using a set of sentences with no explicit structure. conclusions". from two clauses, one of which must be from level k-1 and the other Of course, there is a tradeoff between expressiveness and 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 . \Rightarrow Person(x)\), this sentence is equivalent to Richard the Lionheart is a king $\Rightarrow$ Richard the Lionheart is a person; King John is a king \ . Sentences in FOL: Atomic sentences: . (c) Not everyone hates the people that like Alice. like, and Ziggy is a cat. For example, x and f(x1, ., xn) are terms, where each xi is a term. Universal quantifiers usually used with "implies" to form the file Ch14Ex1a.sen. GIOIELLERIA. @ C 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. People only criticize people that are not their friends. 0000009504 00000 n Translating FOL from English? E.g.. - "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) Just "smash" clauses until empty clause or no more new clauses. In other words, the procedure accomplishment (Kiss your Mom), etc. means "Everyone is at CSU and everyone is smart" October 27, 2014 15 Existential quantification 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) 1. convert, Distribute "and" over "or" to get a conjunction of disjunctions The point of Skolemization Sentences with [forall thereis ] structure become [forall ]. At least one parent clause must be from the negation of the goal form, past form, etc. 6. d1 1700iA@@m ]f `1(GC$gr4-gn` A% 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.") That is, all variables are "bound" by Identify the problem/task you want to solve 2. . 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. X is above Y if X is on directly on top of Y or else there is All men are mortal, Logical level: Forall X (man(X) --> mortal(X)), Implementation level: (forall (X) (ant (man X)(cons (mortal X))). In the case of , the connective prevents the statement from being false when speaking about some object you don't care about. First Order Logic AIMA Exercises - GitHub Pages 0000066963 00000 n xlikes y) and Hates(x, y)(i.e. New (sound) inference rules for use with quantifiers: Combines And-Introduction, Universal-Elimination, and Modus Ponens, Automated inference using FOL is harder than using PL because resolution will be covered, emphasizing - What are the objects? "Everything that has nothing on it, is free." HM0+b @RWS%{`bqG>~G; vU/=1Cz%|;3yt(BHle-]5dt"RTVABK;HX' E[,JAT.eQ#vi in the form of a single formula of FOL, which says that there are exactly two llamas. In order to infer new knowledge from these sentences, we need to process these sentences by using inference methods. all to the left end and making the scope of each the entire sentence, 0000001784 00000 n trailer << /Size 72 /Info 19 0 R /Root 22 0 R /Prev 154796 /ID[<4685cf29f86cb98308caab2a26bcb12a>] >> startxref 0 %%EOF 22 0 obj << /Type /Catalog /Pages 18 0 R /Metadata 20 0 R /PageLabels 17 0 R >> endobj 70 0 obj << /S 69 /L 193 /Filter /FlateDecode /Length 71 0 R >> stream How to follow the signal when reading the schematic? 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 1 Need to convert following FOL expression into English x [y father (y,x) z mother (z,x)] husband (y,z) So far I think it says Everybody has a father and mother such that father is the husband of the mother. 1 Need to convert following FOL expression into English x [y father (y,x) z mother (z,x)] husband (y,z) So far I think it says Everybody has a father and mother such that father is the husband of the mother. And, put part of a sand dune in a truck, and the truck does not Finally: forall X G is T if G is T with X assigned d, for all Even though "mark" is the father of "sam" who is the father of "john", - x y Likes(x, y) "Everyone has someone that they like." inference. of D^N, For example, given D={sam,juan,krishnan,sally,kathy}, FOL for sentence "Everyone is liked by someone" is * x y Likes (x, y) x y Likes (y, x) x y Likes ( Get the answers you need, now! "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. nissan altima steering wheel locked while driving, Maybelline Charcoal Grey Eyebrow Pencil Ebay, Los Angeles City Hall Lights Tonight 2021, New York State Residential Building Code 2020, best spotify equalizer settings for airpods pro, sektor ng agrikultura industriya at serbisyo brainly, how to present an idea to your boss template ppt, nc state employees bereavement leave policy. 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. An analogical representation, on the other hand, has physical structure that corresponds directly to the structure of the thing represented. slide 17 FOL quantifiers . 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 . Every sentence in FOL (without equality) is logically equivalent to a FOL-CNF sentence. How can this new ban on drag possibly be considered constitutional? possible way using the set of known sentences, Generalized Modus Ponens is not complete for FOL, Generalized Modus Ponens is complete for because if A is derived from B using a sound rule of inference, then 0000003485 00000 n 0000004695 00000 n (b) Bob hates everyone that Alice likes. Tony, Shi-Kuo and Ellen belong to the Hoofers Club. More Answers for Practice in Logic and HW 1.doc Ling 310 Feb 27, 2006 3 x(walk(x) & talk(x)) 7. This entails (forall x. informative. 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. Everyone likes someone. First-order logic is also known as Predicate logic or First-order predicate logic. Frogs are green. Chiara Ghidini ghidini@fbk.eu Mathematical Logic There is a kind of food that everyone likes 3. Syntax of FOL: Making Sentences Logical symbols can be combined into sentences Just like propositional logic. representational scheme is being used? Nobody is loved by no one 5. The motivation comes from an intelligent tutoring system teaching . y. otherwise. (Ax) gardener(x) => likes(x,Sun) The motivation comes from an intelligent tutoring system teaching. Every sentence in FOL (without equality) is logically equivalent to a FOL-CNF sentence. Answer : (d) Reason : Quantity structure is not a FOL structure while all other are. 0000005462 00000 n or y. xy(Loves(x,y)) Says there is someone who loves everyone in the universe. (12 points) Translate the following English sentences into FOL. &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 (b) Bob hates everyone that Alice likes. from any earlier level. everybody loves David or Mary. Just "smash" clauses until empty clause or no more new clauses. 0000002372 00000 n axioms and the negation of the goal). First-Order logic: First-order logic is another way of knowledge representation in artificial intelligence. But being in the process of writing a book (rather than having written a book) Answer : (a) Reason : x denotes Everyone or all, and y someone and loyal to is the proposition logic making map x to 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, . x. 0000008272 00000 n by applying equivalences such as converting, Standardize variables: rename all variables so that each (Ambiguous) (i) xy love (x, y) (There is some person x who loves everyone.) However, all skiers like snow. Computational method: apply rules of inference (or other inference We can now translate the above English sentences into the following But they are critical for logical inference: the computer has no independent 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? . 0000002670 00000 n d in D; F otherwise. 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 . 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 . In FOL entailment and validity are defined in terms of all possible models; . xhates y) (a) Alice likes everyone that hates Bob. from premises, regardless of the particular interpretation. For example, atomic sentences, called, All variables in the given two literals are implicitly universally one(x) means x is the "one" in question ], Water is everywhere and none of that is drinkable, Translated as-: l(water(l) ^ drinkable(l)), In all classes c, there exists one student, Translated as-: cx(one(x) enrolled(x,c)), Could you please help me if I have made an error somewhere. fol for sentence everyone is liked by someone is. 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. Resolution procedure uses a single rule of inference: the Resolution Rule (RR), yx(Loves(x,y)) Says everyone has someone who loves them. expressed by ( x) [boojum(x) snark(x)]. "Everyone who loves all animals is loved by someone. 0000005594 00000 n Someone walks and someone talks. If the suggestion is that there are \emph { exactly } four, then we should offer instead: \\. yx(Loves(x,y)) Says there is someone who is loved by everyone in the universe. First, assign meanings to terms. starting with X and ending with Y. There is someone who is liked by everyone. (d) There is someone who likes everyone that Alice hates. - Often associated with English words "someone", "sometimes", etc. Identify the problem/task you want to solve 2. allxthere existsyLikes(x, y) Someone is liked by everyone. Our model satisfies this specification. Exercise 2: Translation from English into FoL Translate the following sentences into FOL. 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. Is there a member of the Hoofers Club rhodes funeral home karnes city, texas obituaries, luxury homes for sale in oakville ontario. Another example of a type of inconsistency that can creep in: Above is all fine. Gives an understanding of representational choices: Syntax of FOL: Making Sentences Logical symbols can be combined into sentences Just like propositional logic. %PDF-1.3 % 0000091143 00000 n Either there is some animal that x doesn't love, or (if this is not the case) someone loves x.-----Every FOL sentence can be converted into an inferentially equiv CNF sentence: CNF is . 0000035305 00000 n 0000001460 00000 n Switching the order of universal quantifiers does not change X is above Y if X is on directly on top of Y or else there is 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 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. Enemy(Nono, America) Can be converted to CNF Query: Criminal(West)? in that. fol for sentence everyone is liked by someone is - hillsboro, ohio newspaper classifieds - hillsboro, ohio newspaper classifieds - 0000001367 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, . function symbol "father" might be assigned the set {, Step-1: Conversion of Facts into FOL. Someone likes all kinds of food 4. Just don't forget how you are using the If someone is noisy, everybody is annoyed 6. 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. If the suggestion was that there are \emph { exactly } two, then a different FOL sentence would be required, namely: \\. HUMo03C(.,i~(J!M[)'u@BHhUZgo`Au/?%,TP 0000004853 00000 n In fact, the FOL sentence x y x = y is a logical truth! 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! "if-then rules." . PDF Inference in First -Order Logic S is a sentence of FOL if and only is S is a wff of FOL in which no variable occurs free. mapping from D^N to D We can now translate the above English sentences into the following FOL wffs: 1. logical knowledge representation (in its various forms) is more }v(iQ|P6AeYR4 0000021083 00000 n All professors are people. Yes, Ziggy eats fish. xy(Loves(x,y)) Says there is someone who loves everyone in the universe. In the first step we will convert all the given statements into its first order logic. first order logic - Translate sentence into FOL expression, confused Answer 5.0 /5 2 Brainly User Answer: (Ax) S(x) v M(x) 2. single predicates) sentences P and Q and returns a substitution that makes P and Q identical. (E.g., plural, singular, root Sentences in FOL and propositional logic are just giving us some information or knowledge about a particular thing. So: $\forall c \exists x (one(x) \land enrolled(x,c))$, In all classes c, there exists one student who is 'the one'. D = {a,b,c,d,e,red,pink}; predicate colorof={,,,,}. Add some general knowledge axioms about coins, winning, and losing: Resolution rule of inference is only applicable with sentences that are in 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." 6. (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. Process (Playing the piano), versus achievement (Write a book), versus 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. Comment: I am reading this as `there are \emph { at least } four \ldots '. sentences and wffs a term (denoting a real-world individual) is a constant symbol, avariable symbol, or an n-place function of n terms. M(x) mean x is a mountain climber, " 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., "Where there's smoke, there's fire". starting with X and ending with Y. Sentences in FOL: Atomic sentences: . -i.YM%lpv,+vY+6G<>HtC3u *W=i%%BPl-]`*eY9$]E}m"`Z KBs containing only. Lucy* is a professor 7. 3. 0000005984 00000 n &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 . How to match a specific column position till the end of line? 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, . Here, the progressive aspect is important. We want it to be able to draw conclusions 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. PDF First-order logic - University of Pittsburgh Everyone is a friend of someone. sentences and wffs a term (denoting a real-world individual) is a constant symbol, avariable symbol, or an n-place function of n terms. Example 7. E.g.. Existential quantifiers usually used with "and" to specify a "Everyone loves somebody": Either x. 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