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Measuring inconsistency in information. (English) Zbl 1411.68015

Studies in Logic (London) 73. London: College Publications (ISBN 978-1-84890-244-2/pbk). xx, 342 p. (2018).

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Publisher’s description: The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.
Both deductive and non-deductive consequence are discussed. The starting point is classical deductive consequence: classical logic is the reference system, and the non-classical deductive systems are seen as extensions, deviations, or variations thereof. The discussion of non-classical deductive consequence focuses on many-valued, intuitionistic, modal, paraconsistent, and substructural logical consequences. The topic of non-deductive consequence is elaborated on from the viewpoints of abductive, inductive, and probabilistic logics. All in all, the major contemporary (classes of) logical systems are here discussed.
The approach is mathematical in essence, and the mathematical background, mainly founded on order relations, is treated thoroughly and in an accessible way for the non-mathematician.
The articles of this volume will be reviewed individually.
Indexed articles:
Grant, John, From measuring infinities to measuring inconsistencies, 1-18 [Zbl 1452.68003]
Thimm, Matthias, On the evaluation of inconsistency measures, 19-60 [Zbl 1515.68323]
Hunter, Anthony, Measuring inconsistency in argument graphs, 61-103 [Zbl 1515.68315]
Ulbricht, Markus; Thimm, Matthias; Brewka, Gerhard, Inconsistency measures for disjunctive logic programs under answer set semantics, 105-146 [Zbl 1515.68310]
Madrid, Nicolás; Ojeda-Aciego, Manuel, Inconsistency measures in general fuzzy logic programming, 147-167 [Zbl 1515.68321]
Costa, Diana; Martins, Manuel A., Inconsistency measures in hybrid logics, 169-194 [Zbl 1423.68481]
Besnard, Philippe, Inconsistency measuring over multisets of formulas, 195-218 [Zbl 1515.68299]
Brown, Bryson, Inconsistency measures and paraconsistent consequence, 219-233 [Zbl 1437.03102]
de Bona, Glauber; Finger, Marcelo; Potyka, Nico; Thimm, Matthias, Inconsistency measurement in probabilistic logic, 235-269 [Zbl 1451.68259]
Decker, Hendrik, Measuring database inconsistency, 271-311 [Zbl 1515.68108]
Grant, John; Martinez, Maria Vanina; Molinaro, Cristian; Parisi, Francesco, On measuring inconsistency in spatio-temporal databases, 313-342 [Zbl 1515.68112]

MSC:

68-06 Proceedings, conferences, collections, etc. pertaining to computer science
03-06 Proceedings, conferences, collections, etc. pertaining to mathematical logic and foundations
03Bxx General logic
68T27 Logic in artificial intelligence
00B15 Collections of articles of miscellaneous specific interest
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