Qingliang Chen

A computationally grounded logic of knowledge, belief and certainty

This paper presents a logic of knowledge, belief and certainty, which allows us to explicitly express the knowledge, belief and certainty of an agent. A computationally grounded model, called interpreted KBC systems, is given for interpreting this logic. The relationships between knowledge, belief and certainty are explored. In particular, certainty entails belief; and to the agent what it is certain of appears to be the knowledge. To formalize those agents that are able to introspect their own belief and certainty, we identify a subclass of interpreted KBC systems, called introspective KBC systems. We provide sound and complete axiomatizations for the logics. We show that the validity problem for the interpreted KBC systems is PSPACE-complete, and the same problem for introspective KBC systems is co-NP complete, thus no harder than that of the propositional logic.

A complete first-order temporal BDI logic for forest multi-agent systems

This paper presents a new complete first-order temporal BDI logic and forest multi-agent system. The main characteristic of the logic is that its semantic model is based on the forest multi-agent system, which enables us to reason about beliefs, desires, and intentions between agents with different layers such as father agent and child agent. The logical reasoning and hierarchical structures of the forest multi-agent system can suitably capture the hierarchical property of the real systems and therefore is practically realistic. We propose further four classes of first-order BDI interpreted systems and four proof systems which are sound and complete with respect to corresponding classes of BDI interpreted systems. Finally, we give a case to show how to characterize the forest multi-agent system by using the hierarchical structure of modules, and to solve the model checking problem of first-order temporal BDI logic for the forest multi-agent system.

Automatic Verification of Web Service Protocols for Epistemic Specifications under Dolev-Yao Model

Web service protocols are designed in XML formats so the message structures within are quite different from the conventional protocols. Therefore, the traditional formal verification techniques which have gain substantial achievements in practice, cannot be applied directly to them because their underlying models are written in Alice\Bob-style descriptions using high-level message formats instead of XML tags. In this paper, we propose a justification-oriented and automatic formal approach to verify, in the standard Dolev-Yao model, security properties expressed as epistemic notions for a Web service protocol, based on a fault-preserving mapping tool called SuD (SOAP under Dolev-Yao). Our approach can shed more light on Web service protocols in another perspective because the concerned properties to be verified are some inherent features of protocols.

Primitive Recursiveness of Real Numbers under Different Representations

In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure-Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computability of real numbers. However, the primitive recursive (p.r., for short) versions of these representations can lead to different notions of p.r. real numbers. Several interesting results about p.r. real numbers can be found in literatures. In this paper we summarize the known results about the primitive recursiveness of real numbers for different representations as well as show some new relationships. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers.

Verification of authentication protocols for epistemic goals via SAT compilation

This paper introduces a new methodology that uses knowledge structures, a specific form of Kripke semantics for epistemic logic, to analyze communication protocols over hostile networks. The paper particularly focuses on automatic verification of authentication protocols. Our approach is based on the actual definitions of a protocol, not on some difficult-to-establish justifications. The proposed methodology is different from many previous approaches to automatic verification of security protocols in that it is justification-oriented instead of falsification-oriented, i.e., finding bugs in a protocol. The main idea is based on observations: separating a principal executing a run of protocol from the role in the protocol, and inferring a principal’s knowledge from the local observations of the principal. And we show analytically and empirically that this model can be easily reduced to Satisfiability (SAT) problem and efficiently implemented by a modern SAT solver.

Primitive recursive real numbers

In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure - Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computable real numbers. Although the computable real numbers can be defined in various equivalent ways, if computable is replaced by primitive recursive (p. r., for short), these definitions lead to a number of different concepts, which we compare in this article. We summarize the known results and add new ones. In particular we show that there is a proper hierarchy among p. r. real numbers by nested interval representation, Cauchy representation, b -adic expansion representation, Dedekind cut representation, and continued fraction expansion representation. Our goal is to clarify systematically how the primitive recursiveness depends on the representations of the real numbers.

Model checking temporal logics of knowledge and its application in security verification

Model checking has being used mainly to check if a system satisfies the specifications expressed in temporal logic and people pay little attention to the problem for model checking logics of knowledge. However, in the distributed systems community, the desirable specifications of systems and protocols have been expressed widely in logics of knowledge. In this paper, based on the SMV, by the semantics of knowledge and set theory, approaches for model checking logics of knowledge and common knowledge are presented. These approaches make SMV’s functions extended from temporal logics to temporal logics of knowledge. We will illustrate in an example the applications to security verifications for a cryptographic protocol.

A complete coalition logic of temporal knowledge for multi-agent systems

Coalition logic (CL) is one of the most influential logical formalisms for strategic abilities of multi-agent systems. CL can specify what a group of agents can achieve through choices of their actions, denoted by [C]ϕ to state that a group of agents C can have a strategy to bring about ϕ by collective actions, no matter what the other agents do. However, CL lacks the temporal dimension and thus can not capture the dynamic aspects of a system. Therefore, CL can not formalize the evolvement of rational mental attitudes of the agents such as knowledge, which has been shown to be very useful in specifications and verifications of distributed systems, and has received substantial amount of studies. In this paper, we introduce coalition logic of temporal knowledge (CLTK), by incorporating a temporal logic of knowledge (Halpern and Vardi’s logic of CKLn) into CL to equip CL with the power to formalize how agents’ knowledge (individual or group knowledge) evolves over the time by coalitional forces and the temporal properties of strategic abilities as well. Furthermore, we provide an axiomatic system for CLTK and prove that it is sound and complete, along with the complexity of the satisfiability problem which is shown to be EXPTIME-complete.

A Concurrent Dynamic Logic of Knowledge, Belief and Certainty for Multi-agent Systems

This paper extends the logic of Knowledge, Belief and Certainty from one agent to multi-agent systems, and gives a good combination between logic of knowledge, belief, certainty in multi-agent systems and actions that have concurrent and dynamic properties. Based on it, we present a concurrent dynamic logic of knowledge, belief and certainty for MAS, which is called CDKBC logic. Furthermore, a CDKBC model is given for interpreting this logic. We construct a CDKBC proof system for the logic and show the proof system is sound and complete, and prove the validity problem for the system is EXPTIME-complete.

Quantified Coalition Logic for BDI-Agents: Completeness and Complexity

This paper introduces a multi-dimensional modal logic of Quantified Coalition Logic of Beliefs, Desires and Intentions (QCLBDI) to reason about how agents’ mental attitudes evolve by cooperation in game-like multi-agent systems. We present a complete axiomatic system of QCLBDI with the formal proof and show that the satisfiability for QCLBDI is PSPACE-complete, computationally no harder than that of CL.