Temporal Logic Of Knowledge Research Articles

Finite sequent calculi for PLTL

Two sequent calculi for temporal logic of knowledge are presented: one containing invariant-like rule and the other containing looping axioms. Its proved that the calculi are equivalent, sound and complete.

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]? to state that a group of agents C can have a strategy to bring about ? 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 CKL n ) 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.

Non-axiomatizability for the linear temporal logic of knowledge with concrete observability

We show that propositional linear temporal logic with knowledge modalities but without common knowledge has an undecidable satisfiability problem when interpreted in a ‘concrete’ semantics with perfect recall or with perfect recall and synchrony.We then conclude that this concrete semantics is not axiomatizable in the semantics, based on local states.

Symbolic Model Checking Knowledge and Time in Multi-Agent System Via Extended Mu-Calculus

Clarke and McMillan presented symbolic approaches to model check temporal logics via mu-calculus and OBDDs.These approaches are very efficient and can be applied to verify many practical systems with extremely large state spaces in excess of 1020 states.However,these approaches cannot model check knowledge logics.But temporal logics of knowledge can describe more accurately the desirable specification of systems and protocols in distributed systems.In this paper,the symbolic approaches for model checking the temporal logic of knowledge via extended mu-calculus and OBDDs are discussed mainly.First the Kripke structure and mu-calculus are extended.Then the symbolic approaches for model checking temporal logics of knowledge via extended mu-calculus and OBDDs are presented.

Temporal Logics of Knowledge and their Applications in Security

Temporal logics of knowledge are useful for reasoning about situations where the knowledge of an agent or component is important, and where change in this knowledge may occur over time. Here we investigate the application of temporal logics of knowledge to the specification and verification of security protocols. We show how typical assumptions relating to authentication protocols can be specified. We consider verification methods for these logics, in particular, focusing on proofs using clausal resolution. Finally we present experiences from using a resolution based theorem prover applied to security protocols specified in temporal logics of knowledge.

Sequent calculi for branching time temporal logics of knowledge and beliefwith awareness: Completeness and decidability

In this paper, we consider branching time temporal logic CT L with epistemic modalities for knowledge (belief) and with awareness operators. These logics involve the discrete-time linear temporal logic operators “next” and “until” with the branching temporal logic operator “on all paths”. In addition, the temporal logic of knowledge (belief) contains an indexed set of unary modal operators “agent i knows” (“agent i believes”). In a language of these logics, there are awareness operators. For these logics, we present sequent calculi with a restricted cut rule. Thus, we get proof systems where proof-search becomes decidable. The soundness and completeness for these calculi are proved.

Algorithm Research on “On the Fly” Model Checking Temporal Logics of Knowledge in Multi-Agent Systems

Algorithm Research on “On the Fly” Model Checking Temporal Logics of Knowledge in Multi-Agent Systems

First-Order Temporal Verification in Practice

First-order temporal logic, the extension of first-order logic with operators dealing with time, is a powerful and expressive formalism with many potential applications. This expressive logic can be viewed as a framework in which to investigate problems specified in other logics. The monodic fragment of first-order temporal logic is a useful fragment that possesses good computational properties such as completeness and sometimes even decidability. Temporal logics of knowledge are useful for dealing with situations where the knowledge of agents in a system is involved. In this paper we present a translation from temporal logics of knowledge into the monodic fragment of first-order temporal logic. We can then use a theorem prover for monodic first-order temporal logic to prove properties of the translated formulas. This allows problems specified in temporal logics of knowledge to be verified automatically without needing a specialized theorem prover for temporal logics of knowledge. We present the translation, its correctness, and examples of its use.

Tableaux for logics of time and knowledge with interactions relating to synchrony

The paper describes tableaux based proof methods for temporal logics of knowledge allowing non-trivial interaction axioms between the modal and temporal components, namely those of synchrony and no learning and synchrony and perfect recall. The interaction axioms allow the description of how knowledge evolves over time and makes reasoning in such logics theoretically more complex. Such logics can be used to specify systems that involve the knowledge of processes or agents and which change over time, for example agent based systems, knowledge games or security protocols. Soundness, completeness and termination results for the tableaux are proved.

Resolution for temporal logics of knowledge

Resolution for temporal logics of knowledge

A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief

ABSTRACT In this paper we define two logics, KLn and BLn, and present tableau-based decision procedures for both. KLn is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BLn is somewhat similar; it is a temporal logic that contains connectives for representing the beliefs of agents. In addition to a complete formal definition of the two logics and their decision procedures, the paper includes a brief review of their applications in AI and mainstream computer science, correctness proofs for the decision procedures, a number of worked examples illustrating the decision procedures, and some pointers to further work.