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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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Cited by 62 (18 self)
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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
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.
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 17 (5 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
Logical Interpolation and Projection onto State in the Duration Calculus (Extended Abstract)
 Presented at the ESSLLI Workshop on Interval Temporal Logics and Duration Calculi
, 2003
"... Dimitar P. Guelev # June 6, 2003 ..."
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On Finding Query Rewritings under Expressive Constraints
, 2009
"... We study a general framework for query rewriting in the presence of general FOL constraints, where standard theorem proving techniques (e.g., tableau or resolution) can be used. The novel results of applying this framework include: 1) if the original constraints are domain independent, then so will ..."
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Cited by 2 (1 self)
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We study a general framework for query rewriting in the presence of general FOL constraints, where standard theorem proving techniques (e.g., tableau or resolution) can be used. The novel results of applying this framework include: 1) if the original constraints are domain independent, then so will be the query rewritten in terms of database predicates; 2) for infinite databases, the rewriting of conjunctive queries over connected views is decidable; 3) one can apply this technique to the guarded fragment of FOL, obtaining results about ontology languages. 1
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
Linear Temporal Logic LTLK extended by MultiAgent Logic Kn with Interacting Agents
"... We study an extension LTLK of the linear temporal logic LTL by implementing multiagent knowledge logic KD45m (which is often referred as multimodal logic S5m). The temporal language of our logic adapts the operations U (until) and N (next) and uses new temporal operations: Uw—weak until, and Us—st ..."
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We study an extension LTLK of the linear temporal logic LTL by implementing multiagent knowledge logic KD45m (which is often referred as multimodal logic S5m). The temporal language of our logic adapts the operations U (until) and N (next) and uses new temporal operations: Uw—weak until, and Us—strong until. We also employ the standard agents ’ knowledge operations Ki from the multiagent logic KD45m and extend them with an operation IntK responsible for knowledge obtained via interaction of agents. The semantic models for LTLK are Kripke/Hintikkalike structures NC based on the linear time. Structures NC use i∈N as indexes for time, and the base set of any NC consists of clusters C(i) (for all i∈N) containing all possible states at the time i. Agents ’ knowledge is modelled in time clusters C(i) via agents ’ knowledge accessibility relations Rj. The logic LTLK is the set of all formulas which are valid (true) in all such models NC w.r.t. all possible valuations. We prove that LTLK is decidable: we reduce the decidability problem to verification of validity for special normal reduced forms of rules in specific models (not LTLK models) of size singleexponential in size of the rules. Furthermore, we extend these results to a linear temporal logic LTLK (Z) based on the time flow indexed by all integer numbers (with additional operations Since and Previous). Also we show that LTLK has the finite model property (fmp) while LTLK (Z) has no standard fmp.