[FOM] Book to appear ("Modalities and Multimodalities")

Walter Carnielli carniell at cle.unicamp.br
Wed Feb 13 18:12:53 EST 2008

``` Dear colleagues:

Springer will  publish an English version  of  our  book  ``Modalità e
Multimodalità"
(originally in Italian) under the title:

"Modalities and Multimodalities"
(W.Carnielli and C. Pizzi)

This book is a completely revised version of its  Italian predecessor,
and intends to provide  a  philosophically and historically based
introduction to modal logic emphasizing  multimodalities, while   stressing
the mathematics behind the  topics in a  clear and gentle pace.

As agreed with Springer, the  material (still in a draft form)
is located in a  protected site, and we will be glad to provide
login  and password to colleagues willing to help in criticizing and
evaluating
the  project; several  colleagues have  already responded to our technical,
philosophical or historical questions  on  (multi)modalities, and we are
acknowledging  their help in the preface.

Here is a  detailed description of the contents:

Chapter 1-  Modal logic and standard logic
1.1 Modal notions and quantifiers
1.2 A non-modal basis for modal logics
1.3 The semantical analysis of PC .
1.4 Constructive completeness of PC
1.5 Decidability of PC
1.6 Post-completeness and other properties of PC
1.7 Exercises

Chapter 2- The syntax of normal modal systems
2.1 The relationship among modal operators
2.2 Minimal properties of modal systems
2.3 Systems between K and S5
2.4 Modalities in S5
2.5 Exercises

Chapter 3- The semantics of normal modal systems
3.1 Matrices and Dugundji's Theorem
3.2 Carnapian models and relational models
3.3 Correspondence theory and bisimulations
3.4 The method of relational tableaux
3.5 Exercises

Chapter 4 -Completeness and canonicity
4.1 The constructive completeness of K and KT
4.2 Completeness by Henkin’s method
4.3 Completeness: models versus frames
4.4 The logic of arithmetical provability
4.5 Exercises

Chapter 5 -Incompleteness and finite models
5.1 An incompleteness result
5.2 Finite model property and filtrations
5.3 Exercises

Chapter 6- Temporal logics
6.1 Logics with two primitive modal operators
6.2 Completeness and incompleteness of PF-logics
6.3 Monomodal fragments of PF-logics
6.4 Other temporal systems
6.5 US-logics and metric tense logics
6.6 Exercises

Chapter 7- Epistemic logic: knowledge and belief
7.1 To know, to believe and their difficulties
7.2 Knowledge, belief and agents
7.3 The minimal logic of knowledge
7.4 The systems Km, KTm, S4m and S5m
7.5 Common knowledge and implicit knowledge
7.6 The logic of belief
7.7 Exercises

Chapter 8- Multimodal logics
8.1 What are multimodalities?
8.2 Multimodal languages
8.3 The elementary multimodal systems
8.4 Axioms for multimodal logics
8.5 Multimodal systems and strict implication
8.6 Multimodal models and completeness
8.7 Exercises

Chapter 9- Towards quantified modal logic
9.1 Propositional quantifiers
9.2 Necessary and contingent identities
9.3 The problem of completeness in first-order modal logic
9.4 Inclusive domains and arbitrary domains
9.5 Quantification and multimodalities
9.6 Exercises

Bibliography

Index of Names
Index of Notation
Index of Subjects

In case of  interest, please write to us.

Best regards,

Walter Carnielli and Claudio Pizzi

+++++++++++++++++++++++++++++++++++++++++++++++++
Walter Carnielli
Centre for Logic, Epistemology and the History of Science – CLE
State University of Campinas –UNICAMP
P.O. Box 6133 13083-970 Campinas -SP, Brazil
Phone: (+55) (19) 3788-6519
Fax: (+55) (19) 3289-3269
e-mail: carniell at cle.unicamp.br
Website: http://www.cle.unicamp.br/prof/carnielli

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