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37
Deciding regular grammar logics with converse through firstorder logic
 JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 2005
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Modal Logic, Transition Systems and Processes
, 1994
"... Transition systems can be viewed either as process diagrams or as Kripke structures. The first perspective is that of process theory, the second that of modal logic. This paper shows how various formalisms of modal logic can be brought to bear on processes. Notions of bisimulation can not only be mo ..."
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Cited by 22 (3 self)
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Transition systems can be viewed either as process diagrams or as Kripke structures. The first perspective is that of process theory, the second that of modal logic. This paper shows how various formalisms of modal logic can be brought to bear on processes. Notions of bisimulation can not only be motivated by operations on transition systems, but they can also be suggested by investigations of modal formalisms. To show that the equational view of processes from process algebra is closely related to modal logic, we consider various ways of looking at the relation between the calculus of basic process algebra and propositional dynamic logic. More concretely, the paper contains preservation results for various bisimulation notions, a result on the expressive power of propositional dynamic logic, and a definition of bisimulation which is the proper notion of invariance for concurrent propositional dynamic logic. Keywords: modal logic, transition systems, bisimulation, process algebra 1 In...
Power and weakness of the modal display calculus
 In Proof theory of modal logic
, 1996
"... The present paper explores applications of Display Logic as defined in [Belnap, 1982] to modal logic. Acquaintance with that paper is presupposed, although we will give all necessary definitions. Display Logic is a rather elegant prooftheoretic system that was developed to explore in depth the poss ..."
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Cited by 19 (0 self)
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The present paper explores applications of Display Logic as defined in [Belnap, 1982] to modal logic. Acquaintance with that paper is presupposed, although we will give all necessary definitions. Display Logic is a rather elegant prooftheoretic system that was developed to explore in depth the possibility of total Gentzenization
Is There a Genuine Modal Perspective on Feature Structures?
, 1996
"... This paper is formal and quite difficult for readers untrained in modal logic; I have no illusions about this and I apologize in advance if I fail to make things as clear and simple as I should. I do believe, however, that much of the complexity in this paper is unavoidable and anything that is simp ..."
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Cited by 18 (6 self)
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This paper is formal and quite difficult for readers untrained in modal logic; I have no illusions about this and I apologize in advance if I fail to make things as clear and simple as I should. I do believe, however, that much of the complexity in this paper is unavoidable and anything that is simpler will be so at the cost of precision. Almost everything will be defined here, so that the discussion will on the whole be selfcontained. But this is really not to say much when it come to mathematical topics. The reader who is seriously interested should perhaps read an introductory book on modal logic and the lucid survey article [ Bull and Segerberg, 1984 ] to get enough background. I can also recommend [ Blackburn, 1993 ] as an introduction into modal logic in connection with avms. It is impossible to go through all technical proofs in great detail; this would be tantamount to writing a book on this topic. But, I hope, the line of argumentation can be understood even without a proper understanding of the technical points. For the message is of wider importance. If I am right, then modal logic, where it fails, fails necessarily Is there a genuine modal perspective on feature structures? 3  and no other framework I know of will not under these circumstances. Secondly, it provides enough technical apparatus to allow to prove significant results. To those who remain unimpressed I can only appeal to their sense of beauty and naturalness. Among the persons who have quite generally helped to shape my views on syntax and logic I wish to thank explicitly those who have contributed to the present paper. These are Mark Ellison and two anonymous referees, who had the questionable pleasure of reading an earlier version of this paper. Moreover, the results on modal feature logic...
HennessyMilner classes and process algebra
 Modal Logic and Process Algebra
, 1995
"... This paper studies HennessyMilner classes, classes of Kripke models where modallogical equivalence coincides with bisimulation. Concepts associated with these classes in the literature (Goldblatt [6], Visser [8]) are studied and compared and the structure of the collection of maximal HennessyMiln ..."
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Cited by 16 (1 self)
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This paper studies HennessyMilner classes, classes of Kripke models where modallogical equivalence coincides with bisimulation. Concepts associated with these classes in the literature (Goldblatt [6], Visser [8]) are studied and compared and the structure of the collection of maximal HennessyMilner classes is investigated (how manyare there, what is their intersection?). The insights into these classes are applied to process algebra. This results in a HennessyMilner process algebra for a nontrivial process language, whose standard graphsemantics is not HennessyMilner. 1
Macneille completions and canonical extensions
 Transactions of the American Mathematical Society
"... Abstract. Let V be a variety of monotone bounded lattice expansions, that is, bounded lattices endowed with additional operations, each of which is order preserving or reversing in each coordinate. We prove that if V is closed under MacNeille completions, then it is also closed under canonical exten ..."
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Cited by 14 (6 self)
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Abstract. Let V be a variety of monotone bounded lattice expansions, that is, bounded lattices endowed with additional operations, each of which is order preserving or reversing in each coordinate. We prove that if V is closed under MacNeille completions, then it is also closed under canonical extensions. As a corollary we show that in the case of Boolean algebras with operators, any such variety V is generated by an elementary class of relational structures. Our main technical construction reveals that the canonical extension of a monotone bounded lattice expansion can be embedded in the MacNeille completion of any sufficiently saturated elementary extension of the original structure. 1.
Modal Logic: A Semantic Perspective
 ETHICS
, 1988
"... This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimul ..."
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Cited by 13 (2 self)
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This chapter introduces modal logic as a tool for talking about graphs, or to use more traditional terminology, as a tool for talking about Kripke models and frames. We want the reader to gain an intuitive appreciation of this perspective, and a firm grasp of the key technical ideas (such as bisimulations) which underly it. We introduce the syntax and semantics of basic modal logic, discuss its expressivity at the level of models, examine its computational properties, and then consider what it can say at the level of frames. We then move beyond the basic modal language, examine the kinds of expressivity offered by a number of richer modal logics, and try to pin down what it is that makes them all ‘modal’. We conclude by discussing an example which brings many of the ideas we discuss into play: games.
Erdős Graphs Resolve Fine's Canonicity Problem
 THE BULLETIN OF SYMBOLIC LOGIC
, 2003
"... We show that there exist 2^ℵ0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any firstorder definable class of relational structures. Using a variant of this construction, we resolve a longstanding question of Fine, by exhibiting ..."
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Cited by 12 (8 self)
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We show that there exist 2^&alefsym;0 equational classes of Boolean algebras with operators that are not generated by the complex algebras of any firstorder definable class of relational structures. Using a variant of this construction, we resolve a longstanding question of Fine, by exhibiting a bimodal logic that is valid in its canonical frames, but is not sound and complete for any firstorder definable class of Kripke frames. The constructions use the result of Erdős that there are finite graphs with arbitrarily large chromatic number and girth.