Logics of temporal-epistemic actions

We propose Dynamic Epistemic Temporal Logic, a dynamic-protocol framework that overcomes the Problem of Synchronicity in the popular Dynamic Epistemic Logic approach to reasoning about multi-agent belief change. Dynamic Epistemic Temporal Logic not only extends the domain of applicability of standard Dynamic Epistemic Logic, but it also clarifies how certain structural properties (such as synchronicity) arise from the inherent structure of the standard "update frames" (or "action models") of Dynamic Epistemic Logic. * This paper is a revised and extended version of .

Logic Journal of IGPL, 2013

We give a relation between a logic of knowledge and change, with a semantics on Kripke models, and a logic of knowledge and time, with a semantics on interpreted systems. In particular, given an epistemic state (pointed Kripke model with equivalence relations) and a formula in a dynamic epistemic logic (a logic describing the consequences of epistemic actions), we construct an interpreted system relative to that epistemic state and that formula that satisfies the translation of the formula into a temporal epistemic logic. The construction involves that the protocol that is implicit in the dynamic epistemic formula, i.e., the set of sequences of actions being executed to evaluate the formula, is made explicit. We first focus on the logic of knowledge and change that is known as public announcement logic, then generalize our results to a dynamic epistemic logic. When compared to Kripke (possible worlds) models, interpreted systems have at least two appealing features: a natural accessibility relation between domain objects, and an equally natural notion of dynamics, modelled by runs. The accessibility relation as we know it from the possible worlds model is in this case grounded; it has a direct and natural interpretation, as follows. In an interpreted system, the role of possible worlds is performed by global states, which are constituted by the agents' local states and the state of the environment. Each agent knows exactly its own local state and the possible local states of other agents: two global states are indistinguishable for an agent if his local compartment is the same. Secondly, an interpreted system defines a number of runs through such global states (i.e., a sequence of global states). Each run corresponds to a possible computation allowed by a protocol. In an object language with temporal and epistemic operators one can then express temporal properties such as liveness and temporal epistemic properties such as perfect recall.

A series of temporal reasoning tasks are identified which motivate the consideration and application of temporal logics in artificial intelligence. There follows a discussion of the broad issues involved in modelling time and constructing a temporal logic. The paper then presents a detailed review of the major approaches to temporal logics: first-order logic approaches, modal temporal logics and reified temporal logics. The review considers the most significant exemplars within the various approaches, including logics due to Russell, Hayes and McCarthy, Prior, McDermott, Allen, Kowalski and Sergot. The logics are compared and contrasted, particularly in their treatments of change and action, the roles they seek to fulfil and the underlying models of time on which they rest. The paper concludes with a brief consideration of the problem of granularity-a problem of considerable significance in temporal reasoning, which has yet to be satisfactorily treated in a temporal logic.

Proceedings of the 6th international joint conference on Autonomous agents and multiagent systems - AAMAS '07, 2007

We introduce CTLKR, a temporal epistemic logic extending CTLK with an epistemic operator N i for n agents, referring to knowledge regarding future states. This modality is defined in terms of the intersection of the transitive reflexive closure of a serial temporal relation and the standard epistemic relation (which is an equivalence relation). We prove that CTLKR has the finite model property, is decidable, and is finitely axiomatisable. Further, we investigate an application of CTLKR to reason about the bit transmission problem.

2006

This paper provides a framework based on temporal defeasible logic to reason about deliberative rule-based cognitive agents. Compared to previous works in this area our framework has the advantage that it can reason about temporal rules. We show that for rule-based cognitive agents deliberation is more than just deriving conclusions in terms of their mental components. Our paper is an extension of in the area of cognitive agent programming.

1996

Abstract This paper shows how past temporal logic can be incorporated into the action description language A 4] and its extensions. Incorporating past temporal logic will allow us to elegantly express e ects of actions that depend not only on the current state of the world but on previous actions and states. It will also allow us to elegantly express dynamic constraints beyond the one-step dynamic constraints discussed in 2].

2009 IEEE/WIC/ACM International Joint Conference on Web Intelligence and Intelligent Agent Technology, 2009

For modelling and verifying agent systems, many researchers have proposed different logical systems. Since agentbased systems are designed to operate in dynamic environments such as the Internet, it is also important to model the temporal aspects of such systems in a systematic way. In this paper, we use a temporalised epistemic logic called TEL for formalising agent-based systems. We also propose a labelled tableau system and a model checking method for this logic. With logic TEL and its associated proof system, we are able to reason about, and verify agent systems operating in dynamic environments.

1998

2009

Temporal logic of knowledge is a combination of temporal and epistemic logic that has been shown to be very useful in areas such as distributed systems, security, and multi-agent systems. However, the complexity of the logic can be prohibitive. We here develop a refined version of such a logic and associated tableau procedure with improved complexity but where important classes of specification can still be described. This new logic represents a combination of an "exactly one" temporal logic with an S5 multi-modal logic again restricted to the "exactly one" form.

Cognitive science, 1982

Much previous work in artificial intelligence has neglected representing time in all its complexity. In particular, it has neglected continuous change and the indeterminacy of the future. To rectify this, I have developed a first-order temporal logic, in which it is possible to name and prove things about facts, events, plans, and world histories. In particular, the logic provides analyses of causality, continuous change in quantities, the persistence of facts (the frame problem), and the relationship between tasks and actions. It may be possible to implement a temporal-inference machine based on this logic, which keeps track of several "maps" of a time line, one per possible history.