Abstract: Human agents draw a variety of inferences effortlessly, spontaneously, and with remarkable efficiency — as though these inferences are a reflex response of their cognitive apparatus. Furthermore, these inferences are drawn with reference to a large body of background knowledge. This remarkable human ability seems paradoxical given the results about the complexity of reasoning reported by researchers in artificial intelligence. It also poses a challenge for cognitive science and computational neuroscience: How can a system of simple and slow neuron-like elements represent a large body of systematic knowledge and perform a range of inferences with such speed? We describe a computational model that is a step toward addressing the cognitive science challenge and resolving the artificial intelligence paradox. We show how a connectionist network can encode millions of facts and rules involving n-ary predicates and variables, and perform a class of inferences in a few hundred msec. Efficient reasoning requires the rapid representation and propagation of dynamic bindings. Our model achieves this by i) representing dynamic bindings as the synchronous firing of appropriate nodes, ii) rules as interconnection patterns

Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logic-based abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subsetminimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.

This paper surveys the main results appeared in the literature on the computational complexity of non-monotonic inference tasks. We not only give results about the tractability/intractability of the individual problems but we also analyze sources of complexity and explain intuitively the nature of easy/hard cases. We focus mainly on non-monotonic formalisms, like default logic, autoepistemic logic, circumscription, closed-world reasoning and abduction, whose relations with logic programming are clear and well studied. Complexity as well as recursion-theoretic results are surveyed. Work partially supported by the ESPRIT Basic Research Action COMPULOG and the Progetto Finalizzato Informatica of the CNR (Italian Research Council). The first author is supported by a CNR scholarship 1 Introduction Non-monotonic logics and negation as failure in logic programming have been defined with the goal of providing formal tools for the representation of default information. One of the ideas und...

We have for several years been working on an approach to knowledge system building that argues for the existence of a close connection between the tasks which the knowledge system is intended to solve, the methods chosen for them and the vocabulary in which knowledge is to be modeled and represented. We trace the historical origins of the idea that we have called Generic Tasks, and outline their evolution and accomplishments based on them. We then critique their original implementations from the perspective of flexible integration. We follow this with an outline of our current generalization of the view in the form of a theory of task structures. We describe the architectural implications of this view and outline some research directions.

When a query fails, it is more cooperative to identify the cause of failure, rather than just to report the empty answer set. If there is not a cause for the query's failure, it is worthwhile to report the part of the query which failed. To identify a minimal failing subquery (MFS) of the query is the best way to do this. (This MFS is not unique; there may be many of them.) Likewise, to identify a maximal succeeding subquery (MSS) can help a user to recast a new query that leads to a non-empty answer set. Database systems do not provide the functionality of these types of cooperative responses. This may be, in part, because algorithmic approaches to finding the MFSs and the MSSs to a failing query are not obvious. The search space of subqueries is large. Despite work on MFSs in the past, the algorithmic complexity of these identification problems had remained uncharted. This paper shows the complexity profile of MFS and MSS identification. It is shown that there exists a simple algorit...

. A problem-solving method describes a reasoning process that efficiently achieves a goal by applying domain knowledge. However, a problem-solving method cannot directly be applied because of the existence of a gap between, on the one hand, a problem-solving method and the domain knowledge it uses, and, on the other hand, a problem-solving method and the goal that it is supposed to achieve. In this paper, we distinguish two types of assumptions based on an architecture of problem-solving methods, that are able to bridge the gap: one type of assumption is used to strengthen a problem-solving method, and the other to weaken the goal to be achieved. We also show how the effect of one assumption type can be substituted by the effect of the other type, and refer to this as "the law of conservation of assumptions". 1 Introduction The notion of problem-solving method (PSM) is present in many current knowledge engineering frameworks such as Generic Tasks [6], Role-Limiting Methods [15], KADS ...

Abduction-- from observations and a theory, find using hypotheses an explanation for the observations -- gained increasing interest during the last years. This form of reasoning has wide applicability in different areas of computer science; in particular, it has been recognized as an important principle of common-sense reasoning. In this paper, we define a general abduction model for logic programming, where the inference operator (i.e., the semantics to be applied on programs), can be specified by the user. Advanced forms of logic programming have been proposed as valuable tools for knowledge representation and reasoning. We show that logic programming semantics can be more meaningful for abductive reasoning than classical inference by providing examples from the area of knowledge representation and reasoning. The main part of the paper is devoted to an extensive study of the computational complexity of the principal problems in abductive reasoning, which are: Given an inst...

Several artificial intelligence architectures and systems based on "deep" models of a domain have been proposed, in particular for the diagnostic task. These systems have several advantages over traditional knowledge based systems, but they have a main limitation in their computational complexity. One of the ways to face this problem is to rely on a knowledge compilation phase, which produces knowledge that can be used more effectively with respect to the original one. In this paper we show how a specific knowledge compilation approach can focus reasoning in abductive diagnosis, and, in particular, can improve the performances of AID, an abductive diagnosis system. The approach aims at focusing the overall diagnostic cycle in two interdependent ways: avoiding the generation of candidate solutions to be discarded a-posteriori and integrating the generation of candidate solutions with discrimination among different candidates. Knowledge compilation is used off-line to produce operational...

Automated handling of tutoring and training functions in educational systems requires the availability of articulate domain models. In this article we further develop the application of qualitative models for this purpose. A framework is presented that defines a key role for qualitative models as interactive simulations of the subject matter. Within this framework our research focuses on automating the diagnosis of learner behaviour. We show how a qualitative simulation model of the subject matter can be reformulated to fit the requirements of general diagnostic engines such as GDE. It turns out that, due to the specific characteristics of such models, additional structuring is required to produce useful diagnostic results. A set of procedures is presented that automatically maps detailed simulation models into a hierarchy of aggregated models by hiding non-essential details and chunking chains of causal dependencies. The result is a highly structured subject matter model that enables the diagnosis of learner behaviour by means of an adapted version of the GDE algorithm. An experiment has been conducted that shows the viability of the approach taken, i.e., given the output of a qualitative simulator the procedures we have developed automatically generate a structured subject matter model and subsequently use this model to successfully diagnoses learner behaviour. 2000 Elsevier Science B.V. All rights reserved.

Various formal theories have been proposed in the literature to capture the notions of diagnosis underlying diagnostic programs. Examples of such notions are: heuristic classification, which is used in systems incorporating empirical knowledge, and model-based diagnosis, which is used in diagnostic systems based on detailed domain models. Typically, such domain models include knowledge of causal, structural, and functional interactions among modelled objects. In this paper, a new set-theoretical framework for the analysis of diagnosis is presented. Basically, the framework distinguishes between `evidence functions', which characterize the net impact of knowledge bases for purposes of diagnosis, and `notions of diagnosis', which define how evidence functions are to be used to map findings observed for a problem case to diagnostic solutions. This set-theoretical framework offers a simple, yet powerful tool for comparing existing notions of diagnosis, as well as for proposing new notions ...