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Inconsistency arises in many areas in advanced computing. Examples include: Merging information from heterogeneous sources; Negotiation in multi-agent systems; Understanding natural language dialogues; and Commonsense reasoning in robotics. Often inconsistency is unwanted, for example, in the specification for a plan, or in sensor fusion in robotics. But sometimes inconsistency is useful, e.g. when...
Specifications of XML documents typically consist of typing information (for example, a DTD), and integrity constraints (for example, keys and foreign keys). We show that combining the two may lead to seemingly reasonable specifications that are nevertheless inconsistent: there is no XML document that both conforms to the DTD and satisfies the constraints. We then survey results on the complexity...
When data sources are virtually integrated there is no common and centralized mechanism for maintaining global consistency. In consequence, it is likely that inconsistencies with respect to certain global integrity constraints (ICs) will occur. In this chapter we consider the problem of defining and computing those answers that are consistent wrt the global ICs when global queries are posed to virtual...
Quantified propositional logic is an extension of classical propositional logic where quantifications over atomic formulas are permitted. As such, quantified propositional logic is a fragment of second-order logic, and its sentences are usually referred to as quantified Boolean formulas (QBFs). The motivation to study quantified propositional logic for paraconsistent reasoning is based on two fundamental...
We address the problem of minimal-change integrity maintenance in the context of integrity constraints in relational databases. Using the framework proposed by Arenas, Bertossi, and Chomicki [5], we focus on two basic computational issues: repair checking (is a database instance a repair of a given database?) and consistent query answers (is a tuple an answer to a given query in every repair of a...
Reasoning in a non-trivial way from inconsistent pieces of information is a major challenge in artificial intelligence, and its importance is reflected by the number of techniques designed so far for dealing with inconsistency (especially the few ones reported in this handbook). Many of these techniques have been investigated in depth from a logical point of view, but far less to what concerns the...
Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon [67]. This work, based on probability theory, can be used in a logical setting when the worlds are the possible events. This work is also the basis of Lozinskii’s work [48] for defining the quantity of information of a formula (or knowledgebase) in propositional...
This chapter analyzes inconsistency issues in spatial databases. In particular, it reviews types of inconsistency, specification of integrity constraints, and treatment of inconsistency in multiple representations and data integration. The chapter focuses on inconsistency associated with the geometric representation of objects, spatial relations between objects, and composite objects by aggregation...
This is an account of the approach to paraconsistency associated with relevant logic. The logic fde of first degree entailments is shown to arise naturally out of the deeper concerns of relevant logic. The relationship between relevant logic and resolution, and especially the disjunctive syllogism, is then examined. The relevant refusal to validate these inferences is defended, and finally it is suggested...
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