A quantitative doxastic logic for probabilistic processes and applications to information-hiding

Abstract

ABSTRACT. We introduce a novel modal logic, namely the doxastic µ-calculus with error control (DµCEC), and propose a formalization of probabilistic anonymity and oblivious transfer in the logic, and the validation of these formalizations on implementations formalized in probabilistic CCS. The distinguishing feature of our logic is to provide a combination of dynamic operators for belief (whence the attribute "doxastic") with a control on the possible error of apprehension of the perceived reality, and for internalized probability. Both operators are dynamic (non-monotonic) thanks to the possibility of combining them with temporal operators, and are parameterized with a lower and upper probability bound (the error control).

Computer-aided decision-making with trust relations and trust domains (cryptographic applications)

“…Future work We could unify our notions of weak and strong trust relation (domain) in a notion of graded trust relation (domain) defined in terms of graded (common) belief instead of plain (common) belief and plain (common) knowledge, respectively [42]. Informally, knowledge is belief with 100% certitude.…”

Approximate Analyzing of Labeled Transition Systems

“…Step (1) until do (7) i f( , ) ∈ then; (8) i f( , ) ∈ then; (9) , := , − , ; (10) e l s e ; (11) , := , − , ; (12) end if; (13) end if; (14) end for ( − loop) (15) end if; (16) end for ( − loop); (17) end for ( − loop); Algorithm 2: Algorithm MILU.…”

“…In recent years, some new process calculus systems have been proposed. For example, probabilistic process algebra [6][7][8][9][10][11][12] and stochastic process algebra [13] are proposed to describe possible or random information; real-time process algebra [14][15][16][17] is proposed to describe the action time. In the field of process algebra, as the most important semantic model, the transition system is widely used, especially labeled transition system [18], which can describe the general behavior of concurrent systems.…”