## Mathematical Aspects of Artificial Intelligence: American Mathematical Society Short Course, January 8-9, 1996, Orlando, FloridaThere exists a history of great expectations and large investments involving artificial intelligence (AI). There are also notable shortfalls and memorable disappointments. One major controversy regarding AI is just how mathematical a field it is or should be. This text includes contributions that examine the connections between AI and mathematics, demonstrating the potential for mathematical applications and exposing some of the more mathematical areas within AI. The goal is to stimulate interest in people who can contribute to the field or use its results. Included in the work by M. Newborn on the famous Deep BLue chess match. He discusses highly mathematical techniques involving graph theory, combinatorics and probability and statistics. G. Shafer offers his development of probability through probability trees with some of the results appearing here for the first time. M. Golumbic treats temporal reasoning with ties to the famous Frame Problem. His contribution involves logic, combinatorics and graph theory and leads to two chapters with logical themes. H. Kirchner explains how ordering techniques in automated reasoning systems make deduction more efficient. Constraint logic programming is discussed by C. Lassez, who shows its intimate ties to linear programming with crucial theorems going back to Fourier. V. Nalwa's work provides a brief tour of computer vision, tying it to mathematics - from combinatorics, probability and geometry to partial differential equations. All authors are gifted expositors and are current contributors to the field. The wide scope of the volume includes research problems, research tools and good motivational material for teaching. |

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### Conteúdo

Reasoning about Time | 19 |

Orderings in Automated Theorem Proving | 55 |

Some Aspects of the Mathematical | 97 |

The Basis of Computer Vision | 139 |

Outsearching Kasparov | 175 |

Mathematical Foundations for Probability and Causality | 207 |

271 | |

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### Termos e frases comuns

algebra allows alw.foretells applications Artificial Intelligence Automated Deduction automated theorem proving Axiom S5 Axioms S8 binary relations Calculus camera catalog causal center of projection chess clade completion Computer Chess Computer Science computer vision constraints critical pairs defined denoted depth-first search diverges edges Editor elimination equational equivalent event space event tree event trellis example exists expected value expert systems Figure finite foretells Fourier's algorithm function graph ground terms happen hash code implicit equalities implies inequalities interval interval graph Lassez Lecture Notes linear programming logic programming martingale mathematical method modulo move multiset Notes in Computer NP-complete obtained optional relations overlaps paramodulation polyhedral set polynomial precedes probability tree problem proof Proposition query reduction ordering requires rewrite rules rewrite system satisfies Axioms scene point score Section sequence situation in F solution solvable Springer-Verlag Statement successor Suppose techniques temporal reasoning theorem proving theory tion transposition table variables well-founded