Implementing the ‘Fool's model’ of combinatory logic

This paper studies Fool's models of combinatory logic, and relates them to Hindley's D-completeness problem. A fool's model is a family of sets of formulas, closed under condensed detachment. Alternatively, it is a model ofCL in naive set theory. We examine Resolution; and the P-W problem. A sequel shows T is D-complete; also, its extensions. We close with an implementation FMO of these ideas.     

Choosing reference classes and building provisional models

A well-known problem in default logic is the ability of naive reasoners to explain bothg and ¬g from a set of observations. This problem is treated in at least two different ways within that camp.One approach is examination of the various explanations and choosing among them on the basis of various explanation comparators. A typical comparator is choosing the explanation that depends on the most specific observation, similar to the notion of narrowest reference class.Others examine default extensions of the observations and choose whatever is true in any extension, or what is true in all extensions or what is true in preferred extensions. Default extensions are sometimes thought of as acceptable models of the world that are discarded as more knowledge becomes available.We argue that the notions of specificity and extension lack clear semantics. Furthermore, we show that the problems these ideas were supposed to solve can be handled easily within a probabilistic framework.     

Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval

Domain truncation is the simple strategy of solving problems ony [-, ] by using a large but finite computational interval, [– L, L] Sinceu(y) is not a periodic function, spectral methods have usually employed a basis of Chebyshev polynomials,T _n(y/L). In this note, we show that becauseu(±L) must be very, very small if domain truncation is to succeed, it is always more efficient to apply a Fourier expansion instead. Roughly speaking, it requires about 100 Chebyshev polynomials to achieve the same accuracy as 64 Fourier terms. The Fourier expansion of a rapidly decaying but nonperiodic function on a large interval is also a dramatic illustration of the care that is necessary in applying asymptotic coefficient analysis. The behavior of the Fourier coefficients in the limitn for fixed intervalL isnever relevant or significant in this application.     

A short note on simultaneous splitting

We show that for any alphabet there is a setL ^* such that ifC is any infinite co-infinite context-free language over , thenL splitsC (i.e., each ofL C,L , C, and is infinite).Preparation of this paper was supported in part by the National Science Foundation under Grant No. MCS77-11360.     

Query answering via cooperative data inference

This paper proposes the use of accessible information (data/knowledge) to infer inaccessible data in a distributed database system. Inference rules are extracted from databases by means of knowledge discovery techniques. These rules can derive inaccessible data due to a site failure or network partition in a distributed system. Such query answering requires combining incomplete and partial information from multiple sources. The derived answer may be exact or approximate. Our inference process involves two phases to reason with reconstructed information. One phase involves using local rules to infer inaccessible data. A second phase involves merging information from different sites. We shall call such reasoning processes cooperative data inference. Since the derived answer may be incomplete, new algebraic tools are developed for supporting operations on incomplete information. A weak criterion called toleration is introduced for evaluating the inferred results. The conditions that assure the correctness of combining partial results, known as sound inference paths, are developed. A solution is presented for terminating an iterative reasoning process on derived data from multiple knowledge sources. The proposed approach has been implemented on a cooperative distributed database testbed, CoBase, at UCLA. The experimental results validate the feasibility of this proposed concept and can significantly improve the availability of distributed knowledge base/database systems.List of notation Mapping - --< Logical implication - = Symbolic equality - ==< Inference path - Satisfaction - Toleration - Undefined (does not exist) - Variable-null (may or may not exist) - ^* Subtuple relationship - ^* s-membership - s-containment - Open subtuple - Open s-membership - Open s-containment - _P Open base - P Program - I Interpretation - DIP Data inference program - t Tuples - R Relations - Ø Empty interpretation - Open s-union - Open s-interpretation - Set of mapping from the set of objects to the set of closed objects - W Set of attributes - _W Set of sound inference paths on the set of attributes W - Set of relational schemas in a DB that satisfy MVD - ⁺ Range closure of W wrt      

Technology,work and culture

Conclusion There has been no attempt in this introduction to put forward a particular method for dealing with these challenges nor to assess the full contribution of the articles in this issue. This outline and discussion has been intended merely to stimulate interdisciplinary debate and provide some of the background to assist in making this possible. A full account would at least have involved a broader review of the background of McLoughlin and Aicholzer and Schienstock in developments within the industrial sociology or industrial relations discipline. Their contributions do, however, provide a good introduction to the traditions within which they are working and so it is not necessary to provide more information here. It is nevertheless important to note in McLoughlin's case that his analysis of technological systems and system architectures is based on earlier work by McLoughlin and his colleagues, cited in the article, on the complex nature of engineering systems and the importance of taking this complexity into account in any discussion of the impact of technology on organisation. If the result of this issue is the stimulation of system designers to read further in such areas or the encouragement of industrial sociologists to become more involved in research directed towards human-oriented system design then it will have served its purpose.     

Human–Machine Interaction in Intelligent Robotic Systems: A Unifying Consideration with Implementation Examples

In this paper, we propose a two-layer sensor fusion scheme for multiple hypotheses multisensor systems. To reflect reality in decision making, uncertain decision regions are introduced in the hypotheses testing process. The entire decision space is partitioned into distinct regions of correct, uncertain and incorrect regions. The first layer of decision is made by each sensor indepedently based on a set of optimal decision rules. The fusion process is performed by treating the fusion center as an additional virtual sensor to the system. This virtual sensor makes decision based on the decisions reached by the set of sensors in the system. The optimal decision rules are derived by minimizing the Bayes risk function. As a consequence, the performance of the system as well as individual sensors can be quantified by the probabilities of correct, incorrect and uncertain decisions. Numerical examples of three hypotheses, two and four sensor systems are presented to illustrate the proposed scheme.     

Rapid Concept Learning for Mobile Robots

Concept learning in robotics is an extremely challenging problem: sensory data is often high-dimensional, and noisy due to specularities and other irregularities. In this paper, we investigate two general strategies to speed up learning, based on spatial decomposition of the sensory representation, and simultaneous learning of multiple classes using a shared structure. We study two concept learning scenarios: a hallway navigation problem, where the robot has to induce features such as opening or wall. The second task is recycling, where the robot has to learn to recognize objects, such as a trash can. We use a common underlying function approximator in both studies in the form of a feedforward neural network, with several hundred input units and multiple output units. Despite the high degree of freedom afforded by such an approximator, we show the two strategies provide sufficient bias to achieve rapid learning. We provide detailed experimental studies on an actual mobile robot called PAVLOV to illustrate the effectiveness of this approach.     

Local determinacy of abstract local dynamical systems

O. Hájek proved in his book Dynamical Systems in the Plane (Chapter III) that there isat most one abstract local dynamical system which is locally equivalent to, or equivalently an extension of, a given elementary dynamical system, and suggested a question of finding reasonable conditions on the latter for the existence ofat least one such abstract local dynamical system. An elementary dynamical system is said to satisfy the No-Intersection Axiom and is called an abstract germ if(x ₁, t) = (x ₂,t) impliesx ₁ =x ₂. We show that is (uniquely) extendable to an abstract local dynamical system if and only if is an abstract germ, and hence the question is completely answered. After introducing various kinds of isomorphisms of abstract germs and abstract local dynamical systems corresponding to those of continuous germs and continuous local dynamical systems, we obtain some sufficient conditions for extendability of isomorphisms and possibility of restriction of them, and thus establish the local determinacy of abstract local dynamical systems up to isomorphisms in some wider categories.Dedicated to Professor Yusuke HAGIHARA in Commemoration of His Seventy-Seventh Anniversary     

Is Solar System Stable? A Remark

It is not yet known (1997) whether the Solar system is stable or not. Common belief is that the Solar system is stable if and only if it is not a resonant system, i.e., whenever its orbital frequencies i satisfy an inequality | nii| for i|ni| N; a similar inequality is true for randomly chosen frequencies. In this paper, we show that the Solar system does not have such resonances, and therefore (if the above-mentioned belief is correct), it is stable.