000 03399nam a22004575i 4500
001 978-1-4020-6867-6
003 DE-He213
005 20161121230830.0
007 cr nn 008mamaa
008 100301s2008 ne | s |||| 0|eng d
020 _a9781402068676
_9978-1-4020-6867-6
024 7 _a10.1007/978-1-4020-6867-6
_2doi
050 4 _aBC1-199
072 7 _aHPL
_2bicssc
072 7 _aPHI011000
_2bisacsh
082 0 4 _a160
_223
100 1 _aOdintsov, Sergei P.
_eauthor.
245 1 0 _aConstructive Negations and Paraconsistency
_h[electronic resource] /
_cby Sergei P. Odintsov.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2008.
300 _aVI, 242 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTrends in Logic ;
_v26
505 0 _aReductio ad Absurdum -- Minimal Logic. Preliminary Remarks -- Logic of Classical Refutability -- The Class of Extensions of Minimal Logic -- Adequate Algebraic Semantics for Extensions of Minimal Logic -- Negatively Equivalent Logics -- Absurdity as Unary Operator -- Strong Negation -- Semantical Study of Paraconsistent Nelson's Logic -- N4?-Lattices -- The Class of N4?-Extensions -- Conclusion.
520 _aThis book presents the author’s recent investigations of the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity (L.E.J. Brouwer) and the strong negation (D. Nelson) are studied in the setting of paraconsistent logic. The paraconsistent logics are those, which admit inconsistent but non-trivial theories, i.e., the logics which allow making inferences in non-trivial fashion from an inconsistent set of hypotheses. Logics in which all inconsistent theories are trivial are called explosive. In the intuitionistic logic Li, the negation is defined as reduction to absurdity. The concept of strong negation is realized in the Nelson logic N3. Both logics are explosive and have paraconsistent analogs: Johansson’s logic Lj and paraconsistent Nelson’s logic N4. It will be shown that refusing the explosion axiom "contradiction implies everything" does not lead to decrease of the expressive power of a logic. To understand, which new expressive possibilities have the logics Lj and N4 as compared to the explosive logics Li and N3, we study the lattices of extensions of the logics Lj and N4. This is the first case when lattices of paraconsistent logics are systematically investigated. The study is based on algebraic methods, demonstrates the remarkable regularity and the similarity of structures of both lattices of logics, and gives essential information on the paraconsistent nature of logics Lj and N4. The methods developed in this book can be applied for investigation of other classes of paraconsistent logics.
650 0 _aPhilosophy.
650 0 _aLogic.
650 0 _aMathematical logic.
650 1 4 _aPhilosophy.
650 2 4 _aLogic.
650 2 4 _aMathematical Logic and Foundations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781402068669
830 0 _aTrends in Logic ;
_v26
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4020-6867-6
912 _aZDB-2-SHU
950 _aHumanities, Social Sciences and Law (Springer-11648)
999 _c504629
_d504629