In this paper we will be concerned with such reasoning in its most general form, that is, in inferences that are defeasible: given more information, we may retract them. The purpose of this paper is to introduce a form of non-monotonic inference based on the notion of a partial model of the world. We take partial models to reflect our partial knowledge of the true state of affairs. We then define non-monotonic inference as the process of filling in unknown parts of the model with conjectures: statements that could turn out to be false, given more complete knowledge. To take a standard example from default reasoning: since most birds can fly, if Tweety is a bird it is reasonable to assume that she can fly, at least in the absence of any information to the contrary. We thus have some justification for filling in our partial picture of the world with this conjecture. If our knowledge includes the fact that Tweety is an ostrich, then no such justification exists, and the conjecture must be retracted.

This paper describes some work on automatically generating finite counterexamples in topology, and the use of counterexamples to speed up proof discovery in intermediate analysis, and gives some examples theorems where human provers are aided in proof discovery by the use of examples.

In many applied sciences there is often a problem of revealing a structure underlying a given collection of objects (situations, measurements, observations, etc.). A specific problem of this type is that of determining a hierarchy of meaningful subcategories in such a collection. This problem has been studied intensively in the area of cluster analysis. The methods developed there, however, formulate subcategories ('clusters') solely on the basis of pairwise'similarity' (or'proximity') of objects, and ignore the issue of the'meaning' of the clusters obtained. The methods do not provide any description of the clusters obtained. This paper presents a method which constructs a hierarchy of subcategories, such that an appropriately generalized description of each subcategory is a single conjunctive statement involving attributes of objects and has a simple conceptual interpretation. The attributes may be many-valued nominal variables or relations on numerical variables. The hierarchy is constructed in such a way that a flexibly defined'cost' of the collection of descriptions which branch from any node is minimized. Experiments with the implemented program, CLUSTER/paf, have shown that for some quite simple problems the traditional methods are unable to produce a structuring of objects most'natural' for people, while the method presented here was able to produce such a solution.

A programming language based on sets; motivation and examples.

K.A.PATON 411 24 Centromere finding: some shape descriptors for small chromosome outlines.

Networks as models of word storage: G. R. Kiss

The objective of this paper is to present a new method for the computer representation of empirically derived causal relationships (CR's). This method draws on the theory of multivariate linear models and path analysis. The method is contrasted with the predicate calculus methods developed by other Al researchers. The representation presented here has been used to store information on medical CR's derived empirically from a large clinical database by a computer program called RX. The principal emphasis in the representation is on capturing the intensities and variances of effects and the variation in the effects across a patient population. Once incorporated into RX's knowledge base, this information is subsequently used by RX in determining the validity of other CR's. The representation uses a directed graph formalism in which the nodes are frames and the arcs contain seven descriptive features of individual CR's: intensity, distribution, direction, mathematical form, setting, validity, and evidence. Because natural systems (such as the human body) are inherently probabilistic, linear models are useful in representing causal flow in them. Knowledge of natural systems is fundamentally probabilistic because of I) irreducible indeterminism in their component processes, 2) difficulties in accurately measuring all relevant variables, 3) variation among individuals in a population, and 4) inadequate scientific theory.

It is noted that no one method is best with a view to the potential role of automated decision for all applications. However, emphasis is given to the limitations of early work that have made artificial intelligence techniques and knowledge aids in that domain 1611.

A clinical investigator graphical capabilities which can plot specific parameters for a keeping the records of his study patients on such a system can patient over time 1126]. However, it is in the analysis of stored use the program's statistical capabilities for data analysis.

In the early days of computing, these goals were central to the new discipline called cybernetics [126], [2]. Over the past two decades, progress toward these goals has come from a variety of fields - notably computer science, psychology, adaptive control theory, pattern recognition, and philosophy. Substantial progress has been made in developing techniques for machine learning in highly restricted environments.