LEADER 04291nam 2200637 a 450 001 9910451264103321 005 20200520144314.0 010 $a1-281-37863-1 010 $a9786611378639 010 $a3-7643-8518-9 024 7 $a10.1007/978-3-7643-8518-7 035 $a(CKB)1000000000440691 035 $a(EBL)371576 035 $a(OCoLC)272310985 035 $a(SSID)ssj0000127203 035 $a(PQKBManifestationID)11144051 035 $a(PQKBTitleCode)TC0000127203 035 $a(PQKBWorkID)10051049 035 $a(PQKB)11693832 035 $a(DE-He213)978-3-7643-8518-7 035 $a(MiAaPQ)EBC371576 035 $a(PPN)127049533 035 $a(Au-PeEL)EBL371576 035 $a(CaPaEBR)ebr10501479 035 $a(CaONFJC)MIL137863 035 $a(EXLCZ)991000000000440691 100 $a20080214d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCompleteness theory for propositional logics$b[electronic resource] /$fWitold A. Pogorzelski, Piotr Wojtylak 205 $a1st ed. 2008. 210 $aBasel ;$aBoston $cBirkha?user$dc2008 215 $a1 online resource (186 p.) 225 1 $aStudies in universal logic 300 $aDescription based upon print version of record. 311 $a3-7643-8517-0 320 $aIncludes bibliographical references (p. [165]-174) and indexes. 327 $aIntroduction -- 1. Basic notions: Propositional languages -- Abstract algebras -- Preliminary lattice-theoretical notions -- Propositional logics -- Brief exposition of the most important propositional logics -- 2. Semantic methods in propositional logic: Preordered sets -- Preordered algebras -- Logical matrices -- Adequacy -- Propositional logic and lattice theory -- 3. Completeness of propositional logic: Generalized completeness -- Post-completeness -- The problem of uniqueness of Lindenbaum extensions -- Some related concepts -- 4. Characterization of propositional connectives: Cn-definitions -- The system (D) -- Variants -- The system (I) -- Classical logic -- Appendix: The fundamental metatheorem for the classical propositional logic -- A proof system for the classical logic. 330 $aCompleteness is one of the most important notions in logic and the foundations of mathematics. Many variants of the notion have been de?ned in literature. We shallconcentrateonthesevariants,andaspects,of completenesswhicharede?ned in propositional logic. Completeness means the possibility of getting all correct and reliable sc- mata of inference by use of logical methods. The word ?all?, seemingly neutral, is here a crucial point of distinction. Assuming the de?nition as given by E. Post we get, say, a global notion of completeness in which the reliability refers only to syntactic means of logic and outside the correct schemata of inference there are only inconsistent ones. It is impossible, however, to leave aside local aspects of the notion when we want to make it relative to some given or invented notion of truth. Completeness understood in this sense is the adequacy of logic in relation to some semantics, and the change of the logic is accompanied by the change of its semantics. Such completeness was e?ectively used by J. ?ukasiewicz and investigated in general terms by A. Tarski and A. Lindenbaum, which gave strong foundations for research in logic and, in particular, for the notion of consequence operation determined by a logical system. The choice of logical means, by use of which we intend to represent logical inferences, is also important. Most of the de?nitions and results in completeness theory were originally developed in terms of propositional logic. Propositional formal systems ?nd many applications in logic and theoretical computer science. 410 0$aStudies in universal logic. 606 $aCompleteness theorem 608 $aElectronic books. 615 0$aCompleteness theorem. 676 $a511.3 700 $aPogorzelski$b Witold$f1944-$0997130 701 $aWojtylak$b Piotr$0997131 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910451264103321 996 $aCompleteness theory for propositional logics$92286647 997 $aUNINA