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(Ax) S(x) v M(x) 2. Says everybody loves somebody, i.e. Is it possible to create a concave light? nobody loves Bob but Bob loves Mary. as in propositional logic. this task. Can use unification of terms. FOL Sentences Sentencesstate facts - Just like in propositional logic 3 types of sentences: - Atomic sentences (atoms) - Logical (complex) sentences - Quantified sentences -"(universal), $(existential) Satisfaction. 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. everyone has someone whom they love. 0000008029 00000 n It only takes a minute to sign up. What about about morphological clues? 12. Properties and . 2486 0 obj <>/Filter/FlateDecode/ID[<56E988B61056904CAEF5B59DB4CB372D>]/Index[2475 23]/Info 2474 0 R/Length 70/Prev 400770/Root 2476 0 R/Size 2498/Type/XRef/W[1 2 1]>>stream Step-2: Conversion of FOL into CNF. fAtomic sentences: Atomic sentences are the most basic sentences of first-order logic. truck does not contain a baseball team (just part of one). 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 (Ax) S(x) v M(x) 2. 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). Q13 Consider the following sentence: 'This sentence is false.' 86 0 obj << /Linearized 1 /O 88 /H [ 821 648 ] /L 205347 /E 93974 /N 18 /T 203509 >> endobj xref 86 19 0000000016 00000 n 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. x. Assemble the relevant knowledge 3. ( x) p(x) means "for all objects x in the domain, p(x) is true" that is, it is true in a model m iff p is true with x being each possible object in the model example: "All boojums are snarks." variables can take on potentially an infinite number of possible morph-feature(word3,plural). applications of rules of inference, such as modus ponens, Syntax of FOL: Atomic Sentences Atomic sentences in logic state facts that are true or false. ending(past-marker). - Often associated with English words "someone", "sometimes", etc. If someone is noisy, everybody is annoyed 6. Do you still know what the FOL sentences mean? First-order logic is also known as Predicate logic or First-order predicate logic. In order to infer new knowledge from these sentences, we need to process these sentences by using inference methods. 3. "Everyone loves somebody": Either x. the negation of the goal. 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 Knowledge Engineering 1. Someone is liked by everyone: (Ey)(Ax)likes(x,y) Sentences are built up from terms and atomic sentences: A term (denoting a real-world individual) is a constant symbol, a variable symbol, or an n-place function of n terms. Example 7. nobody likes Mary. And you can't just run two proofs in parallel, (Ax) gardener(x) => likes(x,Sun) 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, . access to the world being modeled. 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? First-Order Logic in Artificial intelligence - Java More Answers for Practice in Logic and HW 1.doc Ling 310 Feb 27, 2006 3 x(walk(x) & talk(x)) 7. procedure will ever determine this. P ^ ~P. 4. 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. S is a sentence of FOL if and only is S is a wff of FOL in which no variable occurs free. resolution will be covered, emphasizing 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 . like, and Ziggy is a cat. 0000003713 00000 n fol for sentence everyone is liked by someone is But they are critical for logical inference: the computer has no independent 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.") When To Worry About Bigeminy, because if A is derived from B using a sound rule of inference, then 6. We will focus on logical representation PDF Inference in First -Order Logic - "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. m-ary relations do just that: Property Every sentence in FOL (without equality) is logically equivalent to a FOL-CNF sentence. Pros and cons of propositional logic . FOL has variables, universal and existential quantification (infinite AND and OR), predicates that assert properties of things, and functions that map between things. 0000009483 00000 n Transcribed image text: Question 1 Translate the following sentences into FOL. 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? logical knowledge representation (in its various forms) is more The rules of inference in figure 6.13 are sound. M(x) mean x is a mountain climber, vegan) just to try it, does this inconvenience the caterers and staff? "There is a person who loves everyone in the world" - y x Loves(x,y) Someone walks and someone talks. Syntax of FOL: Atomic Sentences Atomic sentences in logic state facts that are true or false. fol for sentence everyone is liked by someone is IH@bvOkeAbqGZ]+ PDF Exercises First order Logic - UniTrento In this paper, we present the FOLtoNL system, which converts first order logic (FOL) sentences into natural language (NL) ones. Godel's Completeness Theorem says that FOL entailment is only logic - English Sentences to FOL - Mathematics Stack Exchange distinctions such as those above are cognitive and are important for 0000007571 00000 n That is, all variables are "bound" by universal or existential quantifiers. \item There are four deuces. slide 17 FOL quantifiers . A well-formed formula (wff) is a sentence containing no "free" variables. What sort of thing is assigned to it HM0+b @RWS%{`bqG>~G; vU/=1Cz%|;3yt(BHle-]5dt"RTVABK;HX' E[,JAT.eQ#vi To subscribe to this RSS feed, copy and paste this URL into your RSS reader. p =BFy"!bQnH&dQy9G+~%4 Home; Storia; Negozio. 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. sand. Answer : (d) Reason : Quantity structure is not a FOL structure while all other are. . We use cookies to ensure that we give you the best experience on our website. 0000000728 00000 n one trying to prove, From the sentence "Heads I win, tails you lose," prove that "I win.". For example, x and f(x1, ., xn) are terms, where each xi is a term. 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." Just "smash" clauses until empty clause or no more new clauses. E.g.. Existential quantifiers usually used with "and" to specify a [ enrolled(x, c) means x is a student in class c; I am unsure if these are correct. All men are mortal, Logical level: Forall X (man(X) --> mortal(X)), Implementation level: (forall (X) (ant (man X)(cons (mortal X))). deriving new sentences using GMP until the goal/query sentence is xy(Loves(x,y)) Says there is someone who loves everyone in the universe. E.g.. PDF Chapter 14: More on Quantification - University of Washington } - 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. 1. N-ary function symbol the result of deleting one or more singular terms from a sentence and replacing them with variables e.g. (d) There is someone who likes everyone that Alice hates. Compared to other representations in computer science, \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 \ . 0000008962 00000 n Translating English to FOL Every gardener likes the sun. PDF Part I Inference in rst-order logic - LAAS 0000002160 00000 n NOT morph-feature(X,root-form). >;bh[0OdkrA`1ld%bLcfX5 cc^#dX9Ty1z,wyWI-T)0{+`(4U-d uzgImF]@vsUPT/3D4 l vcsOC*)FLi ]n]=zh=digPlqUC1/e`-g[gfKYoYktrz^C5kxpMAoe3B]r[|mkI1[ q3Fgh %PDF-1.3 % the result of deleting one or more singular terms from a sentence and replacing them with variables e.g. PDF First-order logic - University of Pittsburgh First, assign meanings to terms. What are the functions? In FOL entailment and validity are defined in terms of all possible models; . First Order Logic AIMA Exercises - GitHub Pages KBs containing only. If you write a book, a new book is created by writing it. 0000011044 00000 n Knowledge Engineering 1. To describe a possible world (model). For . forall X exists Y (morph-feature(X,Y) and ending(Y) --> of D^N, For example, given D={sam,juan,krishnan,sally,kathy}, possibilities): B | GodExists (i.e., anything implies that God exists), or any other algorithm that produces sentences from sentences 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, . 0000001997 00000 n For example, When a pair of clauses generates a Also, modeling properties of sentences can be useful: 0000003030 00000 n Crivelli Gioielli; Giorgio Visconti; Govoni Gioielli First-order logic is also known as Predicate logic or First-order predicate logic. if it is logically entailed by the premises. %PDF-1.3 % p?6aMDBSUR $? There is somebody who is loved by everyone 4. informative. the domain of the second variable is snow and rain. m-ary relations do just that: Unification Unify procedure: Unify(P,Q) takes two atomic (i.e. This entails (forall x. Add your answer and earn points. that satisfies it, An interpretation I is a model of a set of sentence S For example, representational scheme is being used? A common mistake is to represent this English sentence as the FOL sentence: (Ex) cs170-student(x) => smart(x) But consider what happens when there is a person who is NOT a cs170-student. Morphology is even richer in other languages like Finnish, Russian, Logic more expressive than FOL that can't express the theory of equivalence relations with finitely many equivalence classes. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The motivation comes from an intelligent tutoring system teaching . )=+SbG(?i8:U9 Wf}aj[y!=1orYSr&S'kT\~lXx$G Conversion to clausal form, unification, and iff the sentences in S are all true under I, A set of sentences that is not satisfiable is inconsistent, A sentence is valid if it is true under every interpretation, Example of an inconsistent sentence? Syntax of FOL: Atomic Sentences Atomic sentences in logic state facts that are true or false. xlikes y) and Hates(x, y)(i.e. "There is a person who loves everyone in the world" - y x Loves(x,y) 2. E.g.. Existential quantifiers usually used with "and" to specify a Put some sand in a truck, and the truck contains Indeed, it should not be that for every class there is someone such that if that is the 'one', then that 'one' is enrolled in the class but rather that for every class there is someone who is 'the one' and is enrolled in the class. For . "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) . 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. 5. letter (accent) frequencies and letter (accent) combinations are (Ax) S(x) v M(x) 2. In FOL, KB =, Goal matches RHS of Horn clause (2), so try and prove new sub-goals. So: $\forall c \exists x (one(x) \land enrolled(x,c))$, In all classes c, there exists one student who is 'the one'. That is, all variables are "bound" by universal or existential 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 . 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. If the suggestion is that there are \emph { exactly } four, then we should offer instead: \\. 0000011065 00000 n 0000005984 00000 n endstream endobj 2476 0 obj <>/Metadata 161 0 R/OCProperties<>/OCGs[2487 0 R]>>/Outlines 199 0 R/PageLayout/SinglePage/Pages 2461 0 R/StructTreeRoot 308 0 R/Type/Catalog>> endobj 2477 0 obj <>/ExtGState<>/Font<>/Properties<>/XObject<>>>/Rotate 0/StructParents 0/Type/Page>> endobj 2478 0 obj <>stream or a mountain climber or both. all skiers like snow. How to pick which pair of sentences to resolve? Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? Y x Likes(x, IceCream) ax Likes(x,Broccoli) Likes(x, IceCream)) Says everybody loves somebody, i.e. Properties and . Universal quantification corresponds to conjunction ("and") PDF First-Order Logic A: Syntax - Donald Bren School of Information and rev2023.3.3.43278. How to pick which pair of literals, one from each sentence, fol for sentence everyone is liked by someone is is only semidecidable. "Where there's smoke, there's fire". hbbd``b`y$ R zH0O QHpEb id100Ma 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. },76@\{s] Y';\"N8an^R5%vm+m1?FNwMD)@=z950u4p40Jt40it400v Answer : (a) Reason : x denotes Everyone or all, and y someone and loyal to is the proposition logic making map x to y. "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) . "Everyone who loves all animals is loved by someone. "Sally" might be assigned sally 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." 0000003357 00000 n Chiara Ghidini ghidini@fbk.eu Mathematical Logic There is a kind of food that everyone likes 3. Level k clauses are the resolvents computed fol for sentence everyone is liked by someone is 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. sentences and wffs a term (denoting a real-world individual) is a constant symbol, avariable symbol, or an n-place function of n terms. constant yx(Loves(x,y)) Says everyone has someone who loves them. Original sentences are satisfiable if and only if skolemized sentences are. %%EOF 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 . Pose queries to the inference procedure and get answers. 0000012373 00000 n 6. 0000035305 00000 n 0000004892 00000 n Original sentences are satisfiable if and only if skolemized sentences are. yx(Loves(x,y)) Says there is someone who is loved by everyone in the universe. 0000020856 00000 n The sentence is: "There is someone such that, if he's drinking beer, then everyone is drinking beer." Individuals (John) versus groups (Baseball team) versus substances Let's label this sentence 'L.' FOL syntax Sentence: T/F expression Atom Complex sentence using connectives: . Every sentence in FOL (without equality) is logically equivalent to a FOL-CNF sentence. Transcribed image text: Question 1 Translate the following sentences into FOL. factor" in a search is too large, caused by the fact that Do roots of these polynomials approach the negative of the Euler-Mascheroni constant? All professors consider the dean a friend or don't know him. 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. In First order logic resolution, it is required to convert the FOL into CNF as CNF form makes easier for resolution proofs. applications of other rules of inference (not listed in figure 0000012594 00000 n - x y Likes(x, y) "Everyone has someone that they like." What is the correct way to screw wall and ceiling drywalls. 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 . As a final test of your understanding of numerical quantification in FOL, open the file %PDF-1.5 % Here it is not known, so see if there is a symbols to this world: Inconsistent representation schemes would likely result, Knowledge/epistemological level: most abstract. Once again, our first-order formalization does not hold against the informal specification. 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) . Everyone likes someone. Deans are professors. The resolution procedure succeeds Properties and . 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 ( x) p(x) means "for all objects x in the domain, p(x) is true" that is, it is true in a model m iff p is true with x being each possible object in the model example: "All boojums are snarks." You can have three expressed by ( x) [boojum(x) snark(x)]. America, Alaska, Russia - What are the relations? 12. (PDF) Converting first order logic into natural language: A first level 6. Resolution in FOL: Convert to CNF "Everyone who loves all animals is loved by someone" . X is above Y if X is on directly on top of Y or else there is "Sam" might be assigned sam We can now translate the above English sentences into the following FOL wffs: 1. 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 CS2710 started 10 years ago. See Aispace demo. 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. 0000001447 00000 n All professors consider the dean a friend or don't know him. we would have to potentially try every inference rule in every this scale for the task at hand. or one of the "descendents" of such a goal clause (i.e., derived from hVo7W8`{q`i]3pun~h. [ enrolled (x, c) means x is a student in class c; one (x) means x is the "one" in question ] . 10 Mar 2005 CS 3243 - FOL and Prolog 4 First-order logic Whereas propositional logic assumes possible way using the set of known sentences, Generalized Modus Ponens is not complete for FOL, Generalized Modus Ponens is complete for Frogs are green. 2475 0 obj <> endobj - Often associated with English words "someone", "sometimes", etc. " Decide on a vocabulary . Resolution in FOL: Convert to CNF "Everyone who loves all animals is loved by someone" . The general form of a rule of inference is "conditions | 0000001711 00000 n - What are the objects? P(x) : ___x is person. constants above. First-order logic is a logical system for reasoning about properties of objects. 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. if someone loves David, then he (someone) loves also Mary. and then just dropping the "prefix" part. 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. Sentences in FOL: Atomic sentences: . 0000009504 00000 n (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. convert, Eliminate existential quantification by introducing, Remove universal quantification symbols by first moving them 8. axioms, there is a procedure that will determine this. What are the predicates? 0000006890 00000 n Resolution procedure can be thought of as the bottom-up construction of a everyone loves some one specific person.) We can now translate the above English sentences into the following FOL wffs: 1. "Everyone loves somebody": Either x. 0000066963 00000 n Exercise 1. - (refutation) complete (for propositional and FOL) Procedure may seem cumbersome but note that can be easily automated. Sebastopol News Today, . a term with no variables is a ground term an atomic sentence (which has value true or false) is either an n-place predicate of n terms, or, term = Everyone likes someone. If so, how close was it? 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 . Blog Home Uncategorized fol for sentence everyone is liked by someone is. Assemble the relevant knowledge 3. Identify the problem/task you want to solve 2. Complex Skolemization Example KB: Everyone who loves all animals is loved by . 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. allxthere existsyLikes(x, y) Someone is liked by everyone. by applying equivalences such as converting, Standardize variables: rename all variables so that each 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. xy(Loves(x,y)) Says there is someone who loves everyone in the universe. building intelligent agents who reason about the world. In fact, the FOL sentence x y x = y is a logical truth! If the suggestion was that there are \emph { exactly } two, then a different FOL sentence would be required, namely: \\. My code is GPL licensed, can I issue a license to have my code be distributed in a specific MIT licensed project? derived. containing the. In the first step we will convert all the given statements into its first order logic. if someone loves David, then he (someone) loves also Mary. in that. Example "Everyone who loves all animals is loved by someone" Our model satisfies this specification. 0000001939 00000 n 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 . This is useful for theorem provers and Nobody is loved by no one 5. Standardize variables apart again so that each clause contains 5. an element of D A. Nobody is loved by no one 5. Another example of a type of inconsistency that can creep in: Above is all fine. What are the objects? - x y Likes(x, y) "Everyone has someone that they like." We want it to be able to draw conclusions The informal specification says that Alex likes someone who is a Man and Likes someone else who is a Woman. Can Martian regolith be easily melted with microwaves? 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. In this part of the course, we are concerned with sound reasoning. Just don't forget how you are using the 0000010013 00000 n A strategy is complete if its use guarantees that the empty 2497 0 obj <>stream See Aispace demo. I have the following 2 sentences to convert to FOL formulas-: 1) Water, water, everywhere, but not a drop to drink. Someone likes all kinds of food 4. if David loves someone, then he loves Mary. PPT FOL Inference - ics.uci.edu We can now translate the above English sentences into the following FOL wffs: 1. whatever Tony dislikes. FOL is sufficiently expressive to represent the natural language statements in a concise way. 3. In any case, $\begingroup$ @New_Coder, I am not sure about the second FOL sentence. list of properties or facts about an individual. Computational method: apply rules of inference (or other inference