000 03595nam a22005295i 4500
001 978-3-540-40062-2
003 DE-He213
005 20160624101947.0
007 cr nn 008mamaa
008 121227s2003 gw | s |||| 0|eng d
020 _a9783540400622
_9978-3-540-40062-2
024 7 _a10.1007/b94030
_2doi
050 4 _aQ334-342
050 4 _aTJ210.2-211.495
072 7 _aUYQ
_2bicssc
072 7 _aTJFM1
_2bicssc
072 7 _aCOM004000
_2bisacsh
082 0 4 _a006.3
_223
100 1 _aDau, Frithjof.
_eauthor.
245 1 4 _aThe Logic System of Concept Graphs with Negation
_h[electronic resource] :
_bAnd Its Relationship to Predicate Logic /
_cby Frithjof Dau.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2003.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2003.
300 _aXII, 216 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Computer Science,
_x0302-9743 ;
_v2892
505 0 _aStart -- 1 Introduction -- 2 Basic Definitions -- Alpha -- 3 Overview for Alpha -- 4 Semantics for Nonexistential Concept Graphs -- 5 Calculus for Nonexistential Concept Graphs -- 6 Soundness and Completeness -- Beta -- 7 Overview for Beta -- 8 First Order Logic -- 9 Semantics for Existential Concept Graphs -- 10 Calculus for Existential Concept Graphs -- 11 Syntactical Equivalence to FOL -- 12 Summary of Beta -- 13 Concept Graphs without Cuts -- 14 Design Decisions.
520 _aThe aim of contextual logic is to provide a formal theory of elementary logic, which is based on the doctrines of concepts, judgements, and conclusions. Concepts are mathematized using Formal Concept Analysis (FCA), while an approach to the formalization of judgements and conclusions is conceptual graphs, based on Peirce's existential graphs. Combining FCA and a mathematization of conceptual graphs yields so-called concept graphs, which offer a formal and diagrammatic theory of elementary logic. Expressing negation in contextual logic is a difficult task. Based on the author's dissertation, this book shows how negation on the level of judgements can be implemented. To do so, cuts (syntactical devices used to express negation) are added to concept graphs. As we can express relations between objects, conjunction and negation in judgements, and existential quantification, the author demonstrates that concept graphs with cuts have the expressive power of first-order predicate logic. While doing so, the author distinguishes between syntax and semantics, and provides a sound and complete calculus for concept graphs with cuts. The author's treatment is mathematically thorough and consistent, and the book gives the necessary background on existential and conceptual graphs.
650 0 _aComputer science.
650 0 _aComputational complexity.
650 0 _aArtificial intelligence.
650 1 4 _aComputer Science.
650 2 4 _aArtificial Intelligence (incl. Robotics).
650 2 4 _aComputer Science, general.
650 2 4 _aMathematical Logic and Formal Languages.
650 2 4 _aDiscrete Mathematics in Computer Science.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540206071
786 _dSpringer
830 0 _aLecture Notes in Computer Science,
_x0302-9743 ;
_v2892
856 4 0 _uhttp://dx.doi.org/10.1007/b94030
942 _2EBK4818
_cEBK
999 _c34112
_d34112