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Hybrid Logics
"... This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur ..."
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This chapter provides a modern overview of the field of hybrid logic. Hybrid logics are extensions of standard modal logics, involving symbols that name individual states in models. The first results that are nowadays considered as part of the field date back to the early work of Arthur
Pure extensions, proof rules and hybrid axiomatics
 Preliminary proceedings of Advances in Modal Logic (AiML 2004
, 2004
"... We examine the role played by proof rules in general axiomatisations for hybrid logic. We prove three main results. First, all known axiomatisations for the basic hybrid language ..."
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Cited by 20 (6 self)
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We examine the role played by proof rules in general axiomatisations for hybrid logic. We prove three main results. First, all known axiomatisations for the basic hybrid language
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 20 (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.
Is P versus NP formally independent
 Bulletin of the European Association for Theoretical Computer Science
, 2003
"... I have moved back to the University of Chicago and so has the web page for this column. See above for new URL and contact informaion. This issue Scott Aaronson writes quite an interesting (and opinionated) column on whether the P = NP question is independent of the usual axiom systems. Enjoy! ..."
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I have moved back to the University of Chicago and so has the web page for this column. See above for new URL and contact informaion. This issue Scott Aaronson writes quite an interesting (and opinionated) column on whether the P = NP question is independent of the usual axiom systems. Enjoy!
Charles University in Prague Faculty of Mathematics and Physics
, 2009
"... I would like to thank my supervisor Jan Krajíček for careful guidance, patience and support. I would also like to thank my parents, for encouraging me through the whole studies. I declare that I have written this bachelor thesis on my own and listed all ..."
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I would like to thank my supervisor Jan Krajíček for careful guidance, patience and support. I would also like to thank my parents, for encouraging me through the whole studies. I declare that I have written this bachelor thesis on my own and listed all
Abstract Hybrid Logics
"... Hybrid languages are modal languages that have special symbols for naming individual states in models. Their history can be traced back to work of Arthur Prior in the fifties. The subject has recently regained interest, resulting in many new results and techniques. This chapter contains a modern ove ..."
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Hybrid languages are modal languages that have special symbols for naming individual states in models. Their history can be traced back to work of Arthur Prior in the fifties. The subject has recently regained interest, resulting in many new results and techniques. This chapter contains a modern overview of the field. We sketch its history, and survey the basic properties of various hybrid languages, focussing on model theory (completeness, expressivity, definability,
Pure Extensions, Proof Rules, and Hybrid
"... In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the ..."
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In this paper we argue that hybrid logic is the deductive setting most natural for Kripke semantics. We do so by investigating hybrid axiomatics for a variety of systems, ranging from the basic hybrid language (a decidable system with the same complexity as orthodox propositional modal logic) to the strong Priorean language (which offers full firstorder expressivity). We show that hybrid logic offers a genuinely firstorder perspective on Kripke semantics: it is possible to define base logics which extend automatically to a wide variety of frame classes and to prove completeness using the Henkin method. In the weaker languages, this requires the use of nonorthodox rules. We discuss these rules in detail and prove noneliminability and eliminability results. We also show how another type of rule, which reflects the structure of the strong Priorean language, can be employed to give an even wider coverage of frame classes. We show that this deductive apparatus gets progressively simpler as we work our way up the expressivity hierarchy, and conclude the paper by showing that the approach transfers to firstorder hybrid logic. 1