000 04238cam a22003614i 4500
999 _c7516
_d7516
001 15961774
005 20210824093329.0
008 091027s2010 sz a b 001 0 eng
010 _a 2009940118
020 _a9783764399764 (hbk.)
020 _a3764399767 (hbk.)
020 _a3764399775 (ebk.)
020 _a9783764399771 (ebk.)
040 _aUKM
_cUKM
_dCUD
_dBWX
_dRRR
_dCDX
_dDLC
_erda
050 0 0 _aQA9
_b.L475 2010
082 0 4 _a511.3
_222
_bL.W.M
100 1 _aLi, Wei,
_d1943 June-
_eauthor
245 1 0 _aMathematical logic :
_bfoundations for information science /
_cWei Li.
264 1 _aBasel ;
_aBoston :
_bBirkhäuser,
_cc2010.
264 4 _cc2010
300 _axii, 261 pages :
_billustrations ;
_c24 cm.
336 _2rdacontent
_atext
337 _2rdamedia
_aunmediated
338 _2rdacarrier
_avolume
490 1 _aProgress in computer science and applied logic ;
_vv. 25
504 _aIncludes bibliographical references (p. [251]-255) and index.
505 0 _aPreface.- Glossary.- 1. Syntax of First-Order Languages.- 1.1 Symbols of first-order languages.- 1.2 Terms.- 1.3 Logical formulas.- 1.4 Free variables and substitutions.- 1.5 Godel terms of formulas.- 1.6 Proof by structural inductions.- 2. Models of First-Order Languages.- 2.1 Domains and interpretations.- 2.2 Assignments and models.- 2.3 Meanings of terms.- 2.4 Meanings of logical connective symbols.- 2.5 Meanings of formulas.- 2.6 Satisfiability and validity.- 2.7 Valid formulas on .- 2.8 Hintikka set.- 2.9 Herbrand model.- 2.10 Herbrand model with variables.- 2.11 Substitution lemma.- 3. Formal Inference Systems.- 3.1 G inference system.- 3.2 Proof trees, inference trees, and provable sequents.- 3.3 Soundness of the G inference system.- 3.4 Compactness and consistency.- 3.5 Completeness of the G inference system.- 3.6 Some commonly used inference rules.- 3.7 Proof theory and model theory.- 4. Computability and Representability.- 4.1 Formal theories.- 4.2 Elementary arithmetic theory .- 4.3 P-procedures on N.- 4.4 Church-Turhign thesis.- 4.5 Problem of representability.- 4.6 States of P-procedures.- 4.7 System of operational calculus of P-procedure statements.- 4.8 Representation of P-procedure statements.- 4.9 Representability theorem.- 5. Godel Theorems.- 5.1 Self-referential statements.- 5.2 Deciadable sets.- 5.3 Fixed point equation in .- 5.4 Godel incompleteness theorem.- 5.5 Godel consistency theorem.- 5.6 Halt problem.- 6. Sequences of Formal Theories.- 6.1 Two examples.- 6.2 Sequences of formal theories.- 6.3 Proxchemes.- 6.4 Resolution sequences.- 6.5 Sequences of default expansions.- 6.6 Forcing sequences.- 6.7 Discussions about proxchemes.- 7. Refutation by Facts and Revision Calculus.- 7.1 Necessary antecedents of formal consequences.- 7.2 New conjectures and new axioms.- 7.3 Refutation by facts and maximal contraction.- 7.4 R-calculus.- 7.5 Some examples.- 7.6 Reachability of theR-calculus.- 7.7 Soundness and completeness of the R-calculus.- 7.8 Basic theorem of testing.- 8. Version Sequences and Proxchemes.- 8.1 Versions and version sequences.- 8.2 OPEN proxcheme.- 8.3 Convergency of the P-proxcheme.- 8.4 Commutativity of the P-proxcheme.- 8.5 Independency of the P-proxcheme.- 8.6 Ideal proxchemes.- 9. Inductive Inference and Inductive Process.- 9.1 Basic terms, basic sentences, and basic instances.- 9.2 Inductive inference system A.- 9.3 Inductive version and inductive process.- 9.4 GUINA proxcheme.- 9.5 Convergency of the GUINA proxcheme.- 9.6 Commutativity of the GUINA proxcheme.- 9.7 Independency of the GUINA proxcheme.- 10. Metalanguage Environments of First-Order Languages.- 10.1 Environments of three kinds of languages.- 10.2 Basic principles of the environment of metalanguage.- 10.3 Axiomatization method.- 10.4 Formalization method.- 10.5 Workflow of scientific research.- Appendix 1 Sets and Mappings.- Appendix 2 Substitution Lemma and Its Proof.- Appendix 3 Proof of the Representability Theorem.- References.- Index.
650 0 _aLogic, Symbolic and mathematical.
830 0 _aProgress in computer science and applied logic ;
_vv. 25
856 _3Abstract
_uhttp://repository.fue.edu.eg/xmlui/handle/123456789/2757
942 _cBK
_2ddc