A Novel Symbolic Approach to Verifying Epistemic Properties of Programs

Abstract

We introduce a framework for the symbolic verification of epistemic properties of programs expressed in a class of general-purpose programming languages. To this end, we reduce the verification problem to that of satisfiability of first-order formulae in appropriate theories. We prove the correctness of our reduction and we validate our proposal by applying it to two examples: the dining cryptographers problem and the ThreeBallot voting protocol. We put forward an implementation using existing solvers, and report experimental results showing that the approach can perform better than state-of-the-art symbolic model checkers for temporal-epistemic logic.

Program Semantics and a Verification Technique for Knowledge-Based Multi-Agent Systems

“…Logics of Visibility for Programs. Others [20,31,35] looked at how multiagent epistemic logics with imperfect information would apply not to generic systems, but specifically to programs (over an arbitrary first-order domain), and -with that -at agents' visibility of programs variables; this transforms program's state space into a possible-worlds model. In this domain, the epistemic predicate K a (y = 0) denotes that agent a knows that the variable y is equal to 0 (in some program).…”

“…Gorogiannis et al [20] gave a "program-epistemic" logic, which is a dynamic logic with concrete programs (e.g., programs with assignments on variables over first-order domains such as integer, reals, or strings) and having an epistemic predicate logic as its base logic. Moreover, à la the aforesaid [38,31,35], the epistemic model in [20] relies on the observability of the programs' variables by agents. Gorogiannis et al transformed program-epistemic validity into a firstorder validity problem, and in practice, outperformed the then state-of-the-art tools in epistemic properties verification.…”

“…Our Work: Enhanced "Program-epistemic" Logics & Its Verification. We build on top of [20] in several significant ways. Firstly, the verification mechanisation in [20] only supports "classical" programs; this means that [20] cannot support tests on knowledge of agents.…”

“…We build on top of [20] in several significant ways. Firstly, the verification mechanisation in [20] only supports "classical" programs; this means that [20] cannot support tests on knowledge of agents. Yet, such tests are essential in modelling communication of knowledge: e.g., in epistemic puzzles such as the Muddy Children and Cheryl's birthday [27] and in the so-called "knowledge-based" programs used to abstract communication protocols [17].…”

“…Yet, such tests are essential in modelling communication of knowledge: e.g., in epistemic puzzles such as the Muddy Children and Cheryl's birthday [27] and in the so-called "knowledge-based" programs used to abstract communication protocols [17]. Secondly, the logic in [20] allows only for knowledge reasoning after a program P executed, not before its run (e.g., not K alice ( P φ), only P (K alice φ)). Lastly, the framework in [20] assumes a single-agent epistemic logic and does not allow for reasoning about nested knowledges operators (e.g., K alice (K bob φ)).…”