Modalities and Multimodalities

Copertina anteriore
Springer Science & Business Media, 15 set 2008 - 304 pagine
In the last two decades modal logic has undergone an explosive growth, to thepointthatacompletebibliographyofthisbranchoflogic,supposingthat someone were capable to compile it, would ?ll itself a ponderous volume. What is impressive in the growth of modal logic has not been so much the quick accumulation of results but the richness of its thematic dev- opments. In the 1960s, when Kripke semantics gave new credibility to the logic of modalities? which was already known and appreciated in the Ancient and Medieval times? no one could have foreseen that in a short time modal logic would become a lively source of ideas and methods for analytical philosophers,historians of philosophy,linguists, epistemologists and computer scientists. The aim which oriented the composition of this book was not to write a new manual of modal logic (there are a lot of excellent textbooks on the market, and the expert reader will realize how much we bene?ted from manyofthem)buttoo?ertoeveryreader,evenwithnospeci?cbackground in logic, a conceptually linear path in the labyrinth of the current panorama of modal logic. The notion which in our opinion looked suitable to work as a compass in this enterprise was the notion of multimodality, or, more speci?cally, the basic idea of grounding systems on languages admitting more than one primitive modal operator.
 

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Indice

Modal logic and standard logic
1
12 A nonmodal basis for modal logics
4
13 The semantical analysis of PC
9
14 Constructive completeness of PC
12
15 Decidability of PC
14
16 Postcompleteness and other properties of PC
17
17 Exercises
19
18 Further reading
22
64 Other temporal systems
166
65 USlogics metric tense logics and hybrid logics
174
66 Exercises
178
67 Further reading
180
Epistemic logic knowledge and belief
183
72 Knowledge belief and agents
187
73 The minimal logic of knowledge
189
74 The systems KᴹKTᴹS4ᴹ and S5ᴹ
194

The syntax of normal modal systems
25
22 Minimal properties of modal systems
31
23 Systems between K and S5
34
24 Modalities in S5
43
25 Exercises
46
26 Further reading
48
The semantics of normal modal systems
49
32 Carnapian models and relational models
53
33 Correspondence theory and bisimulations
64
34 The method of relational tableaux
72
35 Exercises
81
36 Further reading
84
Completeness and canonicity
87
42 Completeness by Henkins method
92
models versus frames
104
44 The logic of arithmetical provability
107
45 Exercises
114
46 Further reading
115
Incompleteness and finite models
117
52 Finite model property and filtrations
123
53 Exercises
136
54 Further reading
138
Temporal logics
141
62 Completeness and incompleteness of PFlogics
156
63 Monomodal fragments of PFlogics
162
75 Common knowledge and implicit knowledge
196
76 The logic of belief
200
77 Exercises
202
78 Further reading
203
Multimodal logics
205
82 Multimodal languages
206
83 The elementary multimodal systems
209
84 Axioms for multimodal logics
213
85 Multimodal systems and strict implication
220
86 Multimodal models and completeness
222
87 Exercises
235
88 Further reading
237
Towards quantified modal logic
240
92 Necessary and contingent identities
250
93 The problem of completeness in firstorder modal logic
256
94 Inclusive domains and arbitrary domains
263
95 Quantification and multimodalities
267
96 Exercises
270
97 Further reading
271
Bibliography
273
Index of names
289
Index of notation
293
Index of subjects
297
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Informazioni sull'autore (2008)

Walter Carnielli is Full Professor of Logic, Department of Philosophy, State University of Campinas, Brazil. Ex-Director of the Centre for Logic, Epistemology and the History of Science (1998-2004) and full member of the Security and Quantum Information Group-- Institute of Telecommunications, Lisbon, Portugal. Grantee of the Alexander von Humboldt Foundation, Germany, held temporary positions and research appointments in the USA (University of California, Berkeley), as well as in several institutions in Chile, Colombia, Venezuela, Italy, Germany (Münster and Bonn), France, Spain, Portugal and Luxembourg. Carnielli is known for his contribution to the proof theory and semantics for contemporary heterodox (non-classical) logics. Of special significance are his contributions to many-valued logics, paraconsistent logics and combinations of logics. With his students and collaborators Carnielli introduced the possible-translations semantics, which led to a revival in the semantic interpretation of paraconsistent logics, and the concept of logics of formal inconsistency which systematize a great number of extant paraconsistent logics, opening the way to applications of paraconsistency to computer science and to philosophical investigations around the topic. Carnielli has also worked on finite and infinite combinatorics, and shaped, with collaborators, the modulated logics, a wide class of logics dedicated to formalize quantified uncertain reasoning. He is the author or co-author of more than academic 70 publications (papers, books and monographs).

Claudio Pizzi is Full Professor of Philosophy of Science at the Faculty of Letters of the University of Siena (Italy) and contract professor at the University of Milano Bicocca. His main interests are in the field of general modal logic, conditional logic, tense logic and philosophy of causality. In 1973 he translated and edited the Italian version G.E.Hughes and M.J.Cresswell’s "An Introduction to Modal Logic". In the past ten years he has been at the head of a research team which organized the international conferences of the series MBR (Model-Based Reasoning). He is author or coauthor of more that 70 publications , some of which published in Topoi, Notre Dame Journal of Formal Logic, Logique et Analyse, Journal of Philosophical Logic, Studia Logica. His main theoretical contributions concern a theory of rational inference based on the consequence relation (consequential implication) and a theory of causal relations based on iterated conditionals.

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