c. Mary and Sue have the same paternal grandfather. Birds except penguins can fly 2. 4. It tells the truth value of the statement at . Every child is younger than its mother. Provide a resolution proof that tweety can fly. Predicate Calculus. It is an extension to propositional logic. Saying as: 'It is not the case that all things which are birds can fly.' we could code this alternatively as: x (B(x) F(x)) Saying as: 'There is some x which is a bird and cannot fly.' To get a feel for what kind of reasoning must predicate logic be able to support, let us consider the following argument: "No books are . Solution: A predicate that can be true or false, depending on the situation/state [2 points] What does the denition of an operator (e.g. Use predicate logic to state the following sentences. Let us assume the following predicates bird(x): "x is bird" fly(x): "x can fly". EXAMPLES 1.4.1 #4 and #5 illustrate the following fundamental fact: Although the statements "Some are" and "Some aren't" sound similar, they do not 1. Predicate Logic Predicate logic have the following features to express propositions: Variables: x;y;z, etc. The first type of defaults is readily formalized but the other, as some researchers have noticed, is difficult to deal with. "Not all integers are . All the beings that have wings can fly. Solution: Preconditions (a set of uents that have to be true for the ope rator to be A second-order logic can also quantify over formulas of the first order, and a third-order logic can quantify over formulas of the second order. Represent statement into predicate calculus forms : "Not all birds can fly". (c) move(x,y,z) (move x from y to z) consist of? 1. Cumbersome control information. First-order logic is also known as Predicate logic or First-order predicate logic. First-order logic is another way of knowledge representation in artificial intelligence. E is not grounded in the sense above: If we take E as a belief set (relevant for the . x bird (x) fly (x). Predicate Logic The propositional logic is not powerful enough to represent all types of assertions that are used in computer science and mathematics, or to express certain types of relationship between propositions such as equivalence. Modularity sacrificed. The predicate is a sentence containing a specific number of variables, and becomes a statement when specific values are substituted in place of the predicate variables. x bird(x) fly(x). Every child is younger than its mother. Only two students took both French and Greek in spring 2010 4. Organize facts about birds as listing of facts (robins fly) (gannets fly) (western grebes fly) (crows fly) (penguins don't fly) (ostriches don't fly) (common loons fly) (fulmars fly) (arctic loons fly) Approximately 8,600 species of birds in world -Big list -Small in comparison to world population of ~100 billion birds! Penguins can only survive at places with cold temperature. Type I - Particular Affirmative proposition cEvery bird can y. Predicate Logic Outline Predicate logic Predicate logic as formal language Quantifiers Parse Trees Replacing free variables Scope of quantifiers Mixing quantifiers Order of quantifiers Propositional logic It deals with sentence components like not, and, or and if then. (D(), L(x)) (ii) Every bird can fly. Almost all species of birds can fly. NB: Evaluating an argument often calls for subjecting a critical. E.g., "For every x, x > 0" is true if x is a positive integer. Consider the statement, " is greater than 3. (Jan-2012-win-old)[3] A crow is a bird. (Jan-2015-win-new)[3], (June-2017-sum-new)[3] Q(x): x is a rational number. Be sure to define all predicates, constants, and variables. Later we might discover that Fred is an emu. WUCT121 Logic 61 Definition: Truth Set If P(x) is a predicate and x has domain D, the truth set of P(x) is the set of all elements of D that make P(x) true.The truth set is denoted )}{x D : P(x and is read "the set of all x in D such that P(x)." Examples: Let P(x) be the predicate "x2 >x" with x i.e. Consistency not all deductions may be correct. 1. But logical aspects of natural and artificial languages are much . It says that, X is a bird if X can fly (or, if X can fly, then X must be a bird ). (all birds can't fly) Definition: Universal Conditional Quantifier: A universal conditional statement is in the form: x if P(x) then Q(x) Example: x R if x! Subject Predicate Sentence 3.8: Only birds fly. 4. 5 Predicates x > 3 value of propositional function P at x P(x) denotes predicate 1. 3. Instead, they walk. . Predicate Logic More powerful Express a wide range of statements in mathematics and computer science. Aristotle contemplating a bust of Homer by Rembrandt van Rijn. \Not all birds can y.":(8xBird(x) )Fly(x)) ; which is the same as Every bird can fly. The predicate in this question is "respect(x, y)," where x=man, and y= parent. The predicate can be considered as a function. Not in general valid *7. (BI), F(x)) (iii) There is no student in this class who speaks both Greek and Italian. NB: Evaluating an argument often calls for subjecting a critical CS 561, Session 12-13 17 Semantics Referring to individuals Jackie son-of(Jackie), Sam Our convention will be to capitalize at least the rst letter of constant symbols and use lowercase for variables. Not all birds can y. Propositional logic cannot capture the detailed semantics of these sentences. Chapter 2 Predicate Logic Discrete Mathematics II BKTPHCM. Predicate Logic Anvesh Komuravelli 1 Why Predicate Logic? First-order logic is another way of knowledge representation in artificial intelligence. :o I want to formulate the following statements into formulas of predicate logic. 2, then x2! | Propositional Logic-Study of declarative sentences, statements about the world which can be given a truth value-Dealt very well with sentence components like: not, and, or, if, , then-Limitations: Cannot deal with modifiers like there exists, all, among, only. (a) Translate the following sentences into the language of predicate logic, by choosing the indicated symbols for predicates. domain the set of real numbers . (the subject of a sentence), can be substituted with an element from a . b. Domain : !X!! Predicates: The predicate in this question is "fly(bird)." Because all birds are able to fly, it will be portrayed as follows. b. John likes everyone, that is older than $22$ years old and that doesn't like those who are younger than $22$. Predicate Logic Outline Predicate logic Predicate logic as formal language Quantifiers Parse Trees Replacing free variables Scope of quantifiers Mixing quantifiers Order of quantifiers Propositional logic It deals with sentence components like not, and, or and if then. a. Prof.) Ans:- P(x): x is an integer. Ans:- P(x): x is a bird. Valid 9. If an object is not to the right of all the squares, then it is not blue. FMSE lecture 06. The predicate in this question is " respect (x, y)," where x=man, and y= parent. (i) Some old dogs can learn new tricks. Represent statement into predicate calculus forms : "Not all birds can fly". This is equivalent to demonstrating that A is not a subset of B. Consider the following statements. Rule 2 Eagles are carnivorous birds that can fly. Recall that inferences with modus ponens for KB in the Horn normal form are both sound and For example , Ex.1: All birds fly. Some birds can't fly. Conclusion: . Some dogs are not collies. Ti liu lin quan. Although we have not yet de ned the semantics of rst-order logic lets consider some example formulas along with their intuitive natural language interpretations. A sentence like "birds can fly" reads "for all x, if x is a bird, then x can fly." Equivalently this reads, "either x isn't a bird, or x can fly." "Birds cannot fly" reads "there doesn't exist some x such that x is a bird and x can fly." Let us assume the following predicates bird(x): "x is bird" fly(x): "x can fly". James has a friend named Sean, a penguin. | Propositional Logic-Study of declarative sentences, statements about the world which can be given a truth value-Dealt very well with sentence components like: not, and, or, if, , then-Limitations: Cannot deal with modifiers like there exists, all, among, only. 1. Every student is younger than some instructor. x Predicates: 2 : T ;, 3 : T ;, etc. (1) Symbolize the following argument using predicate logic, (2) Establish its validity by a proof in predicate logic, and (3) "Evaluate" the argument as well. Predicate logic is an extension of Propositional logic. John's father loves Rule 4 Ostriches are granivorous birds that can fly. 2. All penguins are birds. Given that a P is usually a Q, and given P(a) is true, it is reasonable to conclude that Q(a) is true unless there is good reason not to Finding that "good reason" is the whole purpose of the all the default reasoning different methods Some boys play cricket. 4 Predicates x > 3 Variable: subject of the statement Predicate: property that the subject of the statement can have. Syntax of Predicate Logic Terms: a reference to an object variables, constants, functional expressions (can be arguments to predicates) . A predicate with variables (called an atomic formula) can be made a proposition by applying one of the following two operations to each of its variables: assign a value to the variable quantify the variable using a quantifier Let us use predicate GreatThan(x, 1) to represent x >1. universal quantifier for every object x in the universe, x > Every man respects his parent. Bow-Yaw Wang (Academia Sinica) Predicate Logic October 13, 202116/156. using predicates penguin (), fly (), and bird () . We cannot say it in propositional logic. Modularity sacrificed. . So, if there is a single pair of odd numbers whose sum is not even, the implication would be false, which is what we want. . - 3 birds can't fly. The method for writing a xy is not similar to yx. Every man respects his parent. Even adding only the induction axiom for the natural numbers makes the logic incomplete. . In this question, the predicate is "respect(x, y)," where x=man, and y= parent. Valid 8. Rule 3 Penguins are carnivorous birds that cannot fly. F(x) = x can fly . All noncats are things that cannot run at more than 50 miles an hour. "A except B" in English normally implies that there are at least some instances of the exception. First, the higher the frequency, the stronger the logic can be. Nor can we show the following logical equivalences: "Not all birds fly" is equivalent to "Some birds don't fly". L What are the \meaning" of these sentences? This means that a statement of the form "All A are B" is true even in the odd case where category A has no members. Consider the premises: P1: Nothing intelligible puzzles me. Every man respects his parent. 1.4 Predicate Logic. Do \not all birds can y" and \some bird cannot y" have the same meaning? Semantically equivalent formulas. The predicate is "fly(bird)." And since there are all birds . Sentences - either TRUE or false but not both are called propositions. In general, a statement involving n variables can be denoted by . FOL is sufficiently expressive to represent the natural language statements in a concise way. Some natural problem is not monotonic non-monotonic logic. "All birds can fly" is trickier: we want to say something about just birds, but is going to give us a statement about all objects. All birds have wings. x bird(x . But we can easily turn it into a plural noun. And since there are all birds who fly so it will be represented as follows. Some Examples of FOL using quantifier: All birds fly.

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