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Weakly complete axiomatization of exogenous quantum propositional logic
 Information and Computation
, 2006
"... A weakly complete finitary axiomatization for EQPL (exogenous quantum propositional logic) is presented. The proof is carried out using a non trivial extension of the FaginHalpernMegiddo technique together with three Henkin style completions. 1 ..."
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A weakly complete finitary axiomatization for EQPL (exogenous quantum propositional logic) is presented. The proof is carried out using a non trivial extension of the FaginHalpernMegiddo technique together with three Henkin style completions. 1
Probabilistic model–checking of quantum protocols
 DCM 2006: PROCEEDINGS OF THE 2ND INTERNATIONAL WORKSHOP ON DEVELOPMENTS IN COMPUTATIONAL MODELS
, 2005
"... We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communicati ..."
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We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantummechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using presentday technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of prism, a probabilistic modelchecking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniques by modelling a selection of quantum protocols (namely superdense coding, quantum teleportation, and quantum error correction) and verifying their basic correctness properties. Our results provide a foundation for further work on modelling and analysing larger systems such as those used for quantum cryptography, in which basic protocols are used as components.
Modal Sequent Calculi Labelled with Truth Values: Completeness, Duality and Analyticity
 LOGIC JOURNAL OF THE IGPL
, 2003
"... Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessi ..."
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Cited by 8 (5 self)
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Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a natural twosorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result
Quantum institutions
 Algebra, Meaning, and Computation – Essays Dedicated to Joseph A. Goguen on the Occasion of His 65th Birthday, volume 4060 of Lecture Notes in Computer Science
, 2006
"... The exogenous approach to enriching any given base logic for probabilistic and quantum reasoning is brought into the realm of institutions. The theory of institutions helps in capturing the precise relationships between the logics that are obtained, and, furthermore, helps in analyzing some of the k ..."
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The exogenous approach to enriching any given base logic for probabilistic and quantum reasoning is brought into the realm of institutions. The theory of institutions helps in capturing the precise relationships between the logics that are obtained, and, furthermore, helps in analyzing some of the key design decisions and opens the way to make the approach more useful and, at the same time, more abstract. 1
Exogenous Probabilistic Computation Tree Logic
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 5 (1 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
Reasoning Formally about Quantum Systems: An Overview
, 2005
"... This article is intended as an introduction to the subject of quantum logic, and as a brief survey of the relevant literature. Also discussed here are logics for speci cation and analysis of quantum information systems, in particular, recent work by P. Mateus and A. Sernadas, and also by R. van der ..."
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This article is intended as an introduction to the subject of quantum logic, and as a brief survey of the relevant literature. Also discussed here are logics for speci cation and analysis of quantum information systems, in particular, recent work by P. Mateus and A. Sernadas, and also by R. van der Meyden and M. Patra. Overall, our objective is to provide a highlevel presentation of the logical aspects of quantum theory. Mateus ' and Sernadas ' EQPL logic is illustrated with a small example, namely the state of an entangled pair of qubits. The &quot;KT&quot; logic of van der Meyden and Patra is demonstrated brie y in the context of the B92 protocol for quantum key distribution. 1
Probabilistic and quantum institutions revisited
"... Abstract. We revisit quantum institutions as in [2] and solve some problems identified therein. Global, probabilistic and quantum exogenous enrichments of logics are adapted to a new notion of global model. For simplicity sake, all the constructions are presented in the realm of satisfaction systems ..."
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Abstract. We revisit quantum institutions as in [2] and solve some problems identified therein. Global, probabilistic and quantum exogenous enrichments of logics are adapted to a new notion of global model. For simplicity sake, all the constructions are presented in the realm of satisfaction systems, which proves to be an appropriate framework for defining the new logics. It also provides suitable constructions for studying the relationship between these enrichments and compare them with the constructions of [2]. Nevertheless, all the constructions are shown to be easily extended to institutions. 1
Reasoning Formally about Quantum Systems: An Overview
, 2005
"... For this issue, Nick Papanikolaou brings us an introduction to the subject of quantum logic and a survey of the relevant literature, including a discussion of logics for specification and analysis of quantum information systems. I am always looking for contributions. If you have any suggestion conce ..."
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For this issue, Nick Papanikolaou brings us an introduction to the subject of quantum logic and a survey of the relevant literature, including a discussion of logics for specification and analysis of quantum information systems. I am always looking for contributions. If you have any suggestion concerning the content of the Logic Column, or even better, if you would like to contribute by writing a survey or tutorial on
Fixpoint Logics for Reasoning about Probabilistic Systems
, 2010
"... Abstract. We consider exogenous logics for reasoning about probabilistic systems: a variant of probabilistic state logic EPPL[24], and its fixpoint extension MEPL, which is enriched with operators from the modal µcalculus. System states correspond to probability distributions over classical states ..."
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Abstract. We consider exogenous logics for reasoning about probabilistic systems: a variant of probabilistic state logic EPPL[24], and its fixpoint extension MEPL, which is enriched with operators from the modal µcalculus. System states correspond to probability distributions over classical states and the system evolution is modeled by parametrized Kripke structures that capture both stochastic and non–deterministic transitions. We introduce two approaches to the verification of properties expressed in these logics, one syntactic (a weakly complete Hilbert calculus) and the other semantic (a model– checking algorithm). The completeness proof of MEPL builds on the decidability of the existential theory of the real numbers and on a polynomialspace sat algorithm for EPPL. The model checking problem for MEPL is also analysed and the logic is related to previous work. The semantics of EPPL and MEPL are defined in terms of probability distributions over sets of propositional symbols, whereas the usual approaches are designed for reasoning about distributions over paths of possible behaviour. The intended application of our logics is as a specification formalism for properties of probabilistic systems. We illustrate the use of the logics for specifying system properties with some simple examples. 1