Bayesian inference has been used successfully for many problems where the aim is to infer the parameters of a model of interest. In this paper we formulate the three dimensional reconstruction problem as the problem of inferring the parameters of a surface model from image data, and show how Bayesian methods can be used to estimate the parameters of this model given the image data. Thus we recover the three dimensional description of the scene. This approach also gives great flexibility. We can specify the geometrical properties of the model to suit our purpose, and can also use different models for how the surface reflects the light incident upon it. In common with other Bayesian inference problems, the estimation methodology requires that we can simulate the data that would have been recorded for any values of the model parameters. In this application this means that if we have image data we must be able to render the surface model. However it also means that we can infer the parameters of a model whose resolution can be chosen irrespective of the resolution of the images, and may be super-resolved. We present results of the inference of surface models from simulated aerial photographs for the case of super-resolution, where many surface elements project into a single pixel in the low-resolution images.

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called plateau moves, dominate the time spent in local search. We analyze and characterize plateaus for three different classes of randomly generated Boolean Satisfiability problems. We identify several interesting features of plateaus that impact the performance of local search algorithms. We show that local minima tend to be small but occasionally may be very large. We also show that local minima can be escaped without unsatisfying a large number of clauses, but that systematically searching for an escape route may be computationally expensive if the local minimum is large. We show that plateaus with exits, called benches, tend to be much larger than minima, and that some benches have very few exit states which local search can use to escape. We show that the solutions (i.e., global minima) of randomly generated problem instances form clusters, which behave similarly to local minima. We revisit several enhancements of local search algorithms and explain their performance in light of our results. Finally we discuss strategies for creating the next generation of local search algorithms.

Halperri argues for alternative non‐Bayesian approaches to uncertainty based on problems he perceives in the Bayesian approach. In particular, he argues for a distinction between degrees of belief and statistical statements (based on the concept of random sampling). In this response I show that there is no difference between these two concepts in the Bayesian framework, and that the replacement of variables by constants in probabilistic predicate calculus expressions is valid, despite Halpern's objections. The main reason for his rejection of the simpler approach is that he does not condition his belief statements on the evidence used to form these beliefs, and so gets into trouble when new evidence is received. This failure to properly take evidence into account invalidates most of his other criticisms. While I approve of his call for more formal rigor in representing Bayesian practice, his claim to have provided a semantics is misleading – what he has provided is not operational.

Abstract This essay addresses a number of issues centered around the question of what is the best method for representing and reasoning about common sense (sometimes called plausible inference). Drew McDermott has shown that a direct translation of commonsense reasoning into logical form leads to insurmountable difficulties, from which McDermott concluded that we must resort to procedural ad hocery. This paper shows that the difficulties McDermott described are a result of insisting on using logic as the language of commonsense reasoning. If, instead, (Bayesian) probability is used, none of the technical difficulties found in using logic arise. For example, in probability, the problem of referential opacity cannot occur and nonmonotonic logics (which McDermott showed don't work anyway) are not necessary. The difficulties in applying logic to the real world are shown to arise from the limitations of truth semantics built into logic–probability substitutes the more reasonable notion of belief. In Bayesian inference, many pieces of evidence are combined to get an overall measure of belief in a proposition. This is much closer to commonsense patterns of thought than long chains of logical inference to the true conclusions. Also it is shown that English expressions of the “IF A THEN B” form are best interpreted as conditional probabilities rather than universally quantified expressions. Bayesian inference is applied to a simple example of linguistic information to illustrate the potential of this type of inference for AI. This example also shows how to deal with vague information, which has so far been the province of fuzzy logic. It is further shown that Bayesian inference gives a theoretical basis for inductive inference that is borne out in practice. Instead of insisting that probability is the best language for commonsense reasoning, a major point of this essay is to show that real inference is a complex interaction between probability, logic, and other formal representation and reasoning systems.

In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained.The map contains the estimates of relationships among objects in the map, and their uncertainties, given all the available information.The procedures provide a general solution to the problem of estimating uncertain relative spatial relationships.The estimates are probabilistic in nature, an advance over the previous, very conservative, worst-case approaches to the problem.Finally, the procedures are developed in the context of state-estimation and filtering theory, which provides a solid basis for numerous extensions.

This paper outlines a procedure for performing induction under uncertainty. This procedure uses a probabilitic representation and uses Bayes' theorem to decide between alternative hypotheses (theories). This procedure is illustrated by a robot with no prior world experience performing induction on data it has gathered about the world. The particular inductive problem is the formation class descriptions both for the tutored and untutored cases. The resulting class definitions are inherenty probabilistic and so do not have any sharply defined membership criterion. This robot example raises some fundamental problems about induction—particularly it is shown that inductively formed theories are not the best way of making predictions. Another difficulty is the need to provide prior probabilities for the set of possible theories. The main criterion for such priors is a proagmatic one aimed at keeping the theory structure as simple as possible, while still reflecting any structure discovered in the data.

This paper describes a representation of time and its associated inference rules that is being applied to process planning. The representation associates a time interval and a duration with every proposition in a world model, so that particular time relationships can be reasoned about explicitly. These time intervals are defined by their beginning and end instants, so interval relationships, such as "before" and "overlaps", are defined indirectly by the corresponding relations between the end instants. This new representation allows simpler rules for deducing the usual planning interval relationships. Similarly, interval durations are associated with each proposition by asserting the maximum and minimum durations, thus allowing the discovery of critical paths and allowing partial plans to be optimized. A planner has been designed to use the above time representation to produce plans for work stations with multiple robots, for example. A method is given for the detection and correction of interactions in the current partial plan that avoids any conflicts and deadlocks that could arise.