Endogenizing Epistemic Actions Will Nalls

Electronic Proceedings in Theoretical Computer Science

Through a series of examples, we illustrate some important drawbacks that the action logic framework suffers from in its ability to represent the dynamics of information updates. We argue that these problems stem from the fact that the action model, a central construct designed to encode agents' uncertainty about actions, is itself effectively common knowledge amongst the agents. In response to these difficulties, we motivate and propose an alternative semantics that avoids them by (roughly speaking) endogenizing the action model. We discuss the relationshop to action logic, and provide a sound and complete axiomatization.

2007

Logics of action, for reasoning about the effects of state change, and logics of belief, accounting for belief revision and update, have much in common. Furthermore, we may undertake an action because we hold a particular belief, and revise our beliefs in the light of observed consequences of an action. So studies of these two aspects are inevitably intertwined. However, we argue, a clear separation of the two is helpful in understanding their interactions. We give a semantic presentation of such a separation, introducing a semantic setting that supports one logic for describing the effects of actions, which are modeled as changing the values of particular atomic properties, or fluents, and another for expressing more complex facts or beliefs about the world. We use a simple state-logic, to account for state change, and show how it can be integrated with a variety of domain-logics, of fact or belief, for reasoning about the world. Stateand domain-logics are linked, syntactically and...

2017

Logics of action, for reasoning about the effects of state change, and logics of belief, accounting for belief revision and update, have much in common. Furthermore, we may undertake an action because we hold a particular belief, and revise our beliefs in the light of observed consequences of an action. So studies of these two aspects are inevitably intertwined. However, we argue, a clear separation of the two is helpful in understanding their interactions. We give a semantic presentation of such a separation, introducing a semantic setting that supports one logic for describing the effects of actions, which are modeled as changing the values of particular atomic properties, or fluents, and another for expressing more complex facts or beliefs about the world. We use a simple state-logic, to account for state change, and show how it can be integrated with a variety of domain-logics, of fact or belief, for reasoning about the world. Stateand domain-logics are linked, syntactically and...

Journal of Logic and Computation, 2007

We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. due to secrecy and deceit, as well as nested knowledge. We give a purely algebraic treatment of the muddy children puzzle, which moreover extends to situations where the children are allowed to lie and cheat. Epistemic actions, that is, information exchanges between agents A, B, . . . ∈ A, are modeled as elements of a quantale. The quantale (Q, , •) acts on an underlying Q-right module (M, ) of epistemic propositions and facts. The epistemic content is encoded by appearance maps, one pair f M A : M → M and f Q A : Q → Q of (lax) morphisms for each agent A ∈ A, which preserve the module and quantale structure respectively. By adjunction, they give rise to epistemic modalities [12], capturing the agents' knowledge on propositions and actions. The module action is epistemic update and gives rise to dynamic modalities [21] -cf. weakest precondition. This model subsumes the crucial fragment of Baltag, Moss and Solecki's [6] dynamic epistemic logic, abstracting it in a constructive fashion while introducing resource-sensitive structure on the epistemic actions.

Erkenntnis, 2000

Dynamic Epistemic Logic makes it possible to model and reason about information change in multi-agent systems. Information change is mathematically modeled through epistemic action Kripke models introduced by Baltag et al. Also, van Ditmarsch interprets the information change as a relation between epistemic states and sets of epistemic states and to describe it formally, he considers a special constructor L B called learning operator. Inspired by this, it seems natural to us that the basic source of information change in a multi-agent system should be learning an announcement by some agents together, privately, concurrently or even wrongly. Hence moving along this path, we introduce the notion of a learning program and prove that all finite K45 action models can be described by our learning programs.

Logics

We build and study dynamic versions of epistemic logic. We study languages parameterized by an action signature that allows one to express epistemic actions such as (truthful) public announcements, completely private announcements to groups of agents, and more. The language L(Σ) is modeled on dynamic logic. Its sentence-building operations include modalities for the execution of programs, and for knowledge and common knowledge. Its program-building operations include action execution, composition, repetition, and choice. We consider two fragments of L(Σ). In L1(Σ), we drop action repetition; in L0(Σ), we also drop common knowledge. We present the syntax and semantics of these languages and sound proof systems for the validities in them. We prove the strong completeness of a logical system for L0(Σ) and the weak completeness of one for L1(Σ). We show the finite model property and, hence, decidability of L1(Σ). We translate L1(Σ) into PDL, obtaining a second proof of decidability. We ...

Synthese, 2015

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known "action models" from Dynamic Epistemic Logic. Our "temporal action models" may be used to define a number of informational actions that can modify the "objective" temporal structure of a model along with the agents' basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in Dynamic Epistemic Logic.

Abstract This paper reports on the use of logic program updates to models actions that bring about changes in knowledge states describing the world and its rules. The LUPS language is employed to specify concurrent update rules to model actions that depend on, and change, rule rich world states, not described simply by propositional uents. This language and corresponding semantics, whose original stable semantics we generalize to the well-founded setting, is brie y recapitulated here.

Artificial Intelligence, 1996

We propose a modal action logic that combines ideas from H.A. Simon's bounded rationality, S. Kripke's possible world semantics, G.H. von Wright's preference logic, Pratt's dynamic logic, Stalnaker's minimal change and more recent approaches to update semantics. ALX (the xth action logic) is sound, complete and decidable, making it the first complete logic for two-place preference operators. ALX avoids important drawbacks of other action logics, especially the counterintuitive necessitation rule for goals (every theorem must be a goal) and the equally counterintuitive closure of goals under logical implication.