Manyvalued logics. A mathematical and computational introduction. (English)
Zbl 06934362
Studies in Logic (London) 67. London: College Publications (ISBN
9781848902503/pbk). xiii,
325 p. (2017).
This book cannot be described better than the
publisher’s description we recall hereafter. However this description mostly
concentrates on “Manyvalued logics”, whereas “Part I” that takes up almost
half of the book, presents “an extensive introduction to logical “\textit{things}”,
i.e. logical languages, systems, and decisions.” Important notions such as
logical consequence, adequateness of a logical system are rigorously defined.
Notions regarding decision procedures in classical logic are introduced, namely
satisfiability and validity, and they are put into relation with the several
proof systems available. It makes the book a selfcontained instrument for the
reader who wishes to do something with manyvalued logics.
Manyvalued logics are those logics that have more than the two classical
truth values, to wit, true and false; in fact, they can have from three to
infinitely many truth values. This property, together with truthfunctionality,
provides a powerful formalism to reason in settings where classical logic – as
well as other nonclassical logics – is of no avail. Indeed, originally
motivated by philosophical concerns, these logics soon proved relevant for a
plethora of applications ranging from switching theory to cognitive modeling,
and they are today in more demand than ever, due to the realization that inconsistency
and vagueness in knowledge bases and information processes are not only
inevitable and acceptable, but also perhaps welcome.
The main modern applications of (any) logic are to be found in the digital
computer, and we thus require the practical knowledge how to computerize –
which also means automate – decisions (i.e. reasoning) in manyvalued logics.
This, in turn, requires a mathematical foundation for these logics. This book
provides both this mathematical foundation and this practical knowledge in a
rigorous, yet accessible, text, while at the same time situating these logics
in the context of the satisfiability problem(s) and automated deduction.
The main text is complemented with a large selection of exercises, a plus
for the reader wishing not only to learn about, but also to do something with,
manyvalued logics.
Reviewer: Albert Hoogewijs
(Gent)
MSC:
Research exposition (monographs, survey articles) pertaining to
mathematical logic and foundations 

Manyvalued logic 

Logic in computer
science 
Keywords:
automated deduction; manyvalued logics; MVSAT; signed tableaux; signed resolution
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