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Deductive Systems in Traditional and Modern Logic
| Deductive Systems in Traditional and Modern Logic |
| Autore | Wybraniec-Skardowska Urszula |
| Pubbl/distr/stampa | Basel, Switzerland, : MDPI - Multidisciplinary Digital Publishing Institute, 2020 |
| Descrizione fisica | 1 electronic resource (298 p.) |
| Soggetto topico |
Research & information: general
Mathematics & science |
| Soggetto non controllato |
quine
logic ontology multiple conclusion rule disjunction property metadisjunction axiomatizations of arithmetic of natural and integers numbers second-order theories Peano's axioms Wilkosz's axioms axioms of integer arithmetic modeled on Peano and Wilkosz axioms equivalent axiomatizations metalogic categoricity independence consistency logic of typical and atypical instances (LTA) logic of determination of objects (LDO) quasi topology structure (QTS) concept object typical object atypical object lattice filter ideal discussive logics the smallest discussive logic discussive operators seriality accessibility relation Kotas' method modal logic deontic logic ontology of situations semantics of law formal theory of law Wittgenstein Wolniewicz non-Fregean logic identity connective sentential calculus with identity situational semantics deduction (dual) tableau Gentzen system deductive refutability refutation systems hybrid deduction-refutation rules derivative hybrid rules soundness completeness natural deduction meta-proof theory synthetic tableaux principle of bivalence cut first-order theory universal axiom Peano's axiomatics of natural numbers Leśniewski's elementary ontology Frege's predication scheme Frege's Zahl-Anzahl distinction term logic Franz Brentano Lewis Carroll logic trees logic diagrams paraconsistent logic paraconsistency Sette's calculus the law of explosion the principle of ex contradictione sequitur quodlibet semantic tree distribution Aristotle's logic syllogistic Jan Łukasiewicz axiomatic system axiomatic refutation temporal logic intuitionistic logic minimal system knowledge sequent-type calculi nonmonotonic logics default logic rejection systems Kripke models logics of evidence and truth |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910557449803321 |
Wybraniec-Skardowska Urszula
|
||
| Basel, Switzerland, : MDPI - Multidisciplinary Digital Publishing Institute, 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Logic - language - ontology : selected works / / Urszula Wybraniec-Skardowska
| Logic - language - ontology : selected works / / Urszula Wybraniec-Skardowska |
| Autore | Wybraniec-Skardowska Urszula |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (305 pages) |
| Disciplina | 401 |
| Collana | Studies in universal logic |
| Soggetto topico |
Language and languages - Philosophy
Logic, Symbolic and mathematical |
| ISBN |
9783031223303
9783031223297 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Contents -- Part I Introduction -- Chapter 1 The Dual Ontological Nature of Language Signs and the Problem of Their Mutual Relations -- 1 Preliminaries -- 2 The Functional Approach Towards Language as a System of Signs. Two Ways of Using Signs -- 3 Ch. S. Pierce's Distinction: Type-token of a Sign -- 4 Controversies Over the Ontological Status of Language Signs and Relations Between Them -- 5 Solving the Problems Under Analysis -- 5.1 The Instantiation View vs the Representation View -- 6 Theoretical Approach to the Problem of Mutual Relations Between Tokens and Types of Signs -- 6.1 Syntax -- 6.2 Semantics -- 6.3 Signs in Language Communication -- 7 Conclusions -- References -- Chapter 2 On the Structure and Contents of the Monograph -- Part II Selected Works -- Chapter 1 On the Type-Token Relationships -- References -- Chapter 2 On the Axiomatic Systems of Syntactically-Categorial Languages -- 1 Introduction -- 2 The Theories TLTk and TETk -- 3 Systems TSCL and TSCω-L -- 4 Systems DTSCL and DTSCω-L -- References -- Chapter 3 The Logical Foundations of Language Syntax Ontology -- Introduction -- 1 Intuitive Understanding of Categorial Language -- 1.1 Initial Syntactic Characteristic of Language -- 1.2 Preliminaries to the Theory of Categorial Languages -- 2 The Formal Theory Tlk - a Concretistic Approach -- 2.1 The Level of Concretes -- Theory T1k -- 2.2 The Level of Types -- Theory T2k -- 3 The Formal Theory Tlp - the Platonizing Approach -- 3.1 The Level of Types -- Theory T2p -- 3.2 The Level of Concretes -- Theory T1p -- 4 Metalogical and Philosophical Consequences -- References -- Chapter 4 On the Eliminatibility of Ideal Linguistic Entities -- 1 Non-uniform Semiotic Characterization of Language -- 2 Preliminary Conventions Concerning Language -- 3 Dual Theories Concepts and Expressions.
4 Theory T1 -- 4.1 Formalization of T1 at the Token Level -- Theory T1(tk) -- 4.1.1 Axioms and Definitions of T1(tk) -- 4.1.2 Major Theorems of the Theory T1(tk) -- 4.2 Formalization of T1 at the Type Level -- Theory T1(tp) -- 5 Theory T2 -- 5.1 Formalization of T2 at the Type Level -- Theory T2(tp) -- 5.2 Formalization of T2 at the Token Level -- Theory T2(tk) -- 6 The Equivalence of the Theories T1 and T2 -- 7 Final Conclusions and Remarks -- References -- Chapter 5 Meaning and Interpretation. Part I -- Introduction -- 1 Preliminaries -- 1.1 The Problem of the Meaning of 'Meaning' -- 1.2 What is a General Theory of Meaning and Interpretation? -- 1.3 The Aim and Assumptions of the Work -- 2 Syntax for Language -- the Theory T -- 2.1 Two Kinds of Syntax: a token-syntax and a type-syntax -- 2.2 Some Basis of the Theory T -- 3 The General Theory of Meaning: the Theory TM -- 3.1 Meaning -- 3.2 Denotation -- 3.3 Meaning and Denotation -- References -- Chapter 6 Meaning and Interpretation. Part II -- 4 The Theory of Meaning and Interpretation: the Theory -- 4.1 Interpretation and Language Communication -- 4.2 Meaning and Interpretation -- 5 Final Remarks -- References -- Chapter 7 Three Principles of Compositionality -- 1 Introduction -- 2 The Theory TC - a Non-formal Characterisation -- 2.1 Ideas -- 2.2 Main Assumptions of the Theory of Syntax -- 2.3 Main Assumptions of the Theory of Semantics and Some Metatheoretical Issues -- 3 The Theory TC- a Formal Approach -- 3.1 Some Formal Foundations of the Theory of Syntax -- 3.2 Formal Foundations of the Theory of Semantics and Some Metatheoretical Issues -- 3.3 Fundamental Theorems of TC -- 4 The Role of the Formal Theory TC in Philosophy -- References -- Chapter 8 On Meta-knowledge and Truth -- Introduction -- 1 Ideas -- 2 Main Assumptions of the Theory of Syntax and Semantics. 2.1 Categorial Syntax and Categorial Semantics -- 2.2 Three Referential Relationships of Wfes -- 2.3 Categorial Indices -- 2.4 Syntactic Operations -- 2.5 Semantic Operations -- 2.6 Knowledge and Cognitive Objects -- 2.7 The Principles of Categorial Agreement -- 2.8 Algebraic Structures of Categorial Language and its Correlates -- 2.9 Compositionality -- 2.10 Concord Between Syntactic Forms and Their Correlates -- 3 Three Notions of Truthfulness -- 3.1 Three Kinds of Models of Language and the Notion of Truth -- 3.2 Three Notions of Truthfulness -- 3.3 Reliability of Cognition of Reality -- 3.4 Operations of Replacement -- 3.5 The Most Important Theorems -- 4 Final Remarks -- References -- Chapter 9 On Language Adequacy -- 1 Introduction -- 2 The Problem Area of Language Adequacy -- 3 An Outline of the Theory of Categorial Language -- 3.1 Categorial Syntax - Theory T -- 3.1.1 General Characteristics of the Categorial Language -- 3.1.2 Two Levels of Formalization of Categorial Syntax -- 3.1.3 The Foundations of the Formal Theory T - the Level of Tokens -- 3.1.4 Foundations of the Formal Theory T - the Level of Types -- 3.2 Categorial Semantics - the Theory ST -- 3.2.1 Intensional Semantics -- 3.2.2 Extensional semantics -- 4 Language Adequacy and its Aspects -- 5 Summary -- References -- Chapter 10 What Is the Sense in Logic and Philosophy of Language? -- 1 Introduction -- 2 Main Ideas of the Formalisation of Categorial Language L -- 3 General Assumption Concerning the Logical Sense of Expressions of Language L -- 3.1 Syntactic and Semantic Unambiguity -- 3.2 Categorial Compatibility -- 3.2.1 Postulate of Categorial Compatibility -- 3.2.2 Type-unifying Logical Senses -- 3.2.3 Semantic Compatibility -- 3.3 Structural Compatibility -- 3.3.1 On the Structure of Expressions and Their Semantic Counterparts -- 3.3.2 Principles of Compositionality. 3.3.3 Main Properties of Functions h(f ) -- 3.3.4 Generalisation of Ajdukiewicz's Cancellation Principles -- 3.3.5 Models of L and the Notion of Truth -- 3.3.6 Some Remarks Concerning the Problem of Categories of First-Order Quantifiers -- 4 Final Remarks -- References -- Chapter 11 Categories of First-Order Quantifiers -- 1 Introduction -- 2 Problem of Quantifiers -- 3 Some Intuitive Foundations of the Theory of Categorial Languages -- 3.1 Main Ideas of Formalization of Categorial Language -- 3.2 Categorial Syntax -- 3.2.1 An Algebraic Structure of Categorial Language -- 3.3 Categorial Semantics -- 3.3.1 An aAlgebraic Ontological Structure Corresponding to the Partial Algebra L -- 4 The Solution of the Problem of Quantifiers of 1st-Order -- 4.1 Different Types of the 1st-Order Quantifiers and Their Syntactic Categories -- 4.2 Denotations of 1st-Order Quantifiers and Their Ontological Categories -- 4.2.1 Fregean Semantics -- 4.2.2 Situational Semantics -- 4.3 The Syntactic and Semantic Compatibility of Quantifiers -- 5 Conclusions -- References -- Chapter 12 Logic and the Ontology of Language -- 1 Introduction -- 1.1 Knowledge-Language-Reality -- 1.2 The Logical Conception of Language -- 1.3 The Dual Ontological Status of Linguistic Expressions -- 1.4 Categories of Linguistic Expression and Ontic Categories of Object -- 2 Outline of a Formal-Logical Theory of Language -- 2.1 On the Logical Theory of Linguistic Syntax -- 2.2 The Foundations of the Formal-Logical Theory of the Semantics and Pragmatics of Language -- 3 On the Ontological Neutrality of Logic -- Appendix -- References -- Chapter 13 A Logical Conceptualization of Knowledge on the Notion of Language Communication -- 1 Introduction -- 2 Three Aspects in Formalization of the TLC Theory -- 2.1 The Cognitive-communicative Function of Natural Language According to its Genesis. 2.2 The Functional Approach to Natural Language Analysis -- 2.3 Two Understandings of manner of use and manner of interpreting Language Expressions in Communication -- 3 Language Syntax -- Theory -- 3.1 Two Levels of Formalization of Syntax of Language -- 3.2 Identifiability of linguistic tokens -- 3.2.1 Concatenations -- 3.2.2 Well-formed Expressions -- 4 A Theory of Language Communication - Theory TLC -- 4.1 Token-level -- 4.1.1 Primitive notions of TLC -- 4.1.2 Act of Communication -- 4.1.3 Adequacy of Communication Acts -- 4.1.4 Miscommunication: Misunderstanding -- 4.1.5 Miscommunication: Non-understanding -- 4.2 Type-level -- 4.2.1 Communication by Means of Expression-types -- 4.2.2 Using types and Interpreting types -- 4.2.3 Problem of Adequacy of Language Communication -- 4.2.4 Notions Relating to Language Communication -- 4.2.5 Dual Conceptual Counterparts -- 4.2.6 Adequacy of Language Communication -- 5 Summary -- References. |
| Record Nr. | UNINA-9910633937003321 |
|
Wybraniec-Skardowska Urszula
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Logic - language - ontology : selected works / / Urszula Wybraniec-Skardowska
| Logic - language - ontology : selected works / / Urszula Wybraniec-Skardowska |
| Autore | Wybraniec-Skardowska Urszula |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (305 pages) |
| Disciplina | 401 |
| Collana | Studies in universal logic |
| Soggetto topico |
Language and languages - Philosophy
Logic, Symbolic and mathematical |
| ISBN |
9783031223303
9783031223297 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Acknowledgements -- Contents -- Part I Introduction -- Chapter 1 The Dual Ontological Nature of Language Signs and the Problem of Their Mutual Relations -- 1 Preliminaries -- 2 The Functional Approach Towards Language as a System of Signs. Two Ways of Using Signs -- 3 Ch. S. Pierce's Distinction: Type-token of a Sign -- 4 Controversies Over the Ontological Status of Language Signs and Relations Between Them -- 5 Solving the Problems Under Analysis -- 5.1 The Instantiation View vs the Representation View -- 6 Theoretical Approach to the Problem of Mutual Relations Between Tokens and Types of Signs -- 6.1 Syntax -- 6.2 Semantics -- 6.3 Signs in Language Communication -- 7 Conclusions -- References -- Chapter 2 On the Structure and Contents of the Monograph -- Part II Selected Works -- Chapter 1 On the Type-Token Relationships -- References -- Chapter 2 On the Axiomatic Systems of Syntactically-Categorial Languages -- 1 Introduction -- 2 The Theories TLTk and TETk -- 3 Systems TSCL and TSCω-L -- 4 Systems DTSCL and DTSCω-L -- References -- Chapter 3 The Logical Foundations of Language Syntax Ontology -- Introduction -- 1 Intuitive Understanding of Categorial Language -- 1.1 Initial Syntactic Characteristic of Language -- 1.2 Preliminaries to the Theory of Categorial Languages -- 2 The Formal Theory Tlk - a Concretistic Approach -- 2.1 The Level of Concretes -- Theory T1k -- 2.2 The Level of Types -- Theory T2k -- 3 The Formal Theory Tlp - the Platonizing Approach -- 3.1 The Level of Types -- Theory T2p -- 3.2 The Level of Concretes -- Theory T1p -- 4 Metalogical and Philosophical Consequences -- References -- Chapter 4 On the Eliminatibility of Ideal Linguistic Entities -- 1 Non-uniform Semiotic Characterization of Language -- 2 Preliminary Conventions Concerning Language -- 3 Dual Theories Concepts and Expressions.
4 Theory T1 -- 4.1 Formalization of T1 at the Token Level -- Theory T1(tk) -- 4.1.1 Axioms and Definitions of T1(tk) -- 4.1.2 Major Theorems of the Theory T1(tk) -- 4.2 Formalization of T1 at the Type Level -- Theory T1(tp) -- 5 Theory T2 -- 5.1 Formalization of T2 at the Type Level -- Theory T2(tp) -- 5.2 Formalization of T2 at the Token Level -- Theory T2(tk) -- 6 The Equivalence of the Theories T1 and T2 -- 7 Final Conclusions and Remarks -- References -- Chapter 5 Meaning and Interpretation. Part I -- Introduction -- 1 Preliminaries -- 1.1 The Problem of the Meaning of 'Meaning' -- 1.2 What is a General Theory of Meaning and Interpretation? -- 1.3 The Aim and Assumptions of the Work -- 2 Syntax for Language -- the Theory T -- 2.1 Two Kinds of Syntax: a token-syntax and a type-syntax -- 2.2 Some Basis of the Theory T -- 3 The General Theory of Meaning: the Theory TM -- 3.1 Meaning -- 3.2 Denotation -- 3.3 Meaning and Denotation -- References -- Chapter 6 Meaning and Interpretation. Part II -- 4 The Theory of Meaning and Interpretation: the Theory -- 4.1 Interpretation and Language Communication -- 4.2 Meaning and Interpretation -- 5 Final Remarks -- References -- Chapter 7 Three Principles of Compositionality -- 1 Introduction -- 2 The Theory TC - a Non-formal Characterisation -- 2.1 Ideas -- 2.2 Main Assumptions of the Theory of Syntax -- 2.3 Main Assumptions of the Theory of Semantics and Some Metatheoretical Issues -- 3 The Theory TC- a Formal Approach -- 3.1 Some Formal Foundations of the Theory of Syntax -- 3.2 Formal Foundations of the Theory of Semantics and Some Metatheoretical Issues -- 3.3 Fundamental Theorems of TC -- 4 The Role of the Formal Theory TC in Philosophy -- References -- Chapter 8 On Meta-knowledge and Truth -- Introduction -- 1 Ideas -- 2 Main Assumptions of the Theory of Syntax and Semantics. 2.1 Categorial Syntax and Categorial Semantics -- 2.2 Three Referential Relationships of Wfes -- 2.3 Categorial Indices -- 2.4 Syntactic Operations -- 2.5 Semantic Operations -- 2.6 Knowledge and Cognitive Objects -- 2.7 The Principles of Categorial Agreement -- 2.8 Algebraic Structures of Categorial Language and its Correlates -- 2.9 Compositionality -- 2.10 Concord Between Syntactic Forms and Their Correlates -- 3 Three Notions of Truthfulness -- 3.1 Three Kinds of Models of Language and the Notion of Truth -- 3.2 Three Notions of Truthfulness -- 3.3 Reliability of Cognition of Reality -- 3.4 Operations of Replacement -- 3.5 The Most Important Theorems -- 4 Final Remarks -- References -- Chapter 9 On Language Adequacy -- 1 Introduction -- 2 The Problem Area of Language Adequacy -- 3 An Outline of the Theory of Categorial Language -- 3.1 Categorial Syntax - Theory T -- 3.1.1 General Characteristics of the Categorial Language -- 3.1.2 Two Levels of Formalization of Categorial Syntax -- 3.1.3 The Foundations of the Formal Theory T - the Level of Tokens -- 3.1.4 Foundations of the Formal Theory T - the Level of Types -- 3.2 Categorial Semantics - the Theory ST -- 3.2.1 Intensional Semantics -- 3.2.2 Extensional semantics -- 4 Language Adequacy and its Aspects -- 5 Summary -- References -- Chapter 10 What Is the Sense in Logic and Philosophy of Language? -- 1 Introduction -- 2 Main Ideas of the Formalisation of Categorial Language L -- 3 General Assumption Concerning the Logical Sense of Expressions of Language L -- 3.1 Syntactic and Semantic Unambiguity -- 3.2 Categorial Compatibility -- 3.2.1 Postulate of Categorial Compatibility -- 3.2.2 Type-unifying Logical Senses -- 3.2.3 Semantic Compatibility -- 3.3 Structural Compatibility -- 3.3.1 On the Structure of Expressions and Their Semantic Counterparts -- 3.3.2 Principles of Compositionality. 3.3.3 Main Properties of Functions h(f ) -- 3.3.4 Generalisation of Ajdukiewicz's Cancellation Principles -- 3.3.5 Models of L and the Notion of Truth -- 3.3.6 Some Remarks Concerning the Problem of Categories of First-Order Quantifiers -- 4 Final Remarks -- References -- Chapter 11 Categories of First-Order Quantifiers -- 1 Introduction -- 2 Problem of Quantifiers -- 3 Some Intuitive Foundations of the Theory of Categorial Languages -- 3.1 Main Ideas of Formalization of Categorial Language -- 3.2 Categorial Syntax -- 3.2.1 An Algebraic Structure of Categorial Language -- 3.3 Categorial Semantics -- 3.3.1 An aAlgebraic Ontological Structure Corresponding to the Partial Algebra L -- 4 The Solution of the Problem of Quantifiers of 1st-Order -- 4.1 Different Types of the 1st-Order Quantifiers and Their Syntactic Categories -- 4.2 Denotations of 1st-Order Quantifiers and Their Ontological Categories -- 4.2.1 Fregean Semantics -- 4.2.2 Situational Semantics -- 4.3 The Syntactic and Semantic Compatibility of Quantifiers -- 5 Conclusions -- References -- Chapter 12 Logic and the Ontology of Language -- 1 Introduction -- 1.1 Knowledge-Language-Reality -- 1.2 The Logical Conception of Language -- 1.3 The Dual Ontological Status of Linguistic Expressions -- 1.4 Categories of Linguistic Expression and Ontic Categories of Object -- 2 Outline of a Formal-Logical Theory of Language -- 2.1 On the Logical Theory of Linguistic Syntax -- 2.2 The Foundations of the Formal-Logical Theory of the Semantics and Pragmatics of Language -- 3 On the Ontological Neutrality of Logic -- Appendix -- References -- Chapter 13 A Logical Conceptualization of Knowledge on the Notion of Language Communication -- 1 Introduction -- 2 Three Aspects in Formalization of the TLC Theory -- 2.1 The Cognitive-communicative Function of Natural Language According to its Genesis. 2.2 The Functional Approach to Natural Language Analysis -- 2.3 Two Understandings of manner of use and manner of interpreting Language Expressions in Communication -- 3 Language Syntax -- Theory -- 3.1 Two Levels of Formalization of Syntax of Language -- 3.2 Identifiability of linguistic tokens -- 3.2.1 Concatenations -- 3.2.2 Well-formed Expressions -- 4 A Theory of Language Communication - Theory TLC -- 4.1 Token-level -- 4.1.1 Primitive notions of TLC -- 4.1.2 Act of Communication -- 4.1.3 Adequacy of Communication Acts -- 4.1.4 Miscommunication: Misunderstanding -- 4.1.5 Miscommunication: Non-understanding -- 4.2 Type-level -- 4.2.1 Communication by Means of Expression-types -- 4.2.2 Using types and Interpreting types -- 4.2.3 Problem of Adequacy of Language Communication -- 4.2.4 Notions Relating to Language Communication -- 4.2.5 Dual Conceptual Counterparts -- 4.2.6 Adequacy of Language Communication -- 5 Summary -- References. |
| Record Nr. | UNISA-996503552503316 |
|
Wybraniec-Skardowska Urszula
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Theory of language syntax : categorial approach / / Urszula Wybraniec-Skardowska
| Theory of language syntax : categorial approach / / Urszula Wybraniec-Skardowska |
| Autore | Wybraniec-Skardowska Urszula |
| Edizione | [1st ed. 1991.] |
| Pubbl/distr/stampa | Dordrecht ; ; Boston ; ; London : , : Kluwer Academic Publishers, , [1991] |
| Descrizione fisica | 1 online resource (288 p.) |
| Disciplina | 415 |
| Collana | Nijhoff international philosophy series |
| Soggetto topico |
Categorial grammar
Formal languages Logic, Symbolic and mathematical |
| ISBN |
1-280-94952-X
9786610949526 0-585-26680-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | The Axiomatic Theory TLTk of Label Tokens -- The Axiomatic System TSCL of Simple Categorial Languages -- The Theory TSC?-L of Categorial ?-languages -- Dual Theories. |
| Record Nr. | UNINA-9910511510303321 |
|
Wybraniec-Skardowska Urszula
|
||
| Dordrecht ; ; Boston ; ; London : , : Kluwer Academic Publishers, , [1991] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||