On the Relationship Between Abduction and Deduction

Theoretical Computer Science, 1994

We present a duality relationship between abduction for de nite abductive programs and model generation on the only-if part of these programs. As was pointed out by Console et all, abductive solutions for an abductive program correspond to models of the only-if part. We extend this observation by showing that the procedural semantics of abduction itself can be interpreted dually as a form of model generation on the only-if part. This model generation extends Satchmo with an e cient treatment of equality-atoms occurring in the head of rules. It is illustrated how this duality allows to improve current procedures for both abduction and model generation by transferring technical results known for one of these computational paradigms to the other.

New Mathematics and Natural Computation

Experience-based reasoning (EBR) is a paradigm used in almost every human activity as a part of human reasoning. However, EBR has not been seriously studied from a logical viewpoint. This paper will attempt to fill this gap by providing a unified logical approach to EBR. More specifically, this paper first examines EBR and inference rules. Then it proposes eight different rules of inference for EBR, which cover all possible EBRs from a logical viewpoint. These eight different rules of inference constitute the fundamentals for all EBR paradigms, and therefore will be the theoretical foundation for EBR. The proposed approach will facilitate research and development of EBR, human reasoning, and common sense reasoning.

Digital Marketplaces Unleashed, 2017

One objective of Industry 4.0 is to further enhance automation and data exchange in manufacturing among the whole value chain in order to provide new services and to decrease the use of resources. Industry 4.0 relies on communicating systems aiming at decentralized decisions for manufacturing requested products and services comprising humans and machines. The availability of systems and their data, e. g., manufacturing or monitoring data, online is an enabler of new applications and services including diagnosis. In this article we focus on the diagnosis aspect and provide insights into a methodology that allows for bringing in diagnosis of interconnected systems as a service. The methodology is based on system models and monitoring observations and thus is highly adaptable to changes in the system. In addition, to the methodology we give examples from applications of diagnosis for wind turbines and other engineered systems.

Journal of the ACM, 1995

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 subset-minimality, 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.

Information Sciences, 2021

The aim of this paper is to provide logical foundations for knowledge-based recommender systems, for which, unlike other problem solving tasks, a comprehensive formalization is not yet available. This goal is justified by the need to compare recommenders based on the way they use knowledge to generate recommendations and, consequently, on the underlying semantics of the recommendation process itself. Moreover, since the here adopted logical formalization has been borrowed from other tasks such as diagnosis, many interesting results and opportunities can be transposed from such tasks to recommendation. While we do not aim at proposing a new recommendation generation technique, we believe that our formalization will be the basis for unifying different approaches to knowledge-based recommendation, revealing their semantics and offering a conceptual framework to compare them. In fact, the framework covers different variations of knowledge-based recommendation, such as context-aware, constraints-based, package and group recommendation, as well as recommendation based on negative preferences.

International Journal of Cooperative Information Systems, 2006

This paper presents a framework for monitoring the compliance of systems composed of Web-services with requirements set for them at runtime. This framework assumes systems composed of Web-services which are co-coordinated by a service composition process expressed in BPEL and uses event calculus to specify the requirements to be monitored. These requirements may include behavioral properties of a system which are automatically extracted from the specification of its composition process in BPEL and/or assumptions that system providers can specify in terms of events extracted from this specification.

Computational Intelligence, 1994

This paper presents a knowledge-based learning method and reports on case studies in different domains. The method integrates abduction and explanation-based learning. Abduction provides an improved method for constructing explanation$. The improvement enlarges the set of examples that can be explained so that one can learn from additional examples using traditional explanation-based macro learning. Abduction also provides a form of knowledge level learning. Descriptions of case studies show how to set up abduction engines for tasks in particular domains. The case studies involve over a hundred examples taken from diverse domains requiring logical, physical, and psychological knowledge and reasoning. The case studies are relevant to a wide range of practical tasks including natural language understanding and plan recognition; qualitative physical reasoning and postdiction; diagnosis and signal interpretation; and decision making under uncertainty. The descriptions of the case studies include an example, its explanation, and discussions of what is learned by macro-learning and by abductive inference. The paper discusses how to provide and represent the domain knowledge and meta-knowledge needed for abduction and search control. The main conclusion is that abductive inference is important for learning. Abduction and macro-learning are complementary and synergistic.

Lecture Notes in Computer Science, 2015

Constraint Handling Rules (CHR) is a general-purpose rulebased programming language. This paper studies the forward and backward propagation of rules, and explores the combination of both execution strategies. Forward propagation transforms input to output, while backward propagation uncovers input from output. This work includes a source-to-source transformation capable of implementing a backward propagation of the rules. Furthermore with the addition of annotating trigger constraints, CHR programs can be executed in a strictlyforward, strictly-backward or combined interleaved quasi-simultaneous manner. A programmer should only write one program and then the annotated transformation empowers the multiple execution strategies. The proposed work is useful for automatic implementation of bidirectional search for any search space through the combined execution strategies. Moreover, it is advantageous for reversible bijective algorithms (such as lossless compression/decompression), requiring only one algorithm direction to be implemented.

Applied Artificial Intelligence, 2004

Lecture Notes in Computer Science, 2005

A model for context-dependent natural language semantics is proposed and formalized in terms of possible worlds. The meaning of a sentence depends on context and at the same time affects that context representing the knowledge about the world collected from a discourse. The model fits well with a "flat" semantic representation as first proposed by , consisting basically of a conjunction of atomic predications in which all variables are existentially quantified with the widest possible scope; in our framework, this provides very concise semantic terms as compared with other representations. There is a natural correspondence between the possible worlds semantics and a constraint solver, and it is shown how such a semantics can be defined using the programming language of Constraint Handling Rules (Frühwirth, 1995). Discourse analysis is clearly a process of abduction in this framework, and it is shown that the mentioned constraint solvers serve as effective and efficient abductive engines for the purpose.