Coalition and Relativised Group Announcement Logic

There are several ways to quantify over public announcements. The most notable are reflected in arbitrary, group, and coalition announcement logics (APAL, GAL, and CAL correspondingly), with the latter being the least studied so far. In the present work, we consider coalition announcements through the lens of group announcements, and provide a complete axiomatisation of a logic with coalition announcements. To achieve this, we employ a generalisation of group announcements. Moreover, we study some logical properties of both coalition and group announcements that have not been studied before.acceptedVersio

Coalition Logic for Specification and Verification of Smart Contract Upgrades

Postponed access: the file will be available after 2023-11-12It has been argued in the literature that logics for reasoning about strategic abilities, and in particular coalition logic (CL), are well-suited for verification of properties of smart contracts on a blockchain. Smart contracts, however, can be upgraded by providing a new version of a contract on a new block. In this paper, we extend one of the recent formalisms for reasoning about updating CL models with a temporal modality connecting a newer version of a model to the previous one. In such a way, we make a step towards verification of properties of smart contracts with upgrades. We also discuss some properties of the resulting logic and the complexity of its model checking problem.acceptedVersio

Quantifying over information change with common knowledge

Public announcement logic (PAL) extends multi-agent epistemic logic with dynamic operators modelling the effects of public communication. Allowing quantification over public announcements lets us reason about the existence of an announcement that reaches a certain epistemic goal. Two notable examples of logics of quantified announcements are arbitrary public announcement logic (APAL) and group announcement logic (GAL). While the notion of common knowledge plays an important role in PAL, and in particular in characterisations of epistemic states that an agent or a group of agents might make come about by performing public announcements, extensions of APAL and GAL with common knowledge still haven’t been studied in detail. That is what we do in this paper. In particular, we consider both conservative extensions, where the semantics of the quantifiers is not changed, as well as extensions where the scope of quantification also includes common knowledge formulas. We compare the expressivity of these extensions relative to each other and other connected logics, and provide sound and complete axiomatisations. Finally, we show how the completeness results can be used for other logics with quantification over information change.publishedVersio

Coalition announcements

Coalition announcement logic is one of the family of logics of quantified announcements. It extends public announcement logic with formulas $\langle \! [ G ] \! \rangle \varphi$ that are read as `there is a truthful public announcement by agents from $G$ such that whatever agents from $A \setminus G$ announce at the same time, $\varphi$ holds after the joint announcement.' The logic has enjoyed comparatively less attention than its siblings --- arbitrary and group announcement logics. The reason for such a situation can be partially attributed to the inherent alternation of quantification in coalition announcements. To deal with the problem, we consider relativised group announcements that separate the coalition's announcement from the anti-coalition's response. We present coalition and relativised group announcement logic and show its completeness. Apart from that, we prove that the complexity of the model-checking problem for coalition announcement logic is PSPACE-complete in the general case, and in P in a special case of positive target formulas. We also study relative expressivity of logics of quantified announcements. In particular we show that arbitrary and coalition announcement logics are not at least as expressive as group announcement logic. Finally, we present a counter-example to the proposed definition of coalition announcements in terms of group announcements, and consider some other interesting properties

Satisfiability of Arbitrary Public Announcement Logic with Common Knowledge is Σ11\Sigma^1_1-hard

Arbitrary Public Announcement Logic with Common Knowledge (APALC) is an extension of Public Announcement Logic with common knowledge modality and quantifiers over announcements. We show that the satisfiability problem of APALC on S5-models, as well as that of two other related logics with quantification and common knowledge, is $\Sigma^1_1$-hard. This implies that neither the validities nor the satisfiable formulas of APALC are recursively enumerable. Which, in turn, implies that APALC is not finitely axiomatisable.Comment: In Proceedings TARK 2023, arXiv:2307.0400

Coalition announcements

Coalition announcement logic is one of the family of logics of quantified announcements. It extends public announcement logic with formulas $\langle \! [ G ] \! \rangle \varphi$ that are read as `there is a truthful public announcement by agents from $G$ such that whatever agents from $A \setminus G$ announce at the same time, $\varphi$ holds after the joint announcement.' The logic has enjoyed comparatively less attention than its siblings --- arbitrary and group announcement logics. The reason for such a situation can be partially attributed to the inherent alternation of quantification in coalition announcements. To deal with the problem, we consider relativised group announcements that separate the coalition's announcement from the anti-coalition's response. We present coalition and relativised group announcement logic and show its completeness. Apart from that, we prove that the complexity of the model-checking problem for coalition announcement logic is PSPACE-complete in the general case, and in P in a special case of positive target formulas. We also study relative expressivity of logics of quantified announcements. In particular we show that arbitrary and coalition announcement logics are not at least as expressive as group announcement logic. Finally, we present a counter-example to the proposed definition of coalition announcements in terms of group announcements, and consider some other interesting properties

Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power

Public announcement logic (PAL) is an extension of epistemic logic with dynamic operators that model the effects of all agents simultaneously and publicly acquiring the same piece of information. One of the extensions of PAL, group announcement logic (GAL), allows quantification over (possibly joint) announcements made by agents. In GAL, it is possible to reason about what groups can achieve by making such announcements. It seems intuitive that this notion of coalitional ability should be closely related to the notion of distributed knowledge, the implicit knowledge of a group. Thus, we study the extension of GAL with distributed knowledge, and in particular possible interaction properties between GAL operators and distributed knowledge. The perhaps surprising result is that, in fact, there are no interaction properties, contrary to intuition. We make this claim precise by providing a sound and complete axiomatisation of GAL with distributed knowledge. We also consider several natural variants of GAL with distributed knowledge, as well as some other related logic, and compare their expressive power.publishedVersio

No Finite Model Property for Logics of Quantified Announcements

Quantification over public announcements shifts the perspective from reasoning strictly about the results of a particular announcement to reasoning about the existence of an announcement that achieves some certain epistemic goal. Depending on the type of the quantification, we get differ- ent formalisms, the most known of which are arbitrary public announcement logic (APAL), group announcement logic (GAL), and coalition announcement logic (CAL). It has been an open question whether the logics have the finite model property, and in the paper we answer the question negatively. We also discuss how this result is connected to other open questions in the field.publishedVersio