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The primary objective of this paper is to present the definition of a new dynamic, linear and modal logic for security protocols. The logic is compact, expressive and formal. It allows the specification of classical security properties (authentication, secrecy and integrity) and also electronic commerce properties (non-repudiation, anonymity, good atomicity, money atomicity, certified delivery, etc.). The logic constructs are interpreted over a trace-based model. Traces reflect valid protocol executions in the presence of a malicious smart intruder. The logic is endowed with a tableau-based proof system that leads to a modular denotational semantics and local model checking.