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Bisimulations for Temporal Logic
 JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 1997
"... We define bisimulations for temporal logic with Since and Until. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until. Our results concern both invariance and definability. We conclude with a brief ..."
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Cited by 24 (2 self)
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We define bisimulations for temporal logic with Since and Until. This new notion is compared to existing notions of bisimulations, and then used to develop the basic model theory of temporal logic with Since and Until. Our results concern both invariance and definability. We conclude with a brief discussion of the wider applicability of our ideas.
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.
Modal Model Theory
 ANNALS OF PURE AND APPLIED LOGIC
, 1995
"... This paper contributes to the model theory of modal logic using bisimulations as the fundamental tool. A uniform presentation is given of modal analogues of wellknown definability and preservation results from firstorder logic. These results include algebraic characterizations of modal equivalen ..."
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This paper contributes to the model theory of modal logic using bisimulations as the fundamental tool. A uniform presentation is given of modal analogues of wellknown definability and preservation results from firstorder logic. These results include algebraic characterizations of modal equivalence, and of the modally definable classes of models; the preservation results concern preservation of modal formulas under submodels, unions of chains, and homomorphisms.
Coalgebraic Lindström Theorems
"... We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke’s result for Kripke models. Both the other two results are based on the properties of bisimulation invariance, ..."
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We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke’s result for Kripke models. Both the other two results are based on the properties of bisimulation invariance, compactness, and a third property: ωbisimilarity, and expressive closure at level ω, respectively. These also provide new results in the case of Kripke models. Discussing the relation between our work and a recent result by van Benthem, we give an example showing that only requiring bisimulation invariance together with compactness does not suffice to characterise basic modal logic.
E������ � E�������
, 2012
"... �e growing need for computer aided processing of knowledge has led to an increasing interest in description logics (DLs), which are applied to encode knowledge in order to make it explicit and accessible to logical reasoning. DLs and in particular the family around the DL �� � have therefore been th ..."
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�e growing need for computer aided processing of knowledge has led to an increasing interest in description logics (DLs), which are applied to encode knowledge in order to make it explicit and accessible to logical reasoning. DLs and in particular the family around the DL �� � have therefore been thoroughly investigated w.r.t. their complexity theory and proof theory. �e question arises which expressiveness these logics actually have. �e expressiveness of a logic can be inferred by a model theoretic characterisation. On concept level, these DLs are akin to modal logics whose model theoretic properties have been investigated. Yet the model theoretic investigation of the DLs with their TBoxes, which are an original part of DLs usually not considered in context of modal logics, have remained unstudied. �is thesis studies the model theoretic properties of ���, ����, ����, as well as ����, �����, ����� � and ��. It presents model theoretic properties, which characterise these logics as fragments of the first order logic (FO). �e characterisations are not only carried out on concept level and on concept
Synthesising Axioms By Games
"... Contents 1 Introduction 2 2 Story 2 3 To the games 4 4 Generalisations 6 5 Discussion 9 Research partially supported by UK EPSRC grants GR/K54946, GR/L85978, GR/L85961. Thanks to ' Agnes Kurucz and Szabolcs Mikul'as for comments. 1 1 Introduction We would like to begin by hoping that y ..."
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Contents 1 Introduction 2 2 Story 2 3 To the games 4 4 Generalisations 6 5 Discussion 9 Research partially supported by UK EPSRC grants GR/K54946, GR/L85978, GR/L85961. Thanks to ' Agnes Kurucz and Szabolcs Mikul'as for comments. 1 1 Introduction We would like to begin by hoping that you had a very happy birthday (we assume you found more enjoyable ways to spend it than reading this), and we wish you many more years of fruitful research. In this short article we would like to discuss from our current perspective the problem of providing axioms for classes of algebras, and the way in which games can contribute to solving it. Towards the end, we will describe general settings in which this can be done. We will be rather discursive and opinionated  you may well disagree with what we say (and we'd like to hear from you about it), but we are certainly not trying to provoke you or implying that you do disagree with us. We will use natural langua