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Social Processes, Program Verification and All That
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2009
"... ... mostly motivating their position by an analogy with proofs in mathematics, and in particular with the impracticality of a strictly formalist approach to this discipline. The recent, impressive achievements in the field of interactive theorem proving provide an interesting ground for a critical r ..."
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... mostly motivating their position by an analogy with proofs in mathematics, and in particular with the impracticality of a strictly formalist approach to this discipline. The recent, impressive achievements in the field of interactive theorem proving provide an interesting ground for a critical revisiting of those theses. We believe that the social nature of proof and program development is uncontroversial and ineluctable but formal verification is not antithetical to it. Formal verification should strive not only to cope, but to ease and enhance the collaborative, organic nature of this process, eventually helping to master the growing complexity of scientific knowledge.
A Dynamic Logics of Dynamical Systems
"... We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important for modeling and understanding many applications, including embedded ..."
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We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important for modeling and understanding many applications, including embedded systems and cyberphysical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. Distributed hybrid systems combine distributed systems with hybrid systems, i.e., they are multiagent hybrid systems that interact through remote communication or physical interaction. Stochastic hybrid systems combine stochastic dynamics with hybrid systems. We survey dynamic logics for specifying and verifying properties for each of those classes of dynamical systems. A dynamic logic is a firstorder modal logic with a pair of parametrized modal operators for each dynamical system to express necessary or possible properties of their transition behavior. Due to their full basis of firstorder modal logic operators, dynamic logics can express a rich variety of system properties, including safety, controllability, reactivity, liveness, and quantified parametrized properties, even about
Notes Towards a Semantics for Proofsearch
"... Algorithmic proofsearch is an essential enabling technology throughout informatics. Proofsearch is the prooftheoretic realization of the formulation of logic not as a theory of deduction but rather as a theory of reduction. Whilst deductive logics typically have a welldeveloped semantics of proo ..."
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Algorithmic proofsearch is an essential enabling technology throughout informatics. Proofsearch is the prooftheoretic realization of the formulation of logic not as a theory of deduction but rather as a theory of reduction. Whilst deductive logics typically have a welldeveloped semantics of proofs, reductive logics are typically wellunderstood only operationally. Each deductive system can, typically, be read as a corresponding reductive system. We discuss some of the problems which must be addressed in order to provide a semantics of proofsearches of comparable value to the corresponding semantics of proofs. Just as the semantics of proofs is intimately related to the model theory of the underlying logic, so too should be the semantics of proofsearches. We discuss how to solve the problem of providing a semantics for proofsearches which adequately models both operational and logical aspects of the reductive system. 1
ISSN 02496399 ISRN INRIA/RR????FR+ENGProof Nets and the Identity of Proofs
, 2006
"... apport de recherche ..."