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We present a logical framework that formally models how a given privateinformation P stored on a given database D, can get captured progressively, byan agent/adversary querying the database repeatedly. Named DLTTS (DistributedLabeled Tagged Transition System), the framework borrows ideas from severaldomains: Probabilistic Automata of Segala, Probabilistic Concurrent Systems,and Probabilistic labelled transition systems. To every node on a DLTTS isattached a tag that represents the 'current' knowledge of the adversary,acquired from the responses of the answering mechanism of the DBMS to his/herqueries, at the nodes traversed earlier, along any given run; this knowledge iscompleted at the same node, with further relational deductions, possibly incombination with 'public' information from other databases given in advance. A'blackbox' mechanism is also part of a DLTTS, and it is meant as an oracle; itsrole is to tell if the private information has been deduced by the adversary atthe current node, and if so terminate the run. An additional special feature isthat the blackbox also gives information on how 'close', or how 'far', theknowledge of the adversary is, from the private information P , at the currentnode. A metric is defined for that purpose, on the set of all 'type compatible'tuples from the given database, the data themselves being typed with theheaders of the base. Despite the transition systems flavor of our framework,this metric is not 'behavioral' in the sense presented in some other works. Itis exclusively database oriented, and allows to define new notions of adjacencyand of indistinguishabilty between databases, more generally than those usuallybased on the Hamming metric (and a restricted notion of adjacency). Examplesare given all along to illustrate how our framework works.  Keywords:Database, Privacy, Transition System, Probability, Distribution.

Distributed Transition Systems with Tags for Privacy Analysis