Negative Reinforcement and Backtrack-Points for Recurrent Neural Networks for Cost-Based Abduction

Abduction is the process of proceeding from data describing a set of observations or events, to a set of hypotheses which best explains or accounts for the data. Cost-based abduction (CKA) is an AI formalism in which evidence to be explained is treated as a goal to be proven, proofs have costs based on how much needs to be assumed to complete the proof, and the set of assumptions needed to complete the least-cost proof are taken as the best explanation for the given evidence. In this paper, we introduce two techniques for improving the performance of high order recurrent networks (HORN) applied to cost-based abduction. In the backtrack-points technique, we use heuristics to recognize early that the network trajectory is moving in the wrong direction; we then restore the network state to a previously-stored point, and apply heuristic perturbations to nudge the network trajectory in a different direction. In the negative reinforcement technique, we add hyperedges to the network to reduce the attractiveness of local-minima. We apply these techniques on a 300-hypothesis, 900-rule particularly-difficult instance of CBA

Generalized Probabilistic Reasoning and Empirical Studies on Computational Efficiency and Scalability

Expert Systems are tools that can be very useful for diagnostic purposes, however current methods of storing and reasoning with knowledge have significant limitations. One set of limitations involves how to store and manipulate uncertain knowledge: much of the knowledge we are dealing with has some degree of uncertainty. These limitations include lack of complete information, not being able to model cyclic information and limitations on the size and complexity of the problems to be solved. If expert systems are ever going to be able to tackle significant real world problems then these deficiencies must be corrected. This paper describes a new method of reasoning with uncertain knowledge which improves the computational efficiency as well as scalability over current methods. The cornerstone of this method involves incorporating and exploiting information about the structure of the knowledge representation to reduce the problem size and complexity. Additionally, a new knowledge representation is discussed that will further increase the capability of expert systems to model a wider variety of real world problems. Finally, benchmarking studies of the new algorithm against the old have led to insights into the graph structure of very large knowledge bases

Intentional Communication: Computationally Easy or Difficult?

Human intentional communication is marked by its flexibility and context sensitivity. Hypothesized brain mechanisms can provide convincing and complete explanations of the human capacity for intentional communication only insofar as they can match the computational power required for displaying that capacity. It is thus of importance for cognitive neuroscience to know how computationally complex intentional communication actually is. Though the subject of considerable debate, the computational complexity of communication remains so far unknown. In this paper we defend the position that the computational complexity of communication is not a constant, as some views of communication seem to hold, but rather a function of situational factors. We present a methodology for studying and characterizing the computational complexity of communication under different situational constraints. We illustrate our methodology for a model of the problems solved by receivers and senders during a communicative exchange. This approach opens the way to a principled identification of putative model parameters that control cognitive processes supporting intentional communication

A linear constraint satisfaction approach to cost-based abduction

Abstract Santos Jr, E., A linear constraint satisfaction approach to cost-based abduction, Artificial Intelligence 65 (1994) 1-27. Abduction is the problem of finding the best explanation for a given set of observations. Within AI, this has been modeled as proving the observation by assuming some set of hypotheses. Cost-based abduction associates a cost with each hypothesis. The best proof is the one which assumes the least costly set. Previous approaches to finding the least cost set have formalized cost-based abduction as a heuristic graph search problem. However, efficient admissible heuristics have proven difficult to find. In this paper, we present a new technique for finding least cost sets by using linear constraints to represent causal relationships. In particular, we are able to recast the problem as a 0-1 integer linear programming problem. We can then use the highly efficient optimization tools of operations research yielding a computationally efficient method for solving cost-based abduction problems. Experiments comparing our linear constraint satisfaction approach to standard graph searching methodologies suggest that our approach is superior to existing search techniques in that our approach exhibits an expected-case polynomial run-time growth rate

Approaches to abductive reasoning : an overview

Abduction is a form of non-monotonic reasoning that has gained increasing interest in the last few years. The key idea behind it can be represented by the following inference rule frac{varphirightarrowomega,}{varphi}omega, i.e., from an occurrence of omega and the rule "varphi implies omega';, infer an occurrence of varphi as a plausible hypothesis or explanation for omega. Thus, in contrast to deduction, abduction is as well as induction a form of "defeasible'; inference, i.e., the formulae sanctioned are plausible and submitted to verification. In this paper, a formal description of current approaches is given. The underlying reasoning process is treated independently and divided into two parts. This includes a description of methods for hypotheses generation and methods for finding the best explanations among a set of possible ones. Furthermore, the complexity of the abductive task is surveyed in connection with its relationship to default reasoning. We conclude with the presentation of applications of the discussed approaches focusing on plan recognition and plan generation