A general interpreted modal calculus:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Haven [u.a.]
Yale Univ. Press
1972
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXVIII, 327 S. |
| ISBN: | 0300014295 |
Internformat
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| 650 | 4 | |a Évidence | |
| 650 | 4 | |a Description (Philosophy) | |
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Datensatz im Suchindex
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| adam_text | Titel: A general interpreted modal calculus
Autor: Bressan, Aldo
Jahr: 1972
Contents Foreword, by Nuel D. Belnap, Jr. xiii Preface xxvii SEMANTICAL SECTION Memoir 1 A Semantical Analysis of a General Modal Language ML with an Application to an Axlomatlzatlon Problem concerning Classical Mechanics 3 Nl. Introduction 3 PART I An Extensional Semantical Analysis of a General ¡/-sorted Modal Language ML 10 Chapter 1 . Formation Rules for ML and EL 10 N2. The type system 10 N3. The modal [/-sorted language ML and the extensional language EL 11 N4. Some conventions. Church’s lambda operator in ML and EL 13 Chapter 2. Semantics for ML 15 N5. On possibility and how we shall deal with it 15 N6. Objects for EL and QIs for ML . Models and value assignments for EL and ML . Modal product and sum. Abbreviations 17 N7. On the QIs for ML 23 N8. Equivalent QIs in a T-case. Our designation rules, excluding the rule for descriptions 27 N9. On some semantical concepts. Some fundamental formulas, considered by Carnap, which combine modalities with quantification 30 vii
Contents viii N10. Useful theorems on equivalent QIs 33 Nil. The semantical rule for descriptions in ML 1 35 N12. The L-truth in ML 1 of some logical axioms proposed for a y-sorted modal calculus MC 41 N13. On extensions of designators in ML . Comparison with those for some languages by Carnap 48 N14. Some L-true matrices in ML and some fallacies. The lambda operator in ML 51 Chapter 3. Translation in a Strong Sense of the v- sorted modal Language ML into the {v + l)-sorted Extensional Language EL + -*~ 55 N15. Explicit translation rules of ML into E L + -*- 55 N16. Designation rules for EL + 1 and semantical justification of the translation rules 58 PART II Some Useful Concepts Definable in the Modal Language ML ; Applications to Questions concerning Foundations of Classical Mechanics and Everyday Life 61 N17. Introduction 61 Chapter 4. Absolute Concepts and the Definition of Mass 65 N18. Absolute attributes. Extensional and inten- sional collections 65 N19. A rigorous procedure, based on ML and absolute concepts, for defining physical magnitudes of mass points in accordance with Mach’s definition of mass. Natural absolute concepts of real number and mass point 69 N20. Why certain absolute concepts were used in the preceding definition 73 N21. Certain disadvantages of existing extensional theories dealing with foundations of mechanics according to Mach, Kirchoff, and Painleve 81 N22. Usefulness of basing foundations of mechanics according to Painleve ’s ideas on the modal language ML 84 Chapter 5. Absolute Attributes in Connection with a Double Use of Common Nouns, with Logic , and with Natural Numbers 86 N23. A double use of common nouns in physics. On substances and qualities 86
Contents IX N24. Extension of the double use of common nouns. Quasi-absolute concepts 91 N25. A new admissible modal axiom 94 N26. On the concept of closure in ML* 97 N27. A natural absolute concept of natural number defined on purely logical grounds in ML* . Peano’s axioms in ML* 99 Notes to Memoir 1 103 SYNTACTICAL SECTION Memoir 2 A Modal v- sorted Logical Calculus MC 1 Valid in the General Modal Language ML 1 119 N28. Introduction 119 Chapter 6. Reduction of Part of the Modal Calculus MC* to Extensional Logic 124 N29. Deduction in the modal y-sorted calculus MC* 124 N30. On the extensional translations of the axioms of the modal calculus MC y 127 N31. Invariance properties of the entailment relation for the extensional translation. Some consequences within the lower predicate calculus 130 N32. The generalization, duality, equivalence, and replacement theorems in MC* 134 N33. Theorems for shortening deductions in MC* . Rules G and C 139 N34. Axioms and basic theorems for identity in MC* 145 Chapter 7. Modal Theorems on Extensional Matrices , Identity, and Descriptions 147 N35. On extensional matrices in MC* . How to reduce theorems on identity in MC* for these matrices to theorems in extensional logic 147 N36. Theorems on identity in MC* for matrices of any kind 151 N37. Some theorems in MC* on (3x), (3^x), and (3^x) that have no extensional analogues 153 N38. On descriptions in MC* 7 154 N39. Some further theorems based on our axioms for descriptions 161 Chapter 8. On Attributes, Functions, and Natural Numbers 165 N40. Axioms for attributes and functions. First theorems 165
X Contents N41. Some properties of the attributes MConst, MSep, and Abs 168 N42. General theorems on equivalence and substitution 171 N43. General theorems on extensionalization. An extensional form of the equivalence theorem in MC y 174 N44. On the concept of closure in MC y 179 N45. On natural numbers in MC 11 183 Notes to Memoir 2 187 Memoir 3 Elementary Possible Cases, Intensional Descriptions, and Completeness in the Modal Calculus M C v 193 N46. Introduction 193 Chapter 9 . Definition in MC^ of Some Analogues of the r- cases and Their Occurrence 197 N47. Definition in ML of the first analogue E1R of the concept of elementary possible case 197 N48. The second analogue El of the concept of elementary possible case 202 N49. Characterizations of Np and o g using E1R and El. A property of El 204 Chapter 10 . A Definition in MC^ of Some Description Operators; Formal Treatment of the Real Elementary Case by Means of a Primitive Constant 210 N50. Definition in MC y of the intensional description operator i u 210 N51. Definition in MC 1 of the combination i u of t u and i ~ ~ 212 N52. An axiom that introduces a constant representing the real elementary case. The calculus MC !/ and the modal operator ^ 215 N53. Semantics for MCp. Comparison of MC^ with a theory by Prior and Meredith 217 N54. Discussion of t u and i u 221 N55. Solution of some philosophical puzzles by means of 7, Lp, and l u- Comparison with some solutions by Thomason and Stalnaker 223
Contents xi Chapter 11 . Definition within MC of Certain Analogues of the QIs for Ml/; the Translation A -* A*~ of EL and EL +1 into MÎ7 230 N56. A set of absolute concepts in MC that can characterize the object system used in our semantical theory for EL + 1 230 N57. The translation A — A* of EL* and EL +1 into ML* 235 N58. Invariance of the entailment relation for the translation A— A* of EL + * into ML 239 Chapter 12 . A Semantical System for ML Defined in ML Itself; Invariance of the Entailment Relation under the Extensional Translation A — AT in Both Senses 247 N59. An assignment of analogues of QIs made within MC 247 N60. Basic properties of AT* for A in certain classes of designators in ML 256 N61. The analogue of =y within ML 259 N62. A basic conditioned equivalence between every designator A in MC and AT* 261 N63. Invariance of the entailment relation for the extensional translation of MC into EC , in both senses 267 N64. Relative completeness for MC 269 Chapter 13 . The Nonrival Character of Various Modal Systems According to a Suggestion by Lemmon 272 N65. Introduction 272 N66. Definition in ML of certain classes of conceivability properties that are possible analogues for various kinds of Kripke’s acceptability relations 274 N67. The necessity operator L a corresponding to the conceivability property a. Cases connected with Fey’s theory T and S4 275 N68. The a-possibility operator M a . L a in connection with the Brouwerian system B and S5 278 N69. On the Barcan formula and its converse 280 N70. Conclusions about our way of carrying out Lemmon’s suggestions. Hints on identity, descriptions, and classes in connection with L a 285
xii Contents Notes to Memoir 3 287 Appendix A A Semantical Invariance Property of Logical Constants in ML y 291 Appendix B A Generalization of Theor. 19.1 293 Appendix C Some Requirements on the Concepts Real and MP in Connection with the Definition of Mass; Consequence concerning MP 297 Appendix D A Property of Real Following from the Preceding Requirements 302 Appendix E On R. Montague’s Work, “Pragmatics and Intensional Logicâ€
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| language | English |
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| spelling | Bressan, Aldo Verfasser aut A general interpreted modal calculus by Aldo Bressan New Haven [u.a.] Yale Univ. Press 1972 XXVIII, 327 S. txt rdacontent n rdamedia nc rdacarrier Description (Philosophie) Modalité (Logique) Sémantique (Philosophie) Évidence Description (Philosophy) Evidence Modality (Logic) Semantics (Philosophy) Modalkalkül (DE-588)4170286-4 gnd rswk-swf Modalkalkül (DE-588)4170286-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001268624&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bressan, Aldo A general interpreted modal calculus Description (Philosophie) Modalité (Logique) Sémantique (Philosophie) Évidence Description (Philosophy) Evidence Modality (Logic) Semantics (Philosophy) Modalkalkül (DE-588)4170286-4 gnd |
| subject_GND | (DE-588)4170286-4 |
| title | A general interpreted modal calculus |
| title_auth | A general interpreted modal calculus |
| title_exact_search | A general interpreted modal calculus |
| title_full | A general interpreted modal calculus by Aldo Bressan |
| title_fullStr | A general interpreted modal calculus by Aldo Bressan |
| title_full_unstemmed | A general interpreted modal calculus by Aldo Bressan |
| title_short | A general interpreted modal calculus |
| title_sort | a general interpreted modal calculus |
| topic | Description (Philosophie) Modalité (Logique) Sémantique (Philosophie) Évidence Description (Philosophy) Evidence Modality (Logic) Semantics (Philosophy) Modalkalkül (DE-588)4170286-4 gnd |
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