Ernest Davis

Constraint propagation with interval labels

Abstract Constraint propagation is often used in AI systems to perform inference about quantities. This paper studies one particular kind of constraint propagation, where quantities are labelled with signs or with intervals, and these labels are propagated through recorded constraints. We review the uses of such inference schemes in AI systems of various kinds, and evaluate their strengths and weaknesses. In particular, we determine the completeness and running time of constraint propagation for various kinds of labels and constraints.

Planning Routes through uncertain territory

Abstract Planning routes and executing them requires both topological and metric information. A natural implementation of a ‘cognitive map’ might therefore consist of an assertional data base for topological information and a ‘fuzzy map’ for the metric information. A fuzzy map captures facts about objects by recording their relative positions, orientations, and scales in convenient frames of reference. It is fuzzy in the sense that coordinates are specified to lie in a range rather than having fixed values. The fuzzy map allows easy retrieval of information. The same information is also represented in a discrimination tree, which allows an object to be retrieved given its location and other attributes. The problem of constructing a fuzzy map is more difficult; we present a partial solution, an algorithm that assimilates a fact first by imposing constraints on the fuzzy coordinates of the objects involved, then by rearranging or growing the tree of frames of reference. Route planning is modelled as a process of finding the overall direction and topology of the path, then filling in the details by deciding how to go around barriers. It uses the retrieval algorithms. Our program SPAM carries out all these processes.

Algorithms for Scheduling Tasks on Unrelated Processors

Several algorithms are presented for the nonpreemptlve assignment of n independent tasks to m unrelated processors One algorithm requires polynomial Ume in n and m and IS at most 2x/~ times worse than optimal in the worst case This is the best polynomial-time algorithm known for scheduling such sets of tasks. An algorithm with slightly better worst case performance requires polynomial time in n but exponential ume in m This 1s the best algorithm known that requires time O(nlogn) for every fixed value of m

What's the Point?*

We present a theory of conversation comprehension in which a line of the conversation is “understood” by relating it to one of seven possible “points”. We define these points, and present examples where it seems plausible that the failure to “get the point” would indeed constitute a failure to understand the conversation. We argue that the recognition of such points must proceed in both a top down and bottom up fashion, and thus is likely to be quite complicated. Finally, we see the processing of information in the conversation to be dependent upon which point classification the user decides upon.

Processes and continuous change in a SAT-based planner

The TM-LPSAT planner can construct plans in domains containing atomic actions and durative actions; events and processes; discrete, real-valued, and interval-valued fluents; reusable resources, both numeric and interval-valued; and continuous linear change to quantities. It works in three stages. In the first stage, a representation of the domain and problem in an extended version of PDDL+ is compiled into a system of Boolean combinations of propositional atoms and linear constraints over numeric variables. In the second stage, a SAT-based arithmetic constraint solver, such as LPSAT or MathSAT, is used to find a solution to the system of constraints. In the third stage, a correct plan is extracted from this solution. We discuss the structure of the planner and show how planning with time and metric quantities is compiled into a system of constraints. The proofs of soundness and completeness over a substantial subset of our extended version of PDDL+ are presented.

How Robust Are Probabilistic Models of Higher-Level Cognition?

An increasingly popular theory holds that the mind should be viewed as a near-optimal or rational engine of probabilistic inference, in domains as diverse as word learning, pragmatics, naive physics, and predictions of the future. We argue that this view, often identified with Bayesian models of inference, is markedly less promising than widely believed, and is undermined by post hoc practices that merit wholesale reevaluation. We also show that the common equation between probabilistic and rational or optimal is not justified.

Constraint Networks of Topological Relations and Convexity

This paper studies the expressivity and computational complexity of networks of constraints of topological relations together with convexity. We consider constraint networks whose nodes are regular regions (a regular region is one equal to the closure of its interior) and whose constraints have the following forms: (i) the eight “base relations” of [12], which describe binary topological relations of containment and adjacency between regions; (ii) the predicate, “X is convex.” We establish tight bounds on the computational complexity of this language: Determining whether such a constraint network is consistent is decidable, but essentially as hard as determining whether a set of comparable size of algebraic constraints over the real numbers is consistent. We also show an important expressivity result for this language: If r and s are bounded, regular regions that are not related by an affine transformation, then they can be distinguished by a constraint network. That is, there is a constraint network and a particular node in that network such that there is a solution where the node is equal to r, but no solution where the node is equal to s.

Commonsense reasoning and commonsense knowledge in artificial intelligence

AI has seen great advances of many kinds recently, but there is one critical area where progress has been extremely slow: ordinary commonsense.

A logical framework for commonsense predictions of solid object behaviour

Abstract Predicting the behaviour of a qualitatively described system of solid objects requires a combination of geometrical, temporal, and physical reasoning. Methods based upon formulating and solving differential equations are not adequate for robust prediction, since the behaviour of a system over extended time may be much simpler than its behaviour over local time. This paper presents a first-order logic in which one can state simple physical problems and derive their solution deductively, without recourse to solving differential equations. This logic is substantially more expressive and powerful than any previous AI representational system in this domain.

A First-order Theory of Communication and Multi-agent Plans

This paper presents a theory expressed in first-order logic for describing and supporting inference about action, knowledge, planning, and communication, in an egalitarian multi-agent setting. The underlying ontology of the theory uses a situationbased temporal model and a possible-worlds model of knowledge. It supports plans and communications of a very general kind, both informative communications and requests. Communications may refer to states of the world or states of knowledge in the past, present, or future. We demonstrate that the theory is powerful enough to represent several interesting multi-agent planning problems and to justify their solutions. We have proven that the theory of knowledge, communication, and planning is consistent with a broad range of physical theories, despite the existence of a number of potential paradoxes.