Dynamic Epistemic Logic with Assignments, Concurrency and Communication Actions (original) (raw)

Dynamic Epistemic Logic with Communication Actions

Electronic Notes in Theoretical Computer Science, 2019

This work proposes a Dynamic Epistemic Logic with Communication Actions that can be performed concurrently. Unlike Concurrent Epistemic Action Logic introduced by Ditmarsch, Hoek and Kooi [14], where the concurrency mechanism is the so called true concurrency, here we use an approach based on process calculus, like CCS and CSP, and Action Models Logic. Our approach makes possible the proof of soundness, completeness and decidability, different from the others approaches. We present an axiomatization and show that the proof of soundness, completeness and decidability can be done using a reduction method.

Logics for Epistemic Actions: Completeness, Decidability, Expressivity

ArXiv, 2022

We consider dynamic versions of epistemic logic as formulated in [1]. That paper proposed a family of logical languages L(Σ) parameterized by action signatures. In addition to L(Σ), we consider two fragments L0(Σ) and L1(Σ) of it. We review the syntax and semantics of these languages L0(Σ),L1(Σ), and L(Σ), as well as the sound proof systems for the validities in them. It was shown in [13] that validity in L(Σ) is Π 1 -complete, so there are no recursively axiomatized complete logical systems for it. On the positive side, this paper proves the strong completeness of the axiomatization of L0(Σ) and the weak completeness of L1(Σ). The work involve a detour into term rewriting theory. And since at the heart of the argument is modal filtration, it gives the finite model property and hence decidability. We also give a translation of L1(Σ) into PDL, hence we obtain a second proof of the decidability of L1(Σ). The paper closes with some results on expressive power. These are mostly concerne...

Action Models with Postconditions

Computación y Sistemas, 2017

This work proposes a extension of dynamic epistemic logic to work with assignment. The difference between this work and others works, such as [7], is the use of actions models, from DEL, to make Boolean assignments to the propositions, instead of creating new mechanisms to make the assignments. We extend the definition of action model by creating the postcondition property of each state of the model, making it possible to assign Boolean values to the propositions.

General Dynamic Dynamic Logic (2012)

in Thomas Bolander, Torben Brauner, Silvio Ghilardi, and Lawrence Moss, eds, Advances in Modal Logic, Volume 9, pp.239--260. College Publications, London, 2012.

Dynamic epistemic logic (DEL) extends purely modal epistemic logic (S5) by adding dynamic operators that change the model structure. Propositional dynamic logic (PDL) extends basic modal logic with programs that allow the de nition of complex modalities. We provide a common generalisation: a logic that is `dynamic' in both senses, and one that is not limited to S5 as its modal base. It also incorporates, and signi cantly generalises, all the features of existing extensions of DEL such as BMS [3] and LCC [21]. Our dynamic operators work in two steps. First, they provide a multiplicity of transformations of the original model, one for each `action' in a purely syntactic `action structure' (in the style of BMS). Second, they specify how to combine these multiple copies to produce a new model. In each step, we use the generality of PDL to specify the transformations. The main technical contribution of the paper is to provide an axiomatisation of this `general dynamic dynamic logic' (GDDL). This is done by providing a computable translation of GDDL formulas to equivalent PDL formulas, thus reducing the logic to PDL, which is decidable. The proof involves switching between representing programs as terms and as automata. We also show that both BMS and LCC are special cases of GDDL, and that there are interesting applications that require the additional generality of GDDL, namely the modelling of private belief update. More recent extensions and variations of BMS and LCC are also discussed.

1995: Reasoning about Action in Dynamic Logic

We study an approach to reasoning about action and change in a dynamic logic setting and provide a solution to problems which are related to tbe frame problem. Unlike most work on the frame problem the logic described in this paper is TTWnotonic and (implicitly) allows for the occurrence of actions of multiple agents. The need to state a large number of "frame axioms" is alleviated by introducing a concept of chronolcgicaJ. pfUervation to dynamic logic. As a side effect, this concept permits to encode temporoi properties in a natural way. We compare the relative merits of our approach and nonmonotonic approaches facing different aspects of the frame problem. It can be shown that the resulting extended systems of propositional dynamic logic preserve (weak) completeness, finite model property and decidability.

Towards a Proof-Theoretic Semantics for Dynamic Logics

ILLC Publications, Master of Logic Thesis (MoL) Series, 2013

This thesis provides an analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics. After an illustration of the basic principles of proof-theoretic semantics, we review some of the most significant proposals of proof systems for dynamic epistemic logics, and we critically reflect on them in the light of proof-theoretic semantic principles. The main original contributions of the present thesis are: (a) a revised version of the display-style calculus D.EAK, which we argue to be more adequate from the proof-theoretic semantic viewpoint; the main feature of this revision is that a smoother proof (so-called Belnap-style) of cut-elimination holds for it, which is problematic for the original version of D.EAK. (b) The introduction of a novel, multi-type display calculus for dynamic epistemic logic, which we refer to as Dynamic Calculus. The presence of types endows the language of the Dynamic Calculus with additional expressivity, and makes it possible to design rules with an even smoother behavior. We argue that this calculus paves the way towards a general methodology for the design of proof systems for the generality of dynamic logics, and certainly for proof systems beyond dynamic epistemic logic. We prove that the Dynamic Calculus adequately captures Baltag-Moss-Solecki's dynamic epistemic logic, and enjoys Belnap-style cut elimination.

Concurrent Games in Dynamic Epistemic Logic

Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence

Action models of Dynamic Epistemic Logic (DEL) represent precisely how actions are perceived by agents. DEL has recently been used to define infinite multi-player games, and it was shown that they can be solved in some cases. However, the dynamics being defined by the classic DEL update product for individual actions, only turn-based games have been considered so far. In this work we define a concurrent DEL product, propose a mechanism to resolve conflicts between actions, and define concurrent DEL games. As in the turn-based case, the obtained concurrent infinite game arenas can be finitely represented when all actions are public, or all are propositional. Thus we identify cases where the strategic epistemic logic ATL*K can be model checked on such games.

Dynamic sequent calculus for the logic of Epistemic Actions and Knowledge

EPiC Series in Computing

We develop a family of display-style, cut-free sequent calculi for dynamic epistemic logics on both an intuitionistic and a classical base. Like the standard display calculi, these calculi are modular: just by modifying the structural rules according to Dosen’s principle, these calculi are generalizable both to different Dynamic Logics (Epistemic, Deontic, etc.) and to different propositional bases (Linear, Relevant, etc.). Moreover, the rules they feature agree with the standard relational semantics for dynamic epistemic logics.

A General Dynamic Dynamic Logic

Dynamic epistemic logic (DEL) extends purely modal epistemic logic (S5) by adding dynamic operators that change the model structure. Propositional dynamic logic (PDL) extends basic modal logic with programs that allow the definition of complex modalities. We provide a common generalisation: a logic that is `dynamic' in both senses, and one that is not limited to S5 as its modal base. It also incorporates, and significantly generalises, all the features of existing extensions of DEL such as BMS [1] and LCC [2]. Our dynamic operators work in two steps. First, they provide a multiplicity of transformations of the original model, one for each `action' in a purely syntactic `action model' (in the style of BMS). Second, they specific how to combine these multiple copies to produce a new model. In each step, we use the generality of PDL to specify the transformations. The main technical contribution of the paper is to provide an axiomatisation of this `general dynamic dynamic logic' (GDDL). This is done by providing a computable translation of GDDL formulas to equivalent PDL formulas, thus reducing the logic to PDL, which is decidable. The proof involves switching between representing programs as terms and as automata. We also show that both BMS and LCC are special cases of GDDL, and that there are interesting applications that require the additional generality of GDDL, namely the modelling of private belief update. [1] Baltag, A., L. S. Moss and S. Solecki, The logic of public announcements, common knowledge and private suspicious, Technical Report SEN-R9922, CWI, Amsterdam (1999). [2] van Benthem, J., J. van Eijck and B. Kooi, Logics of communication and change, Information and computation 204 (2006), pp. 1620–1662.

Dynamic Epistemic Temporal Logic

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 .