Assumption-Based Nonmonotonic Reasoning

1990 ◽  
Vol 13 (4) ◽  
pp. 403-443
Author(s):  
Michael Gelfond ◽  
Halina Przymusinska

Current research in the area of nonmonotonic reasoning suggests that autoepistemic logic provides a general framework for formalizing commonsense reasoning in various domains of discourse. The goal of this paper is to investigate the suitability of autoepistemic logic for formalization of some forms of inheritance reasoning. To this end we propose a new semantics for inheritance networks with exceptions based on autoepistemic logic.


1993 ◽  
Vol 18 (2-4) ◽  
pp. 129-149
Author(s):  
Serge Garlatti

Representation systems based on inheritance networks are founded on the hierarchical structure of knowledge. Such representation is composed of a set of objects and a set of is-a links between nodes. Objects are generally defined by means of a set of properties. An inheritance mechanism enables us to share properties across the hierarchy, called an inheritance graph. It is often difficult, even impossible to define classes by means of a set of necessary and sufficient conditions. For this reason, exceptions must be allowed and they induce nonmonotonic reasoning. Many researchers have used default logic to give them formal semantics and to define sound inferences. In this paper, we propose a survey of the different models of nonmonotonic inheritance systems by means of default logic. A comparison between default theories and inheritance mechanisms is made. In conclusion, the ability of default logic to take some inheritance mechanisms into account is discussed.


Author(s):  
Grigoris Antoniou

This paper discusses the significance of nonmonotonic reasoning, a method from the knowledge representation area, to mainstream software engineering. In particular, we discuss why the use of defaults in specifications is an adequate way of addressing some of the most important problems in requirements engineering, such as: The problem of identifying and dealing with inconsistencies; evolving system requirements; requirements prioritization; and the quality of specifications with respect to naturalness and compactness. We argue that these problems need to be addressed in a principled, formal way, and that default reasoning provides adequate mechanisms to deal with them.


2020 ◽  
Vol 20 (6) ◽  
pp. 942-957
Author(s):  
Yusuf Izmirlioglu ◽  
Esra Erdem

AbstractWe propose a novel formal framework (called 3D-NCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-NCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and NCDC-ASP to 3D. 3D-NCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-NCDC-ASP, and illustrate its usefulness with applications.


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