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1. Modal Logic (Stanford Encyclopedia Of Philosophy)
A Modal is an expression (like ÂnecessarilyÂ or ÂpossiblyÂ) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking,
http://plato.stanford.edu/entries/logic-modal/
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##### Modal Logic
First published Tue Feb 29, 2000; substantive revision Sat May 5, 2007
##### 1. What is Modal Logic?
A list describing the best known of these logics follows. Logic Symbols Expressions Symbolized Modal Logic It is necessary that .. It is possible that .. Deontic Logic O It is obligatory that .. P It is permitted that .. F It is forbidden that .. Temporal Logic G It will always be the case that .. F It will be the case that .. H It has always been the case that .. P It was the case that.. Doxastic Logic B x x believes that ..
##### 2. Modal Logics
The most familiar logics in the modal family are constructed from a weak logic called K (after Saul Kripke). Under the narrow reading, modal logic concerns necessity and possibility. A variety of different systems may be developed for such logics using K as a foundation. The symbols of K K results from adding the following to the principles of propositional logic.

2. Modal Logic - Wikipedia, The Free Encyclopedia
In formal logic, a Modal logic is any logic for handling Modalities concepts like possibility, existence, and necessity. logics for handling a number of
http://en.wikipedia.org/wiki/Modal_logic
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##### Modal logic
Jump to: navigation search In formal logic , a modal logic is any logic for handling modalities : concepts like possibility existence , and necessity . Logics for handling a number of other ideas, such as eventually formerly can could might may must are by extension also called modal logics, since it turns out that these can be treated in similar ways. A formal modal logic represents modalities using unary modal operators . For example, "Jones's murder was a possibility"; "Jones was possibly murdered"; and "It is possible that Jones was murdered", all contain the notion of possibility; in a modal logic this is represented as an operator, Possibly , attaching to the sentence Jones was murdered The basic modal operators are usually written (or L ) for Necessarily and (or M ) for Possibly . In a classical modal logic , each can be expressed by the other and negation Thus it is possible that Jones was murdered if and only if it is not necessary that Jones was not murdered.

3. Modal Logic
A discussion of Modal logic by John McCarthy.
http://www-formal.stanford.edu/jmc/mcchay69/node22.html
Next: Logic of Knowledge Up: DISCUSSION OF LITERATURE Previous: DISCUSSION OF LITERATURE
##### Modal Logic
It is difficult to give a concise definition of modal logic. It was originally invented by Lewis (1918) in an attempt to avoid the `paradoxes' of implication (a false proposition implies any proposition). The idea was to distinguish two sorts of truth: necessary truth and mere contingent truth. A contingently true proposition is one which, though true, could be false. This is formalized by introducing the modal operator (read `necessarily') which forms propositions from propositions. Then p 's being a necessary truth is expressed by 's being true. More recently, modal logic has become a much-used tool for analyzing the logic of such various propositional operators as belief, knowledge and tense. There are very many possible axiomatizations of the logic of none of which seem more intuitively plausible than many others. A full account of the main classical systems is given by Feys (1965), who also includes an excellent bibliography. We shall give here an axiomatization of a fairly simple modal logic, the system M of Feys - von Wright. One adds to any full axiomatization of propositional calculus the following:

 4. Modal Logic A concise introduction to Modal logics by Anthony A. Aaby.http://moonbase.wwc.edu/~aabyan/Logic/Modal.html

5. Modal Logic
8 The Absolutely Strict Systems Modal Sequent-logic 9 The Absolutely Strict Systems - Tableaux 10 The Systems of Complete Modalization - S3Â° and S3
http://www.clas.ufl.edu/users/jzeman/modallogic/
##### Modal Logic
Â© 1973-2002 by J. Jay Zeman
##### The Lewis-Modal Systems
Page Finder Preface Expanded Contents 1: A Note on Notation ... Bibliography Originally Published : Oxford: The Clarendon Press, 1973

6. Modal Logic
Electronic support for Modal logic,by Patrick Blackburn,Maarten de Rijke,and Yde Venema.
http://www.mlbook.org/
##### Modal Logic
Electronic support for Modal Logic,by Patrick Blackburn,Maarten de Rijke,and Yde Venema
modal logic

7. Modal Logic
This is the most important rule of inference in Modal logic. It basically asserts that anything derivable from necessary truths is a necessary truth.
http://mally.stanford.edu/tutorial/modal.html
##### Modal Logic Examples
For convenience, we reproduce the item Logic/Modal Logic of Principia Metaphysica in which the modal logic is defined: In this tutorial, we give examples of the axioms, consider some rules of inference (an in particular, the derived Rule of Necessitation), and then draw out some consequences. To help us reason with modal notions, we may intuitively appeal to the notion of a possible world, i.e., a way things might have gone. Our world is just one possible world of an infinite number of such worlds. For now, let us suppose this idea is well-understood (in Principia Metaphysica it can be precisely defined). Using the notion of a possible world, we may intuitively think of the claim: as the claim: And we may intuitively think of the claim: as the claim: We will exploit these intuitions in what follows to help us to get a picture of (i.e., intuitive model of) the axioms.
##### Examples of the Axioms and Rules
Instance of Axiom 1 Recall that the predicate A!x asserts that x is abstract . Suppose that Rx asserts that x is round . Then this instance of Axiom 1 asserts If the conditional, if x is abstract then x is not round, is necessary, then if it is necessary that x is abstract, it is necessary that x is not round

8. Modal Logic - Cambridge University Press
Now available in paperback, this is a modern, advanced textbook on Modal logic, a field which caught the attention of computer scientists in the late 1970s.
http://books.cambridge.org/0521527147.htm
Home Catalogue Google Book Search Search this book
##### Details
• 20 line diagrams Page extent: 576 pages Size: 228 x 152 mm Weight: 0.914 kg
Textbook
##### Maarten de Rijke
Universiteit van Amsterdam
##### Yde Venema
Universiteit van Amsterdam
##### Paperback
DOI:
• There was also a Hardback of this title but it is no longer available Published August 2002
##### Temporarily unavailable - no date available
(Stock level updated: 03:41 GMT, 24 December 2007)
##### Textbook
Ã¢ÂÂ¢ Now available in paperback Ã¢ÂÂ¢ Two distinct tracks for beginners and experts, carefully signposted Ã¢ÂÂ¢ Appendices cover mathematical prerequisites
##### Contents
1. Basic concepts; 2. Models; 3. Frames; 4. Completeness; 5. Algebras and general frames; 6. Computability and complexity; 7. Extended modal logic.
##### Reviews
Ã¢ÂÂThis book is undoubtedly going to be the definitive book on modal logic for years to come.Ã¢ÂÂ M. Vardi, Rice University Ã¢ÂÂÃ¢ÂÂ¦ will take you from ground level to one of the best vista points on modal logic today. The authors are expert guides: they know the land from first-hand research experience, but they are committed to taking all newcomers there as well.Ã¢ÂÂ Johan van Bentem, University of Amsterdam

9. AiML: Advances In Modal Logic
Modal logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical discipline that deals with
http://www.aiml.net/
home news background conferences volumes ... tools
Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical discipline that deals with (restricted) description languages for talking about various kinds of relational structures. Advances in Modal Logic is a bi-annual international conference and book series in Modal Logic. The aim of the conference series is to report on important new developments in pure and applied modal logic, and to do so at varying locations throughout the world. The book series is based on the conferences. Please consult the background pages for further details.
##### The 10th Asian Logic Conference
(Kobe, Japan, September 1-6, 2008) Several short course lectures (four hours each), plenary invited talks (one hour each) and special sessions are planned apart from contributed talks.
##### Advances in Modal Logic 2006
AiML 2006 was organized by Guido Governatori with Ian Hodkinson and Yde Venema as the programme co-chairs. It was held in Noosa, Queensland, Australia, 25-28 September 2006. Conference local website: http://www.itee.uq.edu.au/~aiml06/

10. Advances In Modal Logic 2008
Advances in Modal logic is an initiative aimed at presenting an upto-date picture of the state of the art in Modal logic and its many applications.
http://aiml08.loria.fr/
##### 9-12 September 2008, Nancy, France
Advances in Modal Logic is an initiative aimed at presenting an up-to-date picture of the state of the art in modal logic and its many applications. The initiative consists of a conference series together with volumes based on the conferences. The conference is the main international forum at which research on all aspects of modal logic is presented. The Advances in Modal Logic Initiative was founded in 1995 and the first AiML Conference was held in 1996 in Berlin, Germany. Since then the AiML Conference has been organised on an bi-annual basis with previous meetings being held in 1998 in Uppsala, Sweden, in 2000 in Leipzig, Germany (jointly with ICTL-2000), in 2002 Toulouse, France, in 2004 in Manchester, UK, and in 2006 in Noosa, Australia. In 2008, Advances in Modal Logic will be organized by LORIA , le Laboratoire Lorrain de Recherche en Informatique et ses Applications (Lorraine Laboratory of IT Research and its Applications), in Nancy, France. The Call for Papers is now available.

11. Handbook Of Modal Logic, 3 - Elsevier
The Handbook of Modal logic contains 20 articles, which collectively introduce contemporary Modal logic, survey current research, and indicate the way in
http://www.elsevier.com/wps/product/cws_home/708884

12. AiML: Tools
In recent years the number of computational tools useful for Modal logics, and related logics, has increased significantly, and is continuously increasing.
http://www.cs.man.ac.uk/~schmidt/tools/
home news background conferences ... tools
In recent years the number of computational tools useful for modal logics, and related logics, has increased significantly, and is continuously increasing. The following is an incomplete list of
If you'd like something added or changed please let Renate Schmidt (schmidt@cs.man.ac.uk) know.
##### Accessible theorem provers
• BLIKSEM - Hans de Nivelle's resolution based theorem prover for modal logic and first-order logic with equality. DLP - An experimental tableaux-based inference system by Peter Patel-Schneider for a range of description logics. FaCT++ - A tableaux-based description logic OWL reasoner by Ian Horrocks and Dmitry Tsarkov. Successor of FaCT Gost - A Lisp implementation of a tableau algorithm for GF1-, a sublogic of the "First Guarded Fragment". KtSeqC - A theorem prover for the minimal tense logic Kt. Logics Workbench (LWB) - A sequent based theorem prover for a range of propositional logics, including modal logics, temporal logics, intuitionistic logics and nonmonotonic logics. WWW interface ModLeanTAP - A lean implementation of a free variable tableau calculus for a range of propositional modal logics.

13. AiML 2006
Advances in Modal logic is an initiative aimed at presenting an upto-date The Advances in Modal logic Initiative was founded in 1995 and the first AiML
http://www.itee.uq.edu.au/~aiml06/
##### 25-28 September 2006, Noosa, Sunshine Coast, Queensland, Australia
Advances in Modal Logic is an initiative aimed at presenting an up-to-date picture of the state of the art in modal logic and its many applications. The initiative consists of a conference series together with volumes based on the conferences.
The conference is the main international forum at which research on all aspects of modal logic is presented. The Advances in Modal Logic Initiative was founded in 1995 and the first AiML Conference was held in 1996 in Berlin, Germany. Since then the AiML Conference has been organised on an bi-annual basis with previous meetings being held in 1998 in Uppsala, Sweden, in 2000 in Leipzig, Germany (jointly with ICTL-2000), in 2002 Toulouse, France, and in 2004 in Manchester, UK.
##### Important Dates
• 27 March 2006: Submission Deadline 26 May 2006: Author Notification 30 June 2006: Camera Ready 25-28 September 2006: Conference
Home Committees Call for Papers Registration ...
Guido Governatori

For problems or questions regarding this Web site contact Guido Governatori
Last updated: 2006-09-17.

14. Philosophical Dictionary: Leibniz-Logos
The formalization of Modal logic for the propositional calculus Also see SEP on Modal logic and medieval theories of Modality, and Michael Huemer.
http://www.philosophypages.com/dy/l5.htm
 Philosophy Pages Search Dictionary Study Guide ... Locke Leibniz, Gottfried W. German mathematician and philosopher who invented the integral calculus independently of Newton and developed an intricate pluralistic philosophy, according to which individual substances are dimensionless mathematical points ( monads ) functioning in a pre-established harmony with each other. For a discussion of his life and works, see Leibniz Lenin, Vladimir Ilyich Russian revolutionary who led the October Revolution of 1917 and became head of state. His State and Revolution at Amazon.com Marx 's principles to the success of the Bolshevik revolution. On Lenin's view, the dictatorship of the proletariat is a temporary expedient that will inevitably lead to the creation of a truly socialist government. In his Materialism and Empiro-Criticism at Amazon.com Philosophical Notebooks (1929), Lenin sought to purge Marxism of any tendency toward subjective idealism by encouraging critical study of Hegel Recommended Reading: Vladimir Lenin, Essential Works of Lenin: 'What Is to Be Done?' and Other Writings at Amazon.com

15. Open Site - Science: Mathematics: Logic: Modal Logic
Modal logic deals with sentences that are qualified by Modalities, the most typical of which are necessity and its dual possibility. What makes these Modal
http://open-site.org/Science/Mathematics/Logic/Modal_Logic
Enter your search terms Submit search form Web open-site.org
Top
... Logic : Modal Logic
Pages Modal logic deals with sentences that are qualified by modalities, the most typical of which are necessity and its dual possibility . What makes these modal operators essentially different from classical logic operators (NOT, AND, etc.) is that they are not truth functions, i.e. the truth value of a compond formula involving modaities depends on more than just the truth values of its subformulas.
##### Varieties of modl logics
Modal logics differ in what collections of modalities they allow, how the existing modal operators are interpreted, and how the logic is axiomatized. Below is an incomplete list of various interpretations of modal operators studied in the literature:
Possible readings of []A: "it is necessary that A", "A is provable", "I know that A", "everyone knows that A", "I believe that A", "A is obligatory", "A will always be true", "A has always been true", etc.
Possible readings of A>B: "B is interpretable in A", "A logically implies B", etc.

16. John Halleck's Logic Systems
This started as a list of Modal logic systems I encountered. In the end it is a list of mostly Modal logic systems. (But even at that, the list has grown
http://home.utah.edu/~nahaj/logic/structures/systems/index.html
##### Logic Systems
This page is the actual full page of serious references. If you are looking for just a few systems but lots of flashy diagrams, you want http://www.cc.utah.edu/~nahaj/logic/structures/ which also gives an explaination of notations used and other housekeeping information. This started as a list of Modal Logic systems I encountered. In the end it is a list of mostly modal logic systems. (But even at that, the list has grown LARGE.) Dr. Peter Suber has a list of the types of logics that covers the various types. It provides a bibliography of the various kinds of logics for a much wider class of logics than I cover, but no cross references of alternate names, and few individual representitives. This list documents the fact that many systems have been investigated under different names, and that some names have historically been applied to several different systems. I'm not aware of any other such cross reference on the net (or anywhere else). If you are aware of such a reference, please drop me a line. "To do" list Jump to systems starting with: A B C D ... Bibliography 0p is called the Trivial System "10 modalities calculus" (Becker) =[ Parry S5 (Lewis) 2' (Feys) =[ Feys T (Feys) 2r (Pledger) =[ Pledger S5 (Lewis) 3q (Pledger) =[ Pledger 4q (Pledger) =[ Pledger Pledger , p270]= S4.1 (McKinsey) = [

17. Modal Logic --Â  Britannica Online Encyclopedia
Britannica online encyclopedia article on Modal logic branch of logic that deals with Modalities (such properties of propositions as necessity, contingency
http://www.britannica.com/eb/article-9053136/modal-logic
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##### modal logic
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18. Restricted Classical Modal Logics -- Mortari 15 (56): 741 -- Logic Journal Of IG
We consider a family of noncongruential Modal logics obtained by restricting the smallest classical Modal logic E and some of its extensions.
http://jigpal.oxfordjournals.org/cgi/content/abstract/15/5-6/741
@import "/resource/css/hw.css"; @import "/resource/css/igpl.css"; Skip Navigation Oxford Journals
Logic Journal of IGPL Advance Access originally published online on October 12, 2007
Logic Journal of IGPL 2007 15(5-6):741-757; doi:10.1093/jigpal/jzm046
most recent
References
##### Restricted Classical Modal Logics
Cezar A. Mortari
Abstract We consider a family of noncongruential modal logics obtained by restricting the smallest classical modal logic E and some of its extensions. We show that these logics are also properly contained in Lemmon's ; semantics for them are adapted from Cresswell's semantics for and from neighborhood semantics for classical modal logics. Some extensions of these logics

19. Modal Logic
Modal logic provides analytical decision support services aimed at business process optimization, risk analysis, forecasting and pricing strategies,
http://modallogic.com/
 Home About Us Contact Us Products ... Library Optimize Business Process Identify performance metrics Develop strategies to maximize performance Implement systems to monitor performance Read more .. Manage Risks Pro-Actively Identify sources of risk Quantify levels of risk and impacts Implement mitigation strategies Read more ..

20. Coalgebra And Modal Logic
Coalgebras and Modal logic. Some colleagues having done work on logics for coalgebras ESSLLI 01 course on `Coalgebras and Modal logic
http://www.mcs.le.ac.uk/~akurz/cml.html
##### Coalgebra and Modal Logic
Coalgebras and Modal Logic
Some colleagues having done work on logics for coalgebras
ESSLLI'01 course on `Coalgebras and Modal Logic'

21. The Modal Logic \$100 Challenge
In Modal logics, the lattice of relationships between the Kripke based logics up to S5 is a well known structure. These relationships have been established
http://www.cs.miami.edu/~tptp/HHDC/
##### Extended for 2007
Logic provides a rich source of challenges, to determine the relationships between different logics, and between different axiomatizations of the same logic. In modal logics, the lattice of relationships between the Kripke based logics up to S5 is a well known structure. These relationships have been established over the years using a variety of techniques. Each logic in such a lattice has a basis, consisting of a set of axioms and a suite of inference rules. Theorems of the logic are the axioms, and any theorems that can be derived from prior theorems using the inference rules. There are three possible relationships between two logics, or two axiomatizations of one logic:
• The logics are equivalent - they have the same theorems. For example, the KM4B axiomatization of the modal logic S5 is equivalent to the KM5 axiomatization.
• One logic is stronger than the other - the theorems of the first are a strict superset of the theorems of the other. For example, modal logic S5 is stronger than S4.
• The logics are incomparable - each has some theorems that the other does not. For example, modal logic K is incomparable with S1.

22. LICS'O5 - IMLA'05
Intuitionistic Modal logics and Applications Workshop (IMLA 05) INVITED TALK Intuitionistic Modal logic observations from algebra and duality
http://www.cs.cmu.edu/~fp/imla05/
Program Committee: Natasha Alechina (Nottingham, UK)
Frank Pfenning
(Carnegie Mellon, USA)
Carsten Schuermann
(Yale, USA)
Alex Simpson
(Edinburgh, UK)
Valeria de Paiva
(PARC, USA)
Contact Information: Dr. Valeria de Paiva
PARC, Palo Alto Research Center
Email: paiva at parc . xerox . com
Prof. Frank Pfenning
Department of Computer Science
Carnegie Mellon University Email: fp at cs . cmu . edu Important Dates: Workshop Date: 30 June 2005 LICS'05 Dates: 26-29 June 2005 Registration and Accommodations LICS/IMLA Registration: https://securestore.cti.depaul.edu/LICS2005/ Local Information: http://lics.cs.depaul.edu/
##### Intuitionistic Modal Logics and Applications Workshop (IMLA '05) June 30, 2005
A Logic in Computer Science Conference affiliated workshop Constructive modal logics and type theories are of increasing foundational and practical relevance in computer science. Sample applications are in type disciplines for programming languages, and meta-logics for reasoning about a variety of computational phenomena. Theoretical and methodological issues center around the question of how the proof-theoretic strengths of constructive logics can best be combined with the model-theoretic strengths of modal logics. Practical issues center around the question which modal connectives with associated laws or proof rules capture computational phenomena accurately and at the right level of abstraction.

Advances in Modal logic is a unique forum for presenting the latest results and new directions of research in Modal logic. The topics dealt with are of
http://www.worldscibooks.com/compsci/5114.html
 Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Bookshop New Titles Editor's Choice Bestsellers Book Series ... Join Our Mailing List ADVANCES IN MODAL LOGIC Volume 3 edited by Frank Wolter (University of Leipzig, Germany) , Heinrich Wansing (Dresden University of Technology, Germany) , Maarten de Rijke (University of Amsterdam, The Netherlands) (King's College London, UK) Advances in Modal Logic is a unique forum for presenting the latest results and new directions of research in modal logic. The topics dealt with are of interdisciplinary interest and range from mathematical, computational, and philosophical problems to applications in knowledge representation and formal linguistics. Volume 3 presents substantial advances in the relational model theory and the algorithmic treatment of modal logics. It contains invited and contributed papers from the third conference on "Advances in Modal Logic", held at the University of Leipzig (Germany) in October 2000. It includes papers on dynamic logic, description logic, hybrid logic, epistemic logic, combinations of modal logics, tense logic, action logic, provability logic, and modal predicate logic. Contents: Homophonic Theory of Truth for Tense Logic (Torben BraÃ¼ner) Weak Necessity on Weak Kleene Matrices (F Correia) Normal Products of Modal Logics (Y Hasimoto) Outline of a Logic of Action (K Segerberg) and other papers Readership: Researchers and advanced students in mathematical logic, philosophical logic, computer science logic, artificial intelligence and formal linguistics.

24. Shadow Â» Blog Archive Â» John McArthy On Modal Logic
Describes some of his latest work on how Modal calculi describe several possible worlds at once, instead of just one; photo, examples.
http://www.garyfeng.com/wordpress/2004/11/30/john-mcarthy-on-modal-logic/
Mike Terry Modal logic
##### John McArthy on Modal logic
Tags: Original URL John McArthy, creater of Lisp, in an extension of his book on philosophical problems in AI, touched on modal logic The idea is that modal calculi describe several possible
worlds at once, instead of just one. Statements are not assigned a
single truth-value, but rather a spectum of truth-values, one in each
possible world. Now, a statement is necessary when it is true in
all
different modal logics (and even then not all of them) one has to be
a bit more subtle, and have a binary relation on the set of possible
in a world when it is true in all alternatives to that world. Now it
turns out that many common axioms of modal propositional logics
correspond directly to conditions of alternativeness. Thus for
instance in the system M above, Ax . 1 corresponds to the reflexiveness of the alternativeness relation; corresponds to its transitivity. If we make the alternativeness relation into an equivalence relation, then this is just like not

25. First-Order Modal Logic - Logic Journals, Books & Online Media | Springer
FirstOrder Modal logic - logic. Fitting and Mendelsohn present a thorough treatment of first-order Modal logic, together with some propositional background
http://www.springer.com/978-0-7923-5335-5
Please select Africa Asia Australia / Oceania Europe France Germany Italy North America South America Switzerland United Kingdom All Author/Editor Title ISBN/ISSN Series Journals Reference Works Series Contact Select your subdiscipline Aesthetics Ethics History of Philosophy Logic Non-Western Philosophy Ontology Phenomenology Philosophy of Languages Philosophy of Law Philosophy of Religion Philosophy of Science Political Philosophy Pragmatism Select a discipline Astronomy Biomedical Sciences Chemistry Computer Science Economics Education Engineering Environmental Sciences Geography Geosciences Humanities Law Life Sciences Linguistics Materials Mathematics Medicine Philosophy Physics Psychology Public Health Social Sciences Statistics Home Philosophy Logic
##### First-Order Modal Logic
Series: Synthese Library , Vol. 277
Fitting , M., Mendelsohn , Richard L.
1999, 292 p., Softcover
ISBN: 978-0-7923-5335-5
The book covers quantification itself, including the difference between actualist and possibilist quantifiers; equality, leading to a treatment of Frege's morning star/evening star puzzle; the notion of existence and the logical problems surrounding it; non-rigid constants and function symbols; predicate abstraction, which abstracts a predicate from a formula, in effect providing a scoping function for constants and function symbols, leading to a clarification of ambiguous readings at the heart of several philosophical problems; the distinction between nonexistence and nondesignation; and definite descriptions, borrowing from both Fregean and Russellian paradigms.

26. DI & CoS - Modal Logic
Several normal propositional Modal logics are systematically presented in the calculus of structures and cut elimination is proved. By Alessio Guglielmi.
http://alessio.guglielmi.name/res/cos/ML/index.html
##### Deep Inference and the Calculus of Structures Modal Logic
• Classical Modal Display Logic in the Calculus of Structures and Minimal and Cut-free Deep Inference Calculi for S5
and Alwen Tiu
We begin by showing how to faithfully encode the Classical Modal Display Logic (CMDL) of Wansing into the Calculus of Structures (CoS) of Guglielmi. Since every CMDL calculus enjoys cut-elimination, we obtain a cut-elimination theorem for all corresponding CoS calculi. We then show how our result leads to a minimal cut-free CoS calculus for modal logic S5. As far as we know, no other existing CoS calculi for S5 enjoy both these properties simultaneously. Pdf 4 May 2007
Journal of Logic and Computation
The family of normal propositional modal logic systems is given a very systematic organisation by their model theory. This model theory is generally given using frame semantics, and it is systematic in the sense that for the most important systems we have a clean, exact correspondence between their constitutive axioms as they are usually given in a Hilbert-Lewis style and conditions on the accessibility relation on frames. By contrast, the usual structural proof theory of modal logic, as given in Gentzen systems, is ad-hoc. While we can formulate several modal logics in the sequent calculus that enjoy cut-elimination, their formalisation arises through system-by-system fine tuning to ensure that the cut-elimination holds, and the correspondence to the formulation in the Hilbert-Lewis systems becomes opaque.

 27. Belief And Modal Logics One way of representing such things is to use Modal logic. In Modal logic, the semantics of expressions is defined in terms of the truth of things inhttp://www.cee.hw.ac.uk/~alison/ai3notes/subsection2_9_1_2.html

28. ESSLLI 2007: Neighborhood Models
Modal logic an Introduction by Brian Chellas (Cambridge University Press, I will introduce neighborhood semantics for Modal logic and discuss some
http://staff.science.uva.nl/~epacuit/nbhd_esslli.html
##### 12 - 17 August, 2007 European Summer School for Logic, Language and Infromation
Dublin, Ireland
Course Information
Literature Course Schedule Day 1 ... Day 5
##### Course Information
Intstructor: Eric Pacuit ( ILLC, University of Amsterdam
Prerequisites: Although the course will be self-contained, it is recommended to have basic knolwedge of modal logic. For example, it will be useful to be familiar with:
1. The first four chapters (skipping the advanced track sections) of Modal Logic by P. Blackburn, M. de Rijke and Y. Venema (Cambridge University Press, 2001).
- and/or -
Modal Logic: an Introduction
by Brian Chellas (Cambridge University Press, 1980).
Content: Dana Scott and Richard Montague (influenced by a paper written by McKinsey and Tarski in 1944) proposed independently in 1970 a new semantic framework for the study of modalities, which today is known as neighborhood semantics. The semantic framework permits the development of elegant models for the family of classical modal logics, including many interesting non-normal modalities from Concurrent Propositional Dynamic Logic, to Coalitional Logic to various monadic operators of high probability used in various branches of game theory. I will introduce neighborhood semantics for modal logic and discuss some applications. The main goal of the corse is to understand the basic techniques and results of neighborhood semantics for modal logics and to understand the exact relationship between the standard relational semantics and neighborhoood semantics for modal logics.

29. Molle Modal Logic Prover
Molle is a crossplatform prover for Modal logic, that exploits the Modal semantic tableaux method. It features a very usable graphical interface,
http://molle.sourceforge.net/
 Home About Download Screen shots ... Send us feedback! Molle is a cross-platform prover for modal logic, that exploits the modal semantic tableaux method. It features a very usable graphical interface, with interactive representation of generated models. Molle is maintained by Dipartimento di Elettronica e Informazione , at Politecnico di Milano

30. Peter Suber, "Non-Standard Logics"
logics of permission and obligation (derived from Modal logics of possibility . A Short Introduction to Modal logic. University of Chicago Press, 1992.
http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm
 A Bibliography of Non-Standard Logics Peter Suber Philosophy Department Earlham College In the kinds of non-standard logics included, this bibliography aims for completeness, although it has not yet succeeded. In the coverage of any given non-standard logic, it does not at all aim for completeness. Instead it aims to include works suitable as introductions for those who are already familiar with standard first-order logic. Looking at these non-standard logics gives us an indirect, but usefully clear and comprehensive idea of the usually hazy notion of "standardness". In standard first-order logics: Wffs are finite in length (although there may be infinitely many of them). Rules of inference take only finitely many premises. There are only two truth-values, "truth" and "falsehood". Truth-values of given proposition symbols do not change within a given interpretation, only between or across interpretations. All propositional operators and connectives are truth-functional. "p ~p" is provable even if we do not have p or ~p separately; that is, the principle of excluded middle holds.

 31. Modal Logic For Philosophers - Cambridge University Press Designed for use by philosophy students, this book provides an accessible, yet technically sound treatment of Modal logic and its philosophical applicationshttp://www.cambridge.org/us/catalogue/catalogue.asp?isbn=9780521682299

32. The Modal Logic Of Agency
In this paper I discuss and develop suggestions concerning how to use systems of Modal logic to analyse notions pertaining to agency.
http://www.hf.uio.no/ifikk/filosofi/njpl/vol2no2/agency/index.html
Next: 1. Introduction: Agency, Goal-directedness Up: Contents
##### The Modal Logic of Agency
Dag Elgesem
The National Committees for Research Ethics
Norway
##### Abstract:
In this paper I discuss and develop suggestions concerning how to use systems of modal logic to analyse notions pertaining to agency. In the first part I deal with the accounts of PÃ¶rn, Brown, and Belnap, thus motivating the search for a more fine-grained framework. The first step in the development of such a framework is the adoption of a rich semantical structure inspired by Gerd Sommerhoff's theory of goal-directedness. Next I argue that this framework can be used as the basis for a sufficiently complex logic of agency. I study the proposed logic in the last part of the paper.
##### Footnotes
I am grateful to Andrew J.I. Jones for helpful comments and suggestions.

33. Axioms For Modal Epistemic Logic
Modal logics, one for each agent. For simplicity s sake it is usually assumed that the agents are homogeneous, i.e., they can be described by the same logic
http://www.informatik.uni-leipzig.de/~duc/Thesis/node11.html
Next: Possible-worlds semantics for epistemic Up: The ``received view'': modal Previous: The language of epistemic Contents
##### Axioms for modal epistemic logic
A modal epistemic logic for agents is obtained by joining together modal logics, one for each agent. For simplicity's sake it is usually assumed that the agents are homogeneous, i.e., they can be described by the same logic. So an epistemic logic for agents consists of copies of a certain modal logic. Such a system is denoted by the same name as the modal system, but with the subscript , e.g., K is the logic consisting of copies of the logic K
Stronger logics can be obtained by adding additional principles, which express the desirable properties of the concept of knowledge, to the basic system K . The following properties are often considered:
(T) (D)
The formula ( T ) states that knowledge must be true. One normally takes this property to be the major one distinguishing knowledge from belief: you can have false beliefs, but you cannot know something that is not true. For that reason (T) is sometimes called the Knowledge Axiom or the Truth Axiom (for knowledge). Systems containing the schema

34. Thinking Clearly Â» Modal Logic
logic Programming, Modal logics, and nonmonontonic logics. You are currently browsing the archives for the Modal logic category.
http://clarkparsia.com/weblog/category/logic/modal/
##### Thinking Clearly
Make lots of money through stealth in shadows
##### A Very Nice Paper
Franz Baadar is a very smart cookie with a lot of excellent, influential work. One of my favorite papers by him is not one that reports results, but instead is an overview piece called Logic-based Knowledge Representation per se Enjoy. Torture, last I checked, is still really, really, really bad. Condemn it today! Posted in OWL Rules Description Logic Modal Logic ... Papers

35. Modal Logic (Phil 513/679) | Richard Zach | Philosophy | University Of Calgary
Modal logic is an extension of ordinary, ÂclassicalÂ logic which allows formalizations of phrases such as Âit is possible thatÂ and Âit is necessary thatÂ
http://www.ucalgary.ca/rzach/513
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##### Course Description
Modal logic is an extension of ordinary, Ã¢ÂÂclassicalÃ¢ÂÂ logic which allows formalizations of phrases such as Ã¢ÂÂit is possible thatÃ¢ÂÂ and Ã¢ÂÂit is necessary thatÃ¢ÂÂ (the alethic modalities). Modal logics have important applications in philosophy, but also in linguistics and computer science. The course will provide an introduction to the basic systems of modal logic, both propositional and predicate, their metatheory, philosophical interpretation, and applications. We will concentrate on the alethic modalities, but also study logics of belief and knowledge, of time, of obligation, and intuitionistic logic
##### Prerequisites
Phil 279 (Logic I) is a prerequisite for this course. Phil 379 (Logic II) is recommended, but not necessary.

 36. Oxford University Press: Modal Logic: Nino B. Cocchiarella In this text, a variety of Modal logics at the sentential, firstorder, and second-order levels are developed with clarity, precision and philosophicalhttp://www.oup.com/us/catalog/general/subject/Philosophy/LogicMathematics/?view=

 37. Coalgebraic Modal Logic: Theory And Applications The aim of the COMOLO project is to study the connection between coalgebras and Modal logic. Coalgebras for functors on the category of sets can be seen ashttp://db.cwi.nl/projecten/project.php4/personen/publiek/project.php4?prjnr=176

38. Zakharyaschev, Michael: Advances In Modal Logic, Volume 2
Zakharyaschev, Michael Advances in Modal logic, Volume 2, university press books, shopping cart, new release notification.
http://www.press.uchicago.edu/cgi-bin/hfs.cgi/00/14408.ctl
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##### The University of Chicago Press
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Zakharyaschev, Michael, Krister Segerberg, Maarten de Rijke, and Heinrich Wansing, editors Advances in Modal Logic, Volume 2 . Distributed for the Center for the Study of Language and Information. 485 p. 6 x 9 2001 Series: (CSLI-LN) Center for the Study of Language and Information - Lecture Notes Cloth \$70.00sc ISBN: 978-1-575862-71-2 (ISBN-10: 1-575862-71-9) Spring 2001
Paper \$32.00sp ISBN: 978-1-575862-72-9 (ISBN-10: 1-575862-72-7) Spring 2001
Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical and computational discipline. It is the main source of formal languages aimed at analyzing complex notions such as common knowledge and formal provability. Modal and modal-like languages also provide us with families of restricted description languages for relational and topological structures; they are being used in many disciplines, ranging from artificial intelligence, computer science and mathematics via natural language syntax and semantics to philosophy.
This volume presents a broad and up-to-date view of the field, with contributions covering both the foundations of modal logic itself and each of the aforementioned application areas. Complemented with an editorial introduction covering the roots of modal logic, this book is indispensable for any advanced student and researcher in non-classical logic and its applications.

39. Advances In Modal Logic 2006
Guido Governatori, Ian M. Hodkinson, Yde Venema (Eds.) Advances in Modal logic 6, papers from the sixth conference on Advances in Modal logic, held in
http://www.informatik.uni-trier.de/~ley/db/conf/aiml/aiml2006.html
##### Advances in Modal Logic 2006: Noosa, Queensland, Australia
Guido Governatori Ian M. Hodkinson Yde Venema (Eds.): Advances in Modal Logic 6, papers from the sixth conference on "Advances in Modal Logic," held in Noosa, Queensland, Australia, on 25-28 September 2006. College Publications 2006, ISBN 1-904987-20-6 BibTeX

40. MATHS: Modal Logic
Studying Modal logics uncovers the halfa-dozen different ways we may want a piece of software to have a property. Some Modal logics make it easy to
http://www.csci.csusb.edu/dick/maths/logic_9_Modalities.html

CNS
Comp Sci Dept R J Botting MATHS ... Contact ] [Search
Tue Jul 25 08:59:19 PDT 2006
##### Introduction
Modal logics were created so we can express ideas like the following without having to use quantifiers and variables:
• For all time, at some time, never, ...
• For all future time, at some time in the past...
• X wants ... to be true.
• At all places....
• In all possible worlds...
• In some worlds...
• It is impossible...
• In all subsystems....
• As long as other subsystems don't do X this system will do Y. These ideas are called modes . There are a large number of logics that attempt to model them. When computerizing complex high risk situations we need to be very clear about what we are asking for. If we want the system to exhibit some property in every possible state, and for all time, then we don't want it merely, at all time, have the option of fulfilling the property sometimes. English is not very good at expressing such distinctions. Studying modal logics uncovers the half-a-dozen different ways we may want a piece of software to have a property. Some modal logics make it easy to calculate whether the logical behavior of a piece of software (a model) satisfies its requirements. Notice that it is useful to be able to reason about time varying properties of complex computerized systems. Indeed checking that software fits such properties has uncovered some difficult to find bugs in real software. However the normal notation is somewhat clumsy and so there has been research on graphic notations ( GIL: [
•  41. BiblioVault - Advances In Modal Logic, Volume 1 Search and browse the BiblioVault s growing collection of older, recently published, and new books from university presses.http://www.bibliovault.org/BV.book.epl?BookId=1205

42. SoundClick Artist: Tom Byrne - Progressive, Melodic, Heavily Orchestrated Rock W
My new band, Modal logic played its first gig, (successfully!) at the Space Rock Spectacular, The Store of All the Worlds (Modal logic Live)
http://www.soundclick.com/tombyrne&ref=9
 document.write(''); Charts User Stations License Songs and Beats Music Store ... SoundClick Music Genres List close Member Profiles Blogs Most Popular Photos Forum close Most Popular Videos Music Videos Videos A-Z close help sign up log in home ... Band by record label close document.write(''); :: navigation main artist page music comments reviews ... add to 'favorite artists' :: artist infos tombyrne official web page Rock Progressive Rock Congleton ... UNITED KINGDOM email: send email Statue Records "Stone Circles and Spacerock" 10 tracks running time 52:00 45 songs available Tom Byrne NEWS My fourth album 'Stone Circles and Spacerock', containing many Soundclick #1s is now available in the Soundclick store. My new band, 'Modal Logic' played its first gig, (successfully!) at the Space Rock Spectacular, Bicester on 30th September 2005. to the music page for more full Neurotransmission full The Only Ones full Radio Freemind full Global Greenhouse (Modal Logic) full Infinity full Three Minutes - Modal Logic Live full Litany of the Taints - Live - Modal Logic full The Store of All the Worlds (Modal Logic - Live) full Rocking to the Cosmic Callsign (Remastered) full Dangerous Vision full Lost Times (Full Version) full D-Rider full The Warlord of the Air full Fahrenheit 451 full Trentham Awake!

This course for senior (fourth year) or graduate students is an introduction to the syntax and semantics of Modal logic. It is also a NICTA colisted
http://www.cse.unsw.edu.au/~cs4412/
##### COMP4412 Introduction to Modal Logic
This course for senior (fourth year) or graduate students is an introduction to the syntax and semantics of modal logic. It is also a NICTA co-listed graduate course. Modal logic is useful in many application areas in CS such as artificial intelligence, computer security, correctness of network protocols, agent technology, and language understanding. However, the course will only provide the common core needed for these applications without going into specifics. It begins with motivations for modality, a quick tour of Kripke structures and typical axioms like K, T, 4 and 5, especially in the settings pertinent to computer science, e.g., in AI, programming languages, and temporal reasoning. Then in a second pass rigorous versions of the intuitive notions are introduced, proceeding to soundess and completeness via the canonical model theorem. Filtrations are introduced, and questions of decidabilty and complexity are discussed. Applications to logics of programs, belief and knowledge are then considered. If time permits, first-order modal logic is briefly examined.
##### Assumed Knowledge
An acquaintance with propositional logic (or its equivalent in switching logic in EE) is assumed, and the ability to do mathematical proofs involving induction, contradiction, etc., which feature in standard discrete mathematics courses at the second year (sophomore) level. Distinction-level junior (third year) students may also enroll with the permission of the instructor. Mail the course instructor Norman Foo (norman at cse.unsw.edu.au) for permission to enroll.

 44. Modal Logics And Philosophy The first text to combine a clear introduction to formal Modal logic with a rigorous presentation of its uses as a tool for philosophical analysis.http://mqup.mcgill.ca/book.php?bookid=941

 45. Modal Logic @ Computer-Dictionary-Online.org Modal logic @ Computer Dictionary Online. Computer terminology definitions including hardware, software, equipment, devices, jargon abbreviations and more.http://www.computer-dictionary-online.org/modal logic.htm?q=modal logic

46. Institutionalising Many-sorted Coalgebraic Modal Logic - ECS EPrints Repository
Cirstea, C. (2002) Institutionalising manysorted coalgebraic Modal logic. In 5th International Workshop on Coalgebraic Methods in Computer Science,
http://eprints.ecs.soton.ac.uk/9146/
@import url(http://eprints.ecs.soton.ac.uk/style/auto.css); @import url(http://eprints.ecs.soton.ac.uk/style/print.css); @import url(http://eprints.ecs.soton.ac.uk/style/nojs.css); Site Search Breadcrumb trail: Intranet Tools RSS 1.0 Feed RSS 2.0 Feed ... Atom Feed
##### Institutionalising many-sorted coalgebraic modal logic
Cirstea, C. (2002) Institutionalising many-sorted coalgebraic modal logic. In: 5th International Workshop on Coalgebraic Methods in Computer Science, 6-7 April 2003, Grenoble, France. This is the latest version of this eprint.
Preview PDF - Requires a PDF viewer such as GSview Xpdf or Adobe Acrobat Reader
##### Abstract
Jacobs [4] describes a modal logic for coalgebras of certain polynomial endofunctors on Set. This logic is here generalised to endofunctors on categories of sorted sets. The structure of the endofunctors considered is then exploited in order to define ways of moving from (coalgebras of) one endofunctor to (coalgebras of) another, and to equip them with translations between the associated modal languages. Furthermore, the resulting translations are shown to preserve and reflect the satisfaction of modal formulae by coalgebras. Creators: Corina Cirstea Editors: L.S. Moss

47. Modal Logic MGS Course 2002/2003
lecture 1 language and models of basic Modal logic; possible interpretations of models, e.g. states in a computation; applications of Modal logic;
http://www.cs.nott.ac.uk/~nza/modal.html
##### Modal Logic (Midlands Graduate School course, April 2003)
• lecture 1: language and models of basic modal logic; possible interpretations of models, e.g. states in a computation; applications of modal logic; overview of systems
• lecture 2: completeness, finite model property and decidability proof for basic modal logic
• lecture 3: bisimulation; preservation of modal formulas under bisimulation; similarities with process algebra; propositional dynamic logic (PDL)
• lecture 4: computational tree logic (CTL); model-checking

Slides of lecture 1 (pdf)

Slides of lecture 2 (pdf)

Slides of lecture 3 (pdf)

Slides of lecture 4 (pdf)
...
Exercises, exam questions, recommended reading (2003)

48. Modal Logic, Stone Duality And Coalgebras
Midlands Graduate School 2006 in the Foundations of Computing at the University of Leicester, Graduate School 8th April 2006 to 12th April 2006.
http://www.cs.le.ac.uk/events/ml06/
##### computer science
HOME MAP CONTACT
##### Modal Logic, Stone Duality and Coalgebras
Date: 12-13 June 2006
Location: ATT LT3, University of Liecester, Leicester Invited Speakers: Contributed talks:

49. An Introduction To Modal Logic | Thad Guy
Guy presents An Introduction to Modal logic commenting on his submission, ÂPlato and Aristotle have contributed many things to the Â
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##### Related Posts:

50. ECSTER Debate Contribution
Does Modal logic, broadly conceived, offer adequate formal representations of Modality? John McCarthy (1997) questions the usefulness of Modal logic for the
http://www.ida.liu.se/ext/etai/rac/notes/1998/02/debet.html
##### Colloquium on Reasoning about Actions and Change
For convenience of reading, this debate item is also available in postscript format.
##### by Heinrich Wansing
The present research note was originally published as an editorial in the Journal of Logic, Language, and Information , Volume 7 (1998), pages iii-vii. It is reproduced here with kind permission from Kluwer Academic Publishers
##### Modality and Modal Logic
Modality as ways in which objects may stand in suitable relations with each other is a basic phenomenon. Prepositions may be necessarily true or false, rational agents may see to it that or believe or doubt that something is the case, each verification of a certain proposition may be provably transformable into a verification of some other proposition, etc. Does modal logic, broadly conceived, offer adequate formal representations of modality? John McCarthy (1997) questions the usefulness of modal logic for the representation of modality in artificial intelligence (AI) and knowledge representation (KR). McCarthy requires for instance that "[i]ntroducing new modalities should involve no more fuss than introduce a new predicate". One may wonder why we should use modal logics at all, especially view of first-order KR formalisms like the situation calculus. Who would not like to avoid fuss? I disagree with McCarthy, and I would like to argue in favour of modal logic. I think that it would be a bad move to avoid modal logic, in particular because modal logic is alive and thriving, perhaps more so than ever. It has become a mature field that can be of great benefit to many areas - including AI and KR.

51. Game Theory And Modal Logic
Prerequisites Some familiarity with the basic notions in standard Modal logic is required. Some vague recollection of basic processalgebra and/or
http://www1.chapman.edu/~jipsen/luatcs99/info/baltag.html
##### Alexandru Baltag
CWI P.O. Box 94079, 1090 GB Amsterdam, The Netherlands Abstract: abstract.ps abstract.pdf Lecture Plan:
• Lecture 1. Logic Games
• Lecture 2. Basic Game-Theory
• Lecture 3. Game Logics
• Lecture 4. Games as Processes
• Lecture 5. Information Update and Epistemic Logic
Email: abaltag@cwi.nl Prerequisites: Some familiarity with the basic notions in standard modal logic is required. Some vague recollection of basic process-algebra and/or coalgebra notions might help, but is not obligatory. A Few References: 1. The 1999 course notes of the "Logic and Games" course given at Stanford University by Johan van Benthem, available at http://turing.wins.uva.nl/~johan/Phil.298.html 2. Notes on "Dynamic Epistemic Logic of Games", notes on "Information Update and Epistemic Logic" and Johan van Benthem's paper "When Are Two Games the Same?", all available at http://www.cwi.nl/~pauly/GameLogic/course.html 3. Proceedings of the ILLC Workshop on Logic and Games, Amsterdam 1999. Available at http://www.cwi.nl/~pauly/GameLogic/workshop.html

52. Foundations Of Computer Science - Modal Logic
Seminars \* Our events \* RESEARCH \* Game Semantics \* Physics and CS \* Modal logic \* FP6 STREP QICS. Modal logic. Will be completed soon.
http://se10.comlab.ox.ac.uk:8080/FOCS/ModalLogic_en.html
##### The Foundations of Computer Science Research Group
FoCS at OUCL
Members Seminars Our events RESEARCH
Game Semantics Physics and CS Modal Logic
FP6 STREP QICS
##### Modal Logic
Will be completed soon.
oucl research tav
FoCS at OUCL
Courses Research People ... News Site last produced on Mon Nov 26 14:37:35 GMT 2007 . Page generated by AWF

53. Theorem(e): Advances In Modal Logic : Call For Paper
invites submission of short or long papers on various aspects of Modal logic, its applications, its history, philosophy etc. DEADLINE 31 March 2008
##### Advances in Modal Logic : call for paper
9-12 September 2008, LORIA, Nancy, France
invites submission of short or long papers on various aspects of modal logic, its applications, its history, philosophy etc.
par henri galinon 3:17 PM CatÂ©gorie: conferences
##### Blog Archive

 54. MySpace.com - Modal Logic - AUSTIN, Texas - Other - Www.myspace.com/logicmodalta MySpace music profile for Modal logic with tour dates, songs, videos, pictures, blogs, band information, downloads and more.http://profile.myspace.com/index.cfm?fuseaction=user.viewprofile&friendid=240675

 55. JSTOR The Problem Of Interpreting Modal Logic TH~ JOUaNAL OF SYMBOLIC LOOTC Volume 12, Number 2, June 1947 THE PROBLEM OF INTE~RET~G Modal logic W. V. QUINE There are logicians, myself among them,http://links.jstor.org/sici?sici=0022-4812(194706)12:2<43:TPOIML>2.0.CO;2-M

56. Re: [ontolog-forum] Is Modal Logic First-order?
Well, John, I almost wrote a ps to my post saying Expect a reply from John Sowa on Dunn s semantics for Modal logic shortly! .
http://ontolog.cim3.net/forum/ontolog-forum/2007-02/msg00321.html
##### Re: [ontolog-forum] Is modal logic first-order?
from [ Christopher Menzel Permanent Link Original To "[ontolog-forum] " < From cmenzel@xxxxxxxx Date Fri, 23 Feb 2007 12:17:46 -0600 Message-id FCB5C6FD-62C1-4177-83D3-71D024CB5A15@xxxxxxxx Well, John, I almost wrote a ps to my post saying "Expect a reply from John Sowa on Dunn's semantics for modal logic shortly!". :-) I'll not bother repeating past debates (see e.g., http://suo.ieee.org/ email/msg10546.html). But just a couple of points: order metalanguage about a first-order object language. After you do that, you can then collapse the two levels and define a single- level Tarski-style model for the combined system. That collapsed form is less readable than the original, but it demonstrates that you can map the modalities into a first-order framework. See http://www.jfsowa.com/pubs/laws.htm Laws, Facts, and Contexts With Dunn's semantics instead of Kripke's semantics, each world w is replaced by a pair (M,L), where M is the set of propositions

57. Modal Logic : Thomas Alspaugh : UCI
Firstorder logic is primarily concerned with truth and its negation. Modal logic additionally considers the concepts of possibility and necessity.
http://www.ics.uci.edu/~alspaugh/logic/modalLogic.html
Last modified Fri Sep 28 13:36 2007) Logic Glossary of logic terms and concepts
Propositional logic (PL)

syntax
...
Modal logic and temporal logic
The meaning of modal logic formulae is expressed more formally in terms of "possible worlds"; reachable from the initial world; "reachable" may be interpreted in a variety of different ways, depending on the type of modal logic under consideration. Finally, and are related by
##### Temporal logic
In computer science, modal logic is most often encountered in the form of temporal logic (TL), a modal logic in which There are a number of TLs, which differ to a certain extent in the temporal operators they support but more fundamentally in the model of time they assume.
##### Operators
Temporal logics introduce operators typically drawn from the ones described below. Some common temporal logic operators Future Past operator informally operator informally
some time in the future
time in the past
in the future
in the past U
S
Examples of Time tt tt ff tt tt tt tt tt ff tt tt tt tt tt ff tt tt tt tt tt ff tt tt ff tt tt tt tt ff ff tt tt tt tt ff ff Examples of U Time U ff ff ff ff tt ff tt tt ff ff ff tt ff ff ff
##### Structure of time
Unlike FOL, whose models have a single well-defined structure, there are a number of model structures for TL, varying in how they represent the possibilities of time. The possibilities are:

58. [math/0701801] Deterministic Modal Bayesian Logic: Derive The Bayesian Inference
Deterministic Modal Bayesian logic derive the Bayesian inference within the Modal logic T. Authors Frederic Dambreville (DGA/CTA/DT/GIP)
http://arxiv.org/abs/math/0701801
##### arXiv.orgmath
Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
Citations p revious n ... ext
##### Title: Deterministic modal Bayesian Logic: derive the Bayesian inference within the modal logic T
Authors: Frederic Dambreville (DGA/CTA/DT/GIP) (Submitted on 28 Jan 2007) Abstract: In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A notion of logical independence is also defined within the logic itself. This logic is shown to be non-trivial and is not reduced to classical propositions. A model is constructed for the logic. Completeness results are proved. It is shown that any unconditioned probability can be extended to the whole logic DmBL. The Bayesian conditional is then recovered from the probabilistic DmBL. At last, it is shown why DmBL is compliant with Lewis' triviality. Comments: Second revision of: Definition of a Deterministic Bayesian Logic Subjects: Logic (math.LO)

59. Project: CoMoLo: Coalgebraic Modal Logic - Theory And Applications (www.onderzoe
Coalgebras are closely related to Modal logic in two ways coalgebras are the natural dynamical models of Modal logic, and Modal logic is the natural logic
http://www.onderzoekinformatie.nl/en/oi/nod/onderzoek/OND1280604/
Login English KNAW Research Information NOD - Dutch Research Database ... Research entire www.onderzoekinformatie.nl site fuzzy match
##### Project: CoMoLo: Coalgebraic Modal Logic - theory and applications
Print View Titel CoMoLo: CoalgebraÂ¯sche Modale Logica - theorie en toepassingen Abstract The relatively new and promising field of coalgebra is well suited to describe state-based systems with (possibly) infinite behaviour. Coalgebras are closely related to modal logic in two ways: coalgebras are the natural dynamical models of modal logic, and modal logic is the natural logic for coalgebras. A feature which interface types describing the operations and actions regulating the communication with the outside world. The aim of this project is to further develop and to exploit this new connection, in particular in order to provide appropiate semantic models and logics for reasoning about object-oriented and distributed systems. The basis is formed by the already existing coalgebraic semantics of the popular object-oriented programming language Java, which is much used in distributed computation. Period Status completed Dissertation Yes Related organisations
Related persons

60. [Om-announce] Advances In Modal Logic 2006: Call For Papers
TOPICS We invite submission on all aspects of Modal logics, including the following applications of Modal logic - computational aspects of Modal logics o
http://openmath.org/pipermail/om-announce/2005-November/000318.html
##### [Om-announce] Advances in Modal Logic 2006: Call for papers
AiML 2006 guido at itee.uq.edu.au
Thu Nov 17 12:05:37 CET 2005

61. Research Papers
University of Edinburgh Models and calculi for concurrent computation, Modal and temporal logics with fixed points, verification and description of
http://www.dcs.ed.ac.uk/~cps/
##### Slides
Slides on "language theory and infinite graphs", Marktoberdorf Summerschool 2005. Slides on "modal and temporal logics", International Winter School on Semantics and Applications, Montevideo, Uruguay, 2003.
##### Recent Papers

62. Modal Logics For Multi Agent Systems
Modal logics are amongst the most suitable and versatile logical formalisms for specification, verification and reasoning about MAS.
http://www2.in.tu-clausthal.de/~wjamroga/courses/MAS2006ESSLLI/
##### Overview of the course
Multi agent systems (MAS) are an important framework for formalizing and reasoning about various problems and scenarios in artificial intelligence, computer science, game theory, social choice theory, etc. Modal logics are amongst the most suitable and versatile logical formalisms for specification, verification and reasoning about MAS. The course will offer an introduction to some of the main developments in the area, building up from simple to rather complex logical systems, and partly reflecting on the hierarchy of aspects of MAS, and their interaction (knowledge, information, actions, strategies, obligations and rights, cooperation and competition of agents and coalitions, etc.). This is an introductory course and the participants are only expected to have very basic background on modal logic. Basic knowledge of first-order logic, multi-agent systems, and extended modal logics such as LTL and CTL would be an advantage.
##### Program of the course
Day 1, Lecture 1:

63. Project-SECSI:Modal Logics With Presburger Contraints
New Results Modal logics with Presburger contraints.
http://ralyx.inria.fr/2006/Raweb/secsi/uid49.html
 Team SECSI Members Overall Objectives Scientific Foundations Application Domains Software New Results Other Grants and Activities Dissemination

 64. IngentaConnect Barwises Information Frames And Modal Logics The article studies Barwise s information frames and settles the problem of Barwise dealing in finding axiomatizations for the Modal logics generated byhttp://www.ingentaconnect.com/content/klu/allo/2002/00000041/00000005/00457696

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