http://hdl.handle.net/1842/3389 Thu, 13 Jun 2013 03:36:40 GMT 2013-06-13T03:36:40Z http://hdl.handle.net/1842/6676 Title: Analogy and mathematical reasoning : a survey Authors: Miller, C.D.F. Abstract: We survey the literature of Artificial Intelligence, and other related work, pertaining to the modelling of mathematical reasoning and its relationship with the use of analogy. In particular, we discuss the contribution of Lenat's program AM to models of mathematical discovery and concept-formation. We consider the use of similarity measures to structure a knowledge space and their role in concept acquisition. Sat, 01 Jan 1983 00:00:00 GMT http://hdl.handle.net/1842/6676 1983-01-01T00:00:00Z http://hdl.handle.net/1842/6675 Title: Computational model of learning Authors: Radford, Timothy John Abstract: The program described learns to improve its performance in the playing of a game, from experience. The main objectives of the project are that the system should observe the following principles: 1) The program should not rely on any special evaluation functions, which would embody domain-specific information. 2) Initial knowledge of the domain should be minimal, and further knowledge gained should be assimilated in terms of prior knowledge 3) The system of representation employed should as far as possible be independent of the domain, again avoiding the incorporation of domain-specific information. In customary Artificial Intelligence terms, the program is referred to as existing in a domain or environment. The model has a goal within this domain and has available certain actions which it may take in order to achieve its goal. The goal is represented as a Structure. This term will be used throughout to denote a set of objects from the domain, constrained by various domain-pertinent relationships. The actions, goals and objects are the initial known facts of the environment. The program has an innate ability to plan simple sequences of actions to achieve its goals. Inevitably, these plans do not take into account enough of the nature of the domain and prove inadequate. In such events the descriptive abilities of the program are invoked to correct the deficiency, and the program's model of its environment is enriched. Tue, 01 Jan 1980 00:00:00 GMT http://hdl.handle.net/1842/6675 1980-01-01T00:00:00Z http://hdl.handle.net/1842/6674 Title: Studies in the completeness and efficiency of theorem-proving by resolution Authors: Kowalski, Robert Anthony Abstract: Inference systems Τ and search strategies E for T are distinguished from proof procedures β = (T,E) The completeness of procedures is studied by studying separately the completeness of inference systems and of search strategies. Completeness proofs for resolution systems are obtained by the construction of semantic trees. These systems include minimal α-restricted binary resolution, minimal α-restricted M-clash resolution and maximal pseudo-clash resolution. Certain refinements of hyper-resolution systems with equality axioms are shown to be complete and equivalent to refinements of the pararmodulation method for dealing with equality. The completeness and efficiency of search strategies for theorem-proving problems is studied in sufficient generality to include the case of search strategies for path-search problems in graphs. The notion of theorem-proving problem is defined abstractly so as to be dual to that of and" or tree. Special attention is given to resolution problems and to search strategies which generate simpler before more complex proofs. For efficiency, a proof procedure (T,E) requires an efficient search strategy E as well as an inference system T which admits both simple proofs and relatively few redundant and irrelevant derivations. The theory of efficient proof procedures outlined here is applied to proving the increased efficiency of the usual method for deleting tautologies and subsumed clauses. Counter-examples are exhibited for both the completeness and efficiency of alternative methods for deleting subsumed clauses. The efficiency of resolution procedures is improved by replacing the single operation of resolving a clash by the two operations of generating factors of clauses and of resolving a clash of factors. Several factoring methods are investigated for completeness. Of these the m-factoring method is shown to be always more efficient than the Wos-Robinson method. Thu, 01 Jan 1970 00:00:00 GMT http://hdl.handle.net/1842/6674 1970-01-01T00:00:00Z http://hdl.handle.net/1842/6673 Title: Planning how to grasp objects in a cluttered environment Authors: Wingham, Paul Michael Abstract: This thesis deals with the problem of finding trajectories of objects through space which do not result in collisions. Specifically, a method is presented which calculates such trajectories in the case of a robot attempting to grasp a certain body in a,,cluttered environment, i.e. where there are other bodies nearby.' We restrict ourselves to bodies with planar faces, robots with certain physical characteristics, and a specific class of trajectories. We present a method of describing bodies in terms of the shape of their faces. The robot's trajectories are not predetermined, but instead are calculated on the basis of the present configuration of bodies in the robot's world. Once the body to be grasped has been chosen, we examine all nearby objects to determine the region of space which is inaccessible to the robot. This region is projected onto a suitable plane, and making use of algorithms to compute the intersection and union of two-dimensional figures, we are able to find a region of the surface of the body to be grasped which is sufficiently distant from neighbouring objects, assuming such a region exists. This region in turn allows us to calculate a set of feasible robot trajectories for grasping the body. We also suggest a possible approach to computing more general trajectories involving both the robot and a body. Sat, 01 Jan 1977 00:00:00 GMT http://hdl.handle.net/1842/6673 1977-01-01T00:00:00Z