Logic: New Applications
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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 02 May 2016 23:16:55 GMTMon, 02 May 2016 23:16:55 GMTNew applications in the Logic categoryhttp://www.mapleprimes.com/images/mapleapps.gifLogic: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=145
Fuzzy Sets in Examples
http://www.maplesoft.com/applications/view.aspx?SID=141714&ref=Feed
<p>This worksheet has been created first as a practical part of short course on the pattern recognition theory for my students. It had intended to their introduce, including visually impressions, with fuzzy sets and basic rules of simple operations with them. MAPLE tools were extremely comfortable for such a task and this experience may be useful for community colleagues.</p><img src="/view.aspx?si=141714/fuzzy-sets.jpg" alt="Fuzzy Sets in Examples" align="left"/><p>This worksheet has been created first as a practical part of short course on the pattern recognition theory for my students. It had intended to their introduce, including visually impressions, with fuzzy sets and basic rules of simple operations with them. MAPLE tools were extremely comfortable for such a task and this experience may be useful for community colleagues.</p>141714Sat, 22 Dec 2012 05:00:00 ZProf. Gennady P. ChuikoProf. Gennady P. ChuikoMathematical Logic. Guidelines. Maple vs. MS Words.
http://www.maplesoft.com/applications/view.aspx?SID=102213&ref=Feed
<p>Maple vs. MS Words. Example<br />It is interesting to someone interested in it?<br />For me it is obvious that the best books and teaching materials of classical mathematics must be formatted in mathematical packages.</p><img src="/view.aspx?si=102213/mrs.jpg" alt="Mathematical Logic. Guidelines. Maple vs. MS Words." align="left"/><p>Maple vs. MS Words. Example<br />It is interesting to someone interested in it?<br />For me it is obvious that the best books and teaching materials of classical mathematics must be formatted in mathematical packages.</p>102213Fri, 04 Mar 2011 05:00:00 ZDonetsk National UniversityDonetsk National UniversityFuzzySets
http://www.maplesoft.com/applications/view.aspx?SID=96899&ref=Feed
<p>FuzzySets for Maple™ is an easy-to-use toolbox for Maple which allows professionals, researchers, and students to learn about, experiment with, and model systems through fuzzy logic and fuzzy sets in the Maple worksheet environment. It transforms Maple into a system which works with fuzzy values and fuzzy sets as seamlessly as the basic system deals with classical logic and sets. The functionality includes most principal areas of fuzzy logic and fuzzy sets, including fuzzy control theory.</p><img src="/view.aspx?si=96899/FuzzySets_logosm.gif" alt="FuzzySets" align="left"/><p>FuzzySets for Maple™ is an easy-to-use toolbox for Maple which allows professionals, researchers, and students to learn about, experiment with, and model systems through fuzzy logic and fuzzy sets in the Maple worksheet environment. It transforms Maple into a system which works with fuzzy values and fuzzy sets as seamlessly as the basic system deals with classical logic and sets. The functionality includes most principal areas of fuzzy logic and fuzzy sets, including fuzzy control theory.</p>96899Wed, 15 Sep 2010 04:00:00 ZDouglas HarderDouglas HarderFinding Minimal Sum for Boolean Expression
http://www.maplesoft.com/applications/view.aspx?SID=5086&ref=Feed
Worksheet which provides methods for minimizing boolean expressions. Example usage is provided.<img src="/view.aspx?si=5086//applications/images/app_image_blank_lg.jpg" alt="Finding Minimal Sum for Boolean Expression" align="left"/>Worksheet which provides methods for minimizing boolean expressions. Example usage is provided.5086Wed, 11 Jul 2007 00:00:00 ZJay PedersenJay PedersenPrime Implicants of Boolean Expression by Concensus method
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Determines prime implicants of boolean expressions using the Consensus method. This is used in simplification of boolean expressions.<img src="/view.aspx?si=4970//applications/images/app_image_blank_lg.jpg" alt="Prime Implicants of Boolean Expression by Concensus method" align="left"/>Determines prime implicants of boolean expressions using the Consensus method. This is used in simplification of boolean expressions.4970Tue, 29 May 2007 00:00:00 ZJay PedersenJay PedersenIntroduction to Fuzzy Sets on a Real Domain
http://www.maplesoft.com/applications/view.aspx?SID=1410&ref=Feed
The RealDomain subpackage of FuzzySets allows the user to construct and work with fuzzy subsets of the real line.
The membership function of a fuzzy subset of the real line is represented by a piecewise function with a range of [0, 1].
The RealDomain subpackage includes a number of constructors of fuzzy subsets of R which simplify the construction of fuzzy sets and set operators and routines for working with fuzzy subsets of R .<img src="/view.aspx?si=1410/FuzzySets_logo.gif" alt="Introduction to Fuzzy Sets on a Real Domain" align="left"/>The RealDomain subpackage of FuzzySets allows the user to construct and work with fuzzy subsets of the real line.
The membership function of a fuzzy subset of the real line is represented by a piecewise function with a range of [0, 1].
The RealDomain subpackage includes a number of constructors of fuzzy subsets of R which simplify the construction of fuzzy sets and set operators and routines for working with fuzzy subsets of R .1410Mon, 01 Nov 2004 00:00:00 ZDouglas HarderDouglas HarderIntroduction to Fuzzy Controllers
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This worksheet uses FuzzySets for Maple to demonstrate several examples solving fuzzy logic problems in Maple.<img src="/view.aspx?si=1398/FuzzySets_logo.gif" alt="Introduction to Fuzzy Controllers" align="left"/>This worksheet uses FuzzySets for Maple to demonstrate several examples solving fuzzy logic problems in Maple.1398Mon, 01 Nov 2004 00:00:00 ZDouglas HarderDouglas HarderMathematical Introduction to Fuzzy Logic, Fuzzy Sets, and Fuzzy Controls
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Classical logic is based on binary logic with two values of truth. In Maple, these two values are true and false .
Fuzzy logic is a multivalued logic with truth represented by a value on the closed interval [0, 1], where 0 is equated with the classical false value and 1 is equated with the classical true value. Values in (0, 1) indicate varying degrees of truth.
For example, the question Is that person over 180 cm feet tall? has only two answers, yes or no .
On the other hand, the question Is that person tall? has many answers. Someone over 190 cm is almost universally considered to be tall. Someone who is 180 cm may be considered to be sort of tall , while someone who is under 160 cm is not usually considered to be tall.<img src="/view.aspx?si=1409/FuzzySets_logo.gif" alt="Mathematical Introduction to Fuzzy Logic, Fuzzy Sets, and Fuzzy Controls" align="left"/>Classical logic is based on binary logic with two values of truth. In Maple, these two values are true and false .
Fuzzy logic is a multivalued logic with truth represented by a value on the closed interval [0, 1], where 0 is equated with the classical false value and 1 is equated with the classical true value. Values in (0, 1) indicate varying degrees of truth.
For example, the question Is that person over 180 cm feet tall? has only two answers, yes or no .
On the other hand, the question Is that person tall? has many answers. Someone over 190 cm is almost universally considered to be tall. Someone who is 180 cm may be considered to be sort of tall , while someone who is under 160 cm is not usually considered to be tall.1409Mon, 01 Nov 2004 00:00:00 ZDouglas HarderDouglas HarderEnumerating All Subsets of a Set
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This worksheet enumerates all subsets of a given set and computes the sum of each subset.
Lists are used instead of sets below, because order of the elements in a set is crucial in order to list all subsets without repetition.<img src="/view.aspx?si=4244//applications/images/app_image_blank_lg.jpg" alt="Enumerating All Subsets of a Set " align="left"/>This worksheet enumerates all subsets of a given set and computes the sum of each subset.
Lists are used instead of sets below, because order of the elements in a set is crucial in order to list all subsets without repetition.4244Thu, 21 Mar 2002 14:42:34 ZYufang HaoYufang HaoMastermind maplet
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This maplet simulates the classic board game Mastermind (TM)<img src="/view.aspx?si=4220/appviewer.aspx.jpg" alt="Mastermind maplet" align="left"/>This maplet simulates the classic board game Mastermind (TM)4220Thu, 24 Jan 2002 13:20:24 ZDouglas HarderDouglas HarderLogic and truth tables
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We're going to use Maple to create truth tables for logical expressions. To do this we are going to define some custom built functions. <img src="/view.aspx?si=4095//applications/images/app_image_blank_lg.jpg" alt="Logic and truth tables " align="left"/>We're going to use Maple to create truth tables for logical expressions. To do this we are going to define some custom built functions. 4095Fri, 17 Aug 2001 13:23:51 ZGregory MooreGregory MooreFuzzy controler for reversed pendulum
http://www.maplesoft.com/applications/view.aspx?SID=3928&ref=Feed
Given an initial state for an unstable nonlinear mechanical system of the reversed pendulum, the purpose is to find a sequence of forces to adjust the system to be in a stable state by inference rules of fuzzy logic.<img src="/view.aspx?si=3928//applications/images/app_image_blank_lg.jpg" alt="Fuzzy controler for reversed pendulum " align="left"/>Given an initial state for an unstable nonlinear mechanical system of the reversed pendulum, the purpose is to find a sequence of forces to adjust the system to be in a stable state by inference rules of fuzzy logic.3928Tue, 10 Jul 2001 11:17:25 ZDr. Laczik BálintDr. Laczik BálintSolving constraint satisfaction problems III: Paint by numbers
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We can generalize the technique of interacting copies to write a single procedure to handle a whole class of puzzles. These puzzles are known as Paint-by-Numbers, and also as Nonograms, or O-e-kaki in Japanese. We are given a rectangular grid of pixels. For each row and column, we are told the lengths of the groups of pixels that are black in that row or column. The challenge is to use that information to figure put the exact placement of the pixels.<img src="/view.aspx?si=3510/paint.gif" alt="Solving constraint satisfaction problems III: Paint by numbers" align="left"/>We can generalize the technique of interacting copies to write a single procedure to handle a whole class of puzzles. These puzzles are known as Paint-by-Numbers, and also as Nonograms, or O-e-kaki in Japanese. We are given a rectangular grid of pixels. For each row and column, we are told the lengths of the groups of pixels that are black in that row or column. The challenge is to use that information to figure put the exact placement of the pixels.3510Mon, 18 Jun 2001 00:00:00 ZCarl DeVoreCarl DeVoreSolving constraint satisfaction problems I: Logic problems
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This is a program for solving or partially solving a class of Constraint Satisfaction Problems (CSPs). Specifically, this program works on CSPs that can be stated in terms of finding an equivalence relation on a finite set, given that the user can specify a partition of the set into Systems of Distinct Representatives (SDRs) of the equivalence classes. In the examples that follow, we will see that many CSPs that do not at first appear to be in this form can be readily put into this form. In particular, many problems that appear in puzzle magazines as "Logic Problems" can be stated in this form.<img src="/view.aspx?si=3508//applications/images/app_image_blank_lg.jpg" alt="Solving constraint satisfaction problems I: Logic problems" align="left"/>This is a program for solving or partially solving a class of Constraint Satisfaction Problems (CSPs). Specifically, this program works on CSPs that can be stated in terms of finding an equivalence relation on a finite set, given that the user can specify a partition of the set into Systems of Distinct Representatives (SDRs) of the equivalence classes. In the examples that follow, we will see that many CSPs that do not at first appear to be in this form can be readily put into this form. In particular, many problems that appear in puzzle magazines as "Logic Problems" can be stated in this form.3508Mon, 18 Jun 2001 00:00:00 ZCarl DeVoreCarl DeVorePascal's triangle and its relationship to the Fibonacci sequence
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An interesting property of Pascal's triangle is that its diagonals sum to the Fibonacci sequence. This application uses Maple to generate a proof of this property.<img src="/view.aspx?si=3617//applications/images/app_image_blank_lg.jpg" alt="Pascal's triangle and its relationship to the Fibonacci sequence" align="left"/>An interesting property of Pascal's triangle is that its diagonals sum to the Fibonacci sequence. This application uses Maple to generate a proof of this property.3617Mon, 18 Jun 2001 00:00:00 ZMaplesoftMaplesoftSolving constraint satisfaction problems II: More difficult logic problems
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This application uses a Maple package called LP that solves word logic problems such as, identify the people around a table given a list of clues about their relationships.<img src="/view.aspx?si=3509//applications/images/app_image_blank_lg.jpg" alt="Solving constraint satisfaction problems II: More difficult logic problems" align="left"/>This application uses a Maple package called LP that solves word logic problems such as, identify the people around a table given a list of clues about their relationships.3509Mon, 18 Jun 2001 00:00:00 ZCarl DeVoreCarl DeVoreSolving constraint satisfaction problems IV: Combinatorial square coloring
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Beverly has a pigeonhole shelf with 36 square holes in a 6x6 grid. She keeps a minature fork, knife, or spoon in each hole such that in each row and column there are exactly two of each. The goal is to deduce the placement of each.<img src="/view.aspx?si=3511/pigeon.gif" alt="Solving constraint satisfaction problems IV: Combinatorial square coloring" align="left"/>Beverly has a pigeonhole shelf with 36 square holes in a 6x6 grid. She keeps a minature fork, knife, or spoon in each hole such that in each row and column there are exactly two of each. The goal is to deduce the placement of each.3511Mon, 18 Jun 2001 00:00:00 ZCarl DeVoreCarl DeVore