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001 978-3-7643-8504-0
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008 131120s2014 sz | s |||| 0|eng d
020 _a9783764385040
_9978-3-7643-8504-0
024 7 _a10.1007/978-3-7643-8504-0
_2doi
050 4 _aQA8.9-10.3
072 7 _aPBC
_2bicssc
072 7 _aPBCD
_2bicssc
072 7 _aMAT018000
_2bisacsh
082 0 4 _a511.3
_223
100 1 _aGasquet, Olivier.
_eauthor.
245 1 0 _aKripke’s Worlds
_h[electronic resource] :
_bAn Introduction to Modal Logics via Tableaux /
_cby Olivier Gasquet, Andreas Herzig, Bilal Said, François Schwarzentruber.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2014.
300 _aXV, 198 p. 73 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aStudies in Universal Logic
505 0 _aPreface -- 1 Modelling things with graphs -- 2 Talking about graphs -- 3 The basics of the model construction method -- 4 Logics with simple constraints on models -- 5 Logics with transitive accessibility relations -- 6 Model Checking -- 7 Modal logics with transitive closure -- Bibliography -- Index.
520 _aPossible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible worlds model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been applied increasingly in domains such as program semantics, artificial intelligence, and more recently in the semantic web. Additionally, all these logics were also studied proof theoretically. The proof systems for modal logics come in various styles: Hilbert style, natural deduction, sequents, and resolution. However, it is fair to say that the most uniform and most successful such systems are tableaux systems. Given a logic and a formula, they allow one to check whether there is a model in that logic. This basically amounts to trying to build a model for the formula by building a tree. This book follows a more general approach by trying to build a graph, the advantage being that a graph is closer to a Kripke model than a tree. It provides a step-by-step introduction to possible worlds semantics (and by that to modal and other nonclassical logics) via the tableaux method. It is accompanied by a piece of software called LoTREC (www.irit.fr/Lotrec). LoTREC allows to check whether a given formula is true at a given world of a given model and to check whether a given formula is satisfiable in a given logic. The latter can be done immediately if the tableau system for that logic has already been implemented in LoTREC. If this is not yet the case LoTREC offers the possibility to implement a tableau system in a relatively easy way via a simple, graph-based, interactive language. >dy>
650 0 _aMathematics.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aMathematics.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aMathematics, general.
700 1 _aHerzig, Andreas.
_eauthor.
700 1 _aSaid, Bilal.
_eauthor.
700 1 _aSchwarzentruber, François.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764385033
830 0 _aStudies in Universal Logic
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-7643-8504-0
912 _aZDB-2-SMA
999 _c93666
_d93666