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28
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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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.
Synchronization of Logics
 Studia Logica
, 1996
"... Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, onestep derivation systems and theory spaces, as well as their functorial ..."
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Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, onestep derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction systems and provide a categorial characterization of the construction. We illustrate the technique in two cases: linear temporal logic versus equational logic; and linear temporal logic versus branching temporal logic. Finally, we lift the synchronization on formulae to the category of logics over consequence systems. Key words: combination of logics, synchronization on formulae, sync...
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 12 (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.
Topology, connectedness, and modal logic
 ADVANCES IN MODAL LOGIC
, 2008
"... This paper presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of ..."
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Cited by 5 (3 self)
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This paper presents a survey of topological spatial logics, taking as its point of departure the interpretation of the modal logic S4 due to McKinsey and Tarski. We consider the effect of extending this logic with the means to represent topological connectedness, focusing principally on the issue of computational complexity. In particular, we draw attention to the special problems which arise when the logics are interpreted not over arbitrary topological spaces, but over (lowdimensional) Euclidean spaces.
Preservation by fibring of the finite model property
 Journal of Logic and Computation
"... Capitalising on the graphtheoretic account of fibring proposed in [31], we show that fibring preserves the finite model property under mild conditions. Illustrations are provided for modal, deontic, paraconsistent and linear logics. ..."
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Cited by 3 (3 self)
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Capitalising on the graphtheoretic account of fibring proposed in [31], we show that fibring preserves the finite model property under mild conditions. Illustrations are provided for modal, deontic, paraconsistent and linear logics.
Multimodal separation logic for reasoning about operational semantics
 In Proc. 24th Conference on the Mathematical Foundations of Programming Semantics
, 2008
"... We show how to reason, in the proof assistant Coq, about realistic programming languages using a combination of separation logic and heterogeneous multimodal logic. A heterogeneous multimodal logic is a logic with several modal operators that are not required to satisfy the same frame conditions. Th ..."
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Cited by 3 (2 self)
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We show how to reason, in the proof assistant Coq, about realistic programming languages using a combination of separation logic and heterogeneous multimodal logic. A heterogeneous multimodal logic is a logic with several modal operators that are not required to satisfy the same frame conditions. The result is a powerful and elegant system for reasoning about programming languages and their semantics. The techniques are quite general and can be adopted to a wide variety of settings.
Logical tools for handling change in agentbased systems
, 2009
"... 1.2 Short overview of the different logics....................................... 9 ..."
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1.2 Short overview of the different logics....................................... 9
Logics of informational attitudes and informative actions
, 2010
"... There is an extensive literature focused on using logical methods to reason about communities of agents engaged in some form of social interaction. Much of the work builds upon existing logical frameworks developed by philosophers and computer scientists incorporating insights and ideas from philoso ..."
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There is an extensive literature focused on using logical methods to reason about communities of agents engaged in some form of social interaction. Much of the work builds upon existing logical frameworks developed by philosophers and computer scientists incorporating insights and ideas from philosophy (especially
Auraconf: a unified approach to authorization and confidentiality
 In Proceedings of the 7th ACM SIGPLAN workshop on Types in language design and implementation, TLDI ’11
, 2011
"... This paper introduces AuraConf, the first programming language with a unified means to specify accesscontrol and confidentially policies. In concert with a proofcarrying access control mechanism, AuraConf allows confidentially policies to be specified declaratively using types and enforced via cry ..."
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This paper introduces AuraConf, the first programming language with a unified means to specify accesscontrol and confidentially policies. In concert with a proofcarrying access control mechanism, AuraConf allows confidentially policies to be specified declaratively using types and enforced via cryptography. Programs written in AuraConf enjoy a formal security guarantee via noninterference. Additionally, the language definition introduces a novel type system where the typechecker may use resources (i.e., private keys) and knowledge of an object’s provenance (i.e., how a ciphertext was computed) to guide analysis.