PPT-Quantifiers, Arithmetic and Fixed-points

Quantifier Elimination Procedures in Z3 Support for Nonlinear arithmetic Fixedpoints features and a preview Quantifier Elimination O ption ELIMQUANTIFIERStrue LRA Linear real arithmetic. brPage 1br 91 points 91 points 91 points 91 points 91 points 91 points brPage 1br 92 points 92 points 92 points 92 points 92 points 92 points Nikolaj . Bjørner. Microsoft Research. Bit-Precise Constraints: . Applications and . Decision Procedures. Tutorial Contents. Bit-vector decision procedures by categories. Bit-wise operations . Vector Segments. Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . Propositional Logic Not Enough. Given the statements: . “All men are mortal.”. “Socrates is a man.”. It follows that “Socrates is mortal.”. This can’t be represented in propositional logic. . An introduction…………. Arithmetic Sequences. ADD. To get next term. Geometric Sequences. MULTIPLY. To get next term. Arithmetic Series. Sum of Terms. Geometric Series. Sum of Terms. Find the next four terms of –9, -2, 5, …. Goals. : . Explain . how to work with nested . quantifiers. S. how that . the order . of quantification . matters. . Work . with . logical . expressions involving multiple . quantifiers.. Copyright © . 4. 3. 2. 1. 0. In addition to level 3.0 and above and beyond what was taught in class,  the student may:. · Make connection with other concepts in math. · Make connection with other content areas.. th. term of an arithmetic sequence, find the partial sum of an arithmetic series, as evidenced by completion . of “I have…who has…”.. 12. 1 Arithmetic Sequences and Series. Arithmetic Sequences. Ben Braun, Joe Rogers. The University of Texas at Austin. November 28, 2012. Why primitive recursive arithmetic?. Primitive recursive arithmetic is consistent.. Many functions over natural numbers are primitive recursive:. Objectives. Identify English sentences that are statements.. Express statements using symbols.. Form the negation of a statement.. Express negations using symbols.. Translate a negation represented by symbols into English.. & Series. Story Time…. When another famous mathematician was in first grade, his teacher asked the class to add up the numbers one through a hundred (1+2+3 etc., all the way up to 100). . Write out the teacher’s request in summation notation, then find the answer (no calculators!) Try to figure out an efficient way!. For example : 5, 10, 15, 20, 25…... In this each term is obtained by adding 5 to the preceding term except first term. The general form of an . Arithmetic . Progression is . a , a +d , a + 2d , a + 3d ………………, a + (n-1)d. Exercise 4. Exercise . Translate . these statements into English, where C(x) is “. x. . is a comedian” and F(x) is “x is funny” and the domain . consists . of all people. . . a)∀. x(C(x)→F(x)) .