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A Partial Taxonomy of Substitutability and Interchangeability
A Partial Taxonomy of Substitutability and Interchangeability

... Basic Interchangeability Concepts ...
Full Dynamic Substitutability by SAT Encoding
Full Dynamic Substitutability by SAT Encoding

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A New Operator for ABox Revision in DL-Lite Sibei Gao Guilin Qi
A New Operator for ABox Revision in DL-Lite Sibei Gao Guilin Qi

PDF
PDF

... the associated queries. It may be more intuitive to think of pre-ordering the set of pairs (query, reply), i.e., the graph of the answer function. This view of the situation would make no essential difference, since these pairs are in canonical bijection with the queries. We emphasize that the timi ...
3.4 – Exponential and Logarithmic Equations
3.4 – Exponential and Logarithmic Equations

ABSTRACT Title of Document: APPLICATION OF ANT COLONY OPTIMIZATION TO THE ROUTING AND
ABSTRACT Title of Document: APPLICATION OF ANT COLONY OPTIMIZATION TO THE ROUTING AND

... and there is no networking problem to solve. However, it should be noted that the network size should be scalable, that transceivers are expensive so that each node may be equipped with only a few of then, and that technological constrains dictate that the number of WDM channels that can be supporte ...
Human-Guided Tabu Search - Computer Science
Human-Guided Tabu Search - Computer Science

... each with nodes, and edges connecting nodes on adjacent levels. The goal is to rearrange nodes within their level to minimize the number of intersections between edges. A screenshot of the Crossing application is shown in Figure 1. The Delivery application is a variation of the Traveling Salesman ...
The Problem of Logical-Form Equivalence
The Problem of Logical-Form Equivalence

Actions and Specificity
Actions and Specificity

... fragile(vase)} by applying (3), (5), (2), and performing the required AC1– unification computations. This demonstrates that actions defined for a certain class are automatically inherited by its subclasses. It also demonstrates that variables such as O , L1 , and L2 may occur within the conditions, ...
Systems of Equations and Inequalities 6A Systems of Linear
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artificial intelligence - MET Engineering College
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... 1.1.4 The state of art What can A1 do today? Autonomous planning and scheduling: A hundred million miles from Earth, NASA's Remote Agent program became the first on-board autonomous planning program to control the scheduling of operations for a spacecraft (Jonsson et al., 2000). Remote Agent generat ...
Applying Gauss elimination from boolean equation systems to
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Chapter 7: Solving Systems of Linear Equations and Inequalities
Chapter 7: Solving Systems of Linear Equations and Inequalities

... POPULATION For Exercises 51–54, use the following information. The U.S. Census Bureau divides the country into four sections. They are the Northeast, the Midwest, the South, and the West. 51. In 1990, the population of the Midwest was about 60 million. During the 1990s, the population of this area i ...
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Foundations of Artificial Intelligence

... Examples: Classification of AI Topics ...
Constraint Programming: In Pursuit of the Holy Grail
Constraint Programming: In Pursuit of the Holy Grail

... As mentioned above, we can see BT as a merge of the generating and testing phases of GT algorithm. The variables are labelled sequentially and as soon as all the variables relevant to a constraint are instantiated, the validity of the constraint is checked. If a partial solution violates any of the ...
Solving Systems of Equations and Inequalities
Solving Systems of Equations and Inequalities

... of 6 feet per second. To be a good sport, Nadia likes to give Peter a head start of 20 feet. How long does Nadia take to catch up with Peter? At what distance from the start does Nadia catch up with Peter? In that example we came up with two equations: Nadia’s equation: d = 6t Peter’s equation: d = ...
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Dedukti
Dedukti

... the realm of formal proofs is today a tower of Babel, just like the realm of theories was, before the design of predicate logic. The reason why these formalisms have not been defined as theories in predicate logic is that predicate logic, as a logical framework, has several limitations, that make it ...
Systems of Linear Equations and Inequalities
Systems of Linear Equations and Inequalities

... system of two linear equations can have one solution, an infinite number of solutions, or no solution. • If a system has at least one solution, it is said to be consistent. The graphs intersect at one point or are the same line. • If a consistent system has exactly one solution, it is said to be ind ...
KRR Lectures — Contents
KRR Lectures — Contents

... many commonsense reasoning problems. While mathematical models exist they are not always well-suited for AI problem domains. We shall look at some ways of representing qualitative spatial information. ...
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preliminary version

Real-Time Search for Autonomous Agents and
Real-Time Search for Autonomous Agents and

... Section 4 considers the case of heuristic search where the goal may change during the course of the search. For example, the goal may be a target that actively avoids the problem solver. A mo¨ ing target search (MTS) algorithm is thus presented to solve this problem. We prove that if the average spe ...
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Connecting a Logical Framework to a First

What is Approximate Reasoning? - CORE Scholar
What is Approximate Reasoning? - CORE Scholar

< 1 2 3 4 5 6 ... 33 >

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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