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Intermediate - CEMC - University of Waterloo
Intermediate - CEMC - University of Waterloo

Logic Programming, Functional Programming, and Inductive
Logic Programming, Functional Programming, and Inductive

... rules in logic programs. The rules in an inductive definition contain no variables. A schematic rule (like the rule for cousin) abbreviates an infinite set of rules: all ground instances under the Herbrand universe. In the semantics of logic programming, such theory has long been used as a technical ...
Learning Targets - KMHSrm223
Learning Targets - KMHSrm223

Artificial Intelligence - Academic year 2016/2017
Artificial Intelligence - Academic year 2016/2017

... until it finds one, say , whose value is not nil; then the corresponding is evaluated and its value is returned as the value of the whole cond expression ...
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3.2

... The amount of interest from each account is: 0.06x and 0.08y. And since we are concerned with both amounts of interest adding up to $520, the following equation results: 0.06x + 0.08y = 520. 3) Solve the system and answer the problem’s question. The system x + y = 7000 0.06x + 0.08y = 520 Blitzer, I ...
Problem Solving and Search in Artificial Intelligence - DBAI
Problem Solving and Search in Artificial Intelligence - DBAI

...  A feature space F that contains measurable characteristics of the instances generated by a computational feature extraction process applied to P  Set A of all considered algorithms for tackling the problem  The performance space Y represents the mapping of each algorithm to a set of performance ...
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Equations - Adding and Subtracting

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LT 8 Systems of Equations Packet B

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3.2 Lesson

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4. - Humble ISD

... need to first simplify by combining like terms or clearing fractions. Then add or subtract to collect variable terms on one side of the equation. Finally, use properties of equality to isolate the variable. ...
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Cognitive Approach to Creativity Cognitive View of Creativity

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Module 10 lesson 6 Parametric Equations. When modeling the path

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First-Order Logic - Sonoma State University

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How Does Resolution Works in Propositional Calculus and

... very easy and simple and then no need to substitution. When clauses containing variables resolution becomes complicated and then need a proper substitution through the cancellation of complementary literals. So substitution is an important role in resolution. Unification has been used in my work for ...
P(x)
P(x)

... sentences, and subst(Theta, Pi) = subst(Theta, Qi) for i=1,...,N, derive new sentence: subst(Theta, R) – subst(Theta, alpha) denotes the result of applying a set of substitutions defined by Theta to the sentence alpha – A substitution list Theta = {v1/t1, v2/t2, ..., vn/tn} means to replace all occu ...
P(x) - Carnegie Mellon School of Computer Science
P(x) - Carnegie Mellon School of Computer Science

solving Linear equations in One Variable
solving Linear equations in One Variable

... Jamal is building a rectangular deck. The length of the deck will be 1 foot longer than twice the width. The deck will be attached to Jamal’s house on one of its longer sides, and a railing will be attached to the other sides. Jamal calculates that he will need 49 feet of railing. What are the dimen ...
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Unification (computer science)

Unification, in computer science and logic, is an algorithmic process of solving equations between symbolic expressions.Depending on which expressions (also called terms) are allowed to occur in an equation set (also called unification problem), and which expressions are considered equal, several frameworks of unification are distinguished. If higher-order variables, that is, variables representing functions, are allowed in an expression, the process is called higher-order unification, otherwise first-order unification. If a solution is required to make both sides of each equation literally equal, the process is called syntactical unification, otherwise semantical, or equational unification, or E-unification, or unification modulo theory.A solution of a unification problem is denoted as a substitution, that is, a mapping assigning a symbolic value to each variable of the problem's expressions. A unification algorithm should compute for a given problem a complete, and minimal substitution set, that is, a set covering all its solutions, and containing no redundant members. Depending on the framework, a complete and minimal substitution set may have at most one, at most finitely many, or possibly infinitely many members, or may not exist at all. In some frameworks it is generally impossible to decide whether any solution exists. For first-order syntactical unification, Martelli and Montanari gave an algorithm that reports unsolvability or computes a complete and minimal singleton substitution set containing the so-called most general unifier.For example, using x,y,z as variables, the singleton equation set { cons(x,cons(x,nil)) = cons(2,y) } is a syntactic first-order unification problem that has the substitution { x ↦ 2, y ↦ cons(2,nil) } as its only solution.The syntactic first-order unification problem { y = cons(2,y) } has no solution over the set of finite terms; however, it has the single solution { y ↦ cons(2,cons(2,cons(2,...))) } over the set of infinite trees.The semantic first-order unification problem { a⋅x = x⋅a } has each substitution of the form { x ↦ a⋅...⋅a } as a solution in a semigroup, i.e. if (⋅) is considered associative; the same problem, viewed in an abelian group, where (⋅) is considered also commutative, has any substitution at all as a solution.The singleton set { a = y(x) } is a syntactic second-order unification problem, since y is a function variable.One solution is { x ↦ a, y ↦ (identity function) }; another one is { y ↦ (constant function mapping each value to a), x ↦ (any value) }.The first formal investigation of unification can be attributed to John Alan Robinson, who used first-order syntactical unification as a basic building block of his resolution procedure for first-order logic, a great step forward in automated reasoning technology, as it eliminated one source of combinatorial explosion: searching for instantiation of terms. Today, automated reasoning is still the main application area of unification.Syntactical first-order unification is used in logic programming and programming language type system implementation, especially in Hindley–Milner based type inference algorithms.Semantic unification is used in SMT solvers and term rewriting algorithms.Higher-order unification is used in proof assistants, for example Isabelle and Twelf, and restricted forms of higher-order unification (higher-order pattern unification) are used in some programming language implementations, such as lambdaProlog, as higher-order patterns are expressive, yet their associated unification procedure retains theoretical properties closer to first-order unification.
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