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The Resource Completeness Theory for Propositional Logics, by Witold A. Pogorzelski, Piotr Wojtylak, (electronic resource)
Completeness Theory for Propositional Logics, by Witold A. Pogorzelski, Piotr Wojtylak, (electronic resource)
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The item Completeness Theory for Propositional Logics, by Witold A. Pogorzelski, Piotr Wojtylak, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Completeness Theory for Propositional Logics, by Witold A. Pogorzelski, Piotr Wojtylak, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 Completeness 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
 Language

 eng
 eng
 Edition
 1st ed. 2008.
 Extent
 1 online resource (186 p.)
 Note
 Description based upon print version of record
 Contents

 Introduction
 1. Basic notions: Propositional languages
 Abstract algebras
 Preliminary latticetheoretical 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
 Postcompleteness
 The problem of uniqueness of Lindenbaum extensions
 Some related concepts
 4. Characterization of propositional connectives: Cndefinitions
 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
 Isbn
 9781281378637
 Label
 Completeness Theory for Propositional Logics
 Title
 Completeness Theory for Propositional Logics
 Statement of responsibility
 by Witold A. Pogorzelski, Piotr Wojtylak
 Language

 eng
 eng
 Summary
 Completeness 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
 http://library.link/vocab/creatorName
 Pogorzelski, Witold A
 Dewey number
 511.3
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 vFND9WdsP9E
 PtjOw5cKjI
 Language note
 English
 LC call number
 QA8.910.3
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Wojtylak, Piotr.
 Series statement
 Studies in Universal Logic,
 http://library.link/vocab/subjectName

 Logic, Symbolic and mathematical
 Mathematical Logic and Foundations
 Label
 Completeness Theory for Propositional Logics, by Witold A. Pogorzelski, Piotr Wojtylak, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. [165]174) and indexes
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Introduction  1. Basic notions: Propositional languages  Abstract algebras  Preliminary latticetheoretical 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  Postcompleteness  The problem of uniqueness of Lindenbaum extensions  Some related concepts  4. Characterization of propositional connectives: Cndefinitions  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
 Dimensions
 unknown
 Edition
 1st ed. 2008.
 Extent
 1 online resource (186 p.)
 Form of item
 online
 Isbn
 9781281378637
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9783764385187
 Specific material designation
 remote
 System control number

 (CKB)1000000000440691
 (EBL)371576
 (OCoLC)272310985
 (SSID)ssj0000127203
 (PQKBManifestationID)11144051
 (PQKBTitleCode)TC0000127203
 (PQKBWorkID)10051049
 (PQKB)11693832
 (DEHe213)9783764385187
 (MiAaPQ)EBC371576
 (EXLCZ)991000000000440691
 Label
 Completeness Theory for Propositional Logics, by Witold A. Pogorzelski, Piotr Wojtylak, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. [165]174) and indexes
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Introduction  1. Basic notions: Propositional languages  Abstract algebras  Preliminary latticetheoretical 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  Postcompleteness  The problem of uniqueness of Lindenbaum extensions  Some related concepts  4. Characterization of propositional connectives: Cndefinitions  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
 Dimensions
 unknown
 Edition
 1st ed. 2008.
 Extent
 1 online resource (186 p.)
 Form of item
 online
 Isbn
 9781281378637
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9783764385187
 Specific material designation
 remote
 System control number

 (CKB)1000000000440691
 (EBL)371576
 (OCoLC)272310985
 (SSID)ssj0000127203
 (PQKBManifestationID)11144051
 (PQKBTitleCode)TC0000127203
 (PQKBWorkID)10051049
 (PQKB)11693832
 (DEHe213)9783764385187
 (MiAaPQ)EBC371576
 (EXLCZ)991000000000440691
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/CompletenessTheoryforPropositionalLogicsby/ZXRCYef20gY/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/CompletenessTheoryforPropositionalLogicsby/ZXRCYef20gY/">Completeness Theory for Propositional Logics, by Witold A. Pogorzelski, Piotr Wojtylak, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>