Abstract We propose a logic of knowledge for impure simplicial complexes. Impure simplicial complexes represent synchronous distributed systems under uncertainty over which processes are still active (are alive) and which processes have failed or crashed (are dead). Our work generalizes the logic of knowledge for pure simplicial complexes, where all processes are alive, by Goubault et al. In our semantics, given a designated face in a complex, a formula can only be true or false there if it is defined. The following are undefined: dead processes cannot know or be ignorant of any proposition, and live processes cannot know or be ignorant of factual propositions involving processes they know to be dead. The semantics are therefore three-valued, with undefined as the third value. We propose an axiomatization that is a version of the modal logic S5. We also show that impure simplicial complexes correspond to certain Kripke models where agents’ accessibility relations are equivalence relations on a subset of the domain only.

Abstract We provide novel epistemic logical language and semantics for modeling and analysis of byzantine fault-tolerant multi-agent systems, with the intent of not only facilitating reasoning about the agents’ fault status but also supporting model updates for repair and state recovery. Besides the standard knowledge modalities, our logic provides additional agent-specific hope modalities capable of expressing that an agent is not faulty, and also dynamic modalities enabling change to the agents’ correctness status. These dynamic modalities are interpreted as model updates that come in three flavors: fully public, more private, and/or involving factual change. Tailored examples demonstrate the utility and flexibility of our logic for modeling a wide range of fault-detection, isolation, and recovery (FDIR) approaches in mission-critical distributed systems. By providing complete axiomatizations for all variants of our logic, we also create a foundation for building future verification tools for this important class of fault-tolerant applications.

Abstract We introduce pattern models, a dynamic epistemic logic for analyzing distributed systems. First, we present a version of pattern models where the full-information protocol, widely studied in distributed computability, is static in the product definition of pattern models. Next, we parametrize such a logic so as to add the capability to model dynamics of arbitrary deterministic protocols. We thus give a systematic construction of pattern models for a large variety of distributed-computing models called dynamic-network models. Using pattern models, the epistemic dynamics of a proper subclass of dynamic-network models called oblivious can be described using a static pattern model, hence using constant space. For this case, we present a sufficient unsolvability condition for the consensus task that can be easily verified analyzing the structure of the initial epistemic model and the pattern model for a given oblivious dynamic-network model.

We introduce Boolean Observation Games, a subclass of multi-player finite strategic games with incomplete information and qualitative objectives. In Boolean observation games, each player is associated with a finite set of propositional variables of which only it can observe the value, and it controls whether and to whom it can reveal that value. It does not control the given, fixed, value of variables. Boolean observation games are a generalization of Boolean games, a well-studied subclass of strategic games but with complete information, and wherein each player controls the value of its variables. In Boolean observation games, player goals describe multi-agent knowledge of variables. As in classical strategic games, players choose their strategies simultaneously and therefore observation games capture aspects of both imperfect and incomplete information. They require reasoning about sets of outcomes given sets of indistinguishable valuations of variables. An outcome relation between such sets determines what the Nash equilibria are. We present various outcome relations, including a qualitative variant of ex-post equilibrium. We identify conditions under which, given an outcome relation, Nash equilibria are guaranteed to exist. We also study the complexity of checking for the existence of Nash equilibria and of verifying if a strategy profile is a Nash equilibrium. We further study the subclass of Boolean observation games with ‘knowing whether’ goal formulas, for which the satisfaction does not depend on the value of variables. We show that each such Boolean observation game corresponds to a Boolean game and vice versa, by a different correspondence, and that both correspondences are precise in terms of existence of Nash equilibria.

Abstract It is known that without synchronization via a global clock one cannot obtain common knowledge by communication. Moreover, it is folklore that without communicating higher-level information one cannot obtain arbitrary higher-order shared knowledge. Here, we make this result precise in the setting of gossip where agents make one-to-one telephone calls to share secrets: we prove that “everyone knows that everyone knows that everyone knows all secrets” is unsatisfiable in a logic of knowledge for gossiping. We also prove that, given n agents, $2n-3$ calls are optimal to reach “someone knows that everyone knows all secrets” and that $n - 2 + \binom{n}{2}$ calls are optimal to reach “everyone knows that everyone knows all secrets.”

Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed under containment. Pure simplicial complexes describe message passing in asynchronous systems where all processes (agents) are alive, whereas impure simplicial complexes describe message passing in synchronous systems where processes may be dead (have crashed). Properties of impure simplicial complexes can be described in a three-valued multi-agent epistemic logic where the third value represents formulae that are undefined, e.g., the knowledge and local propositions of dead agents. In this work we present an axiomatization for the logic of the class of impure complexes and show soundness and completeness. The completeness proof involves the novel construction of the canonical simplicial model and requires a careful manipulation of undefined formulae.

Abstract Group announcement logic (GAL) and coalition announcement logic (CAL) allow us to reason about whether it is possible for groups and coalitions of agents to achieve their desired epistemic goals through truthful public communication. The difference between groups and coalitions in such a context is that the latter make their announcements in the presence of possible adversarial counter-announcements. As epistemic goals may involve some agents remaining ignorant, counter-announcements may preclude coalitions from reaching their goals. We study the relative expressivity of GAL and CAL and provide some results involving their more well-known sibling APAL. We also discuss how the presence of memory alters the relationship between groups and coalition.

Abstract Arbitrary public announcement logic (APAL) is a logic of change of knowledge with modalities representing quantification over announcements. We present two rather different versions of APAL wherein this quantification is restricted to formulas only containing a subset of all propositional variables: SAPAL and SCAPAL. Such restrictions are relevant in principle for the specification of multi-agent system dynamics. We also present another version of APAL, quantifying over all announcements implied by or implying a given formula: IPAL. We then determine the relative expressivity of all these logics and APAL. We also present complete axiomatizations of SAPAL and SCAPAL and show undecidability of satisfiability for all logics involved, by arguments nearly identical to those for APAL. We show that the IPAL quantifier, motivated by the satisfaction clause for substructural implication, yields a new substructural dynamic consequence relation.

Various extensions of public announcement logic have been proposed with quantification over announcements. The best-known extension is called arbitrary public announcement logic, APAL. It contains a primitive language construct Box phi intuitively expressing that "after every public announcement of a formula, formula phi is true". The logic APAL is undecidable and it has an infinitary axiomatization. Now consider restricting the APAL quantification to public announcements of Boolean formulas only, such that Box phi intuitively expresses that "after every public announcement of a Boolean formula, formula phi is true". This logic can therefore called Boolean arbitrary public announcement logic, BAPAL. The logic BAPAL is the subject of this work. Unlike APAL it has a finitary axiomatization. Also, BAPAL is not at least as expressive as APAL. A further claim that BAPAL is decidable is deferred to a companion paper.

We propose a multi-agent epistemic logic of asynchronous announcements, where truthful announcements are publicly sent but individually received by agents, and in the order in which they were sent. Additional to epistemic modalities the logic contains dynamic modalities for making announcements and for receiving them. What an agent believes is a function of her initial uncertainty and of the announcements she has received. Beliefs need not be truthful, because announcements already made may not yet have been received. As announcements are true when sent, certain message sequences can be ruled out, just like inconsistent cuts in distributed computing. We provide a complete axiomatization for this asynchronous announcement logic ( AA ). It is a reduction system that also demonstrates that any formula in AA is equivalent to one without dynamic modalities, just as for public announcement logic. A detailed example modelling message exchanging processes in distributed computing in AA closes our investigation.

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In this contribution we present arbitrary arrow update model logic (AAUML). This is a dynamic epistemic logic or update logic. In update logics, static/basic modalities are interpreted on a given relational model whereas dynamic/update modalities induce transformations (updates) of relational models. In AAUML the update modalities formalize the execution of arrow update models, and there is also a modality for quantification over arrow update models. Arrow update models are an alternative to the well-known action models. We provide an axiomatization of AAUML. The axiomatization is a rewrite system allowing to eliminate arrow update modalities from any given formula, while preserving truth. Thus, AAUML is decidable and equally expressive as the base multi-agent modal logic. Our main result is to establish arrow update synthesis: if there is an arrow update model after which φ, we can construct (synthesize) that model from φ. We also point out some pregnant differences in update expressivity between arrow update logics, action model logics, and refinement modal logic.

Abstract We define a Public Announcement Separation Logic (PASL) that allows us to consider epistemic possible worlds as resources that can be shared or separated, in the spirit of separation logics. After studying its semantics and illustrating its interest for modelling systems, we provide a sound and complete tableau calculus that deals with resource, agent and announcement constraints and give also a countermodel extraction method.

A well-studied phenomenon in network theory are optimal schedules to distribute information by one-to-one communication between nodes. One can take these communicative actions to be ‘telephone calls’, and this process of spreading information is known as gossiping [4]. It is typical to assume a global scheduler who simply executes a possibly non-deterministic protocol. Such a protocol can be seen as consisting of a sequence of instructions “first, agent a calls b, then c, next, d calls b ...”. We investigate epistemic gossip protocols, where an agent a will call another agent not because it is so instructed but based on its knowledge or ignorance of the factual information that is distributed over the network. Such protocols therefore don't need a central schedular, but they come at a cost: they may take longer to terminate than non-epistemic, globally scheduled, protocols. We describe various epistemic protocols, we give their logical properties, and we model them in a number of ways.

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When agents know a protocol, this leads them to have expectations about future observations. Agents can update their knowledge by matching their actual observations with the expected ones. They eliminate states where they do not match. In this paper, we study how agents perceive protocols that are not commonly known, and propose a logic to reason about knowledge in such scenarios.

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Publication impact factors are more important now than 10 or 20 years ago, both for individual researchers and for journals. Citation indices such as Thomson Reuters (formerly ISI) Web of Knowledge, (http://wokinfo.com/) or Publish or Perish (www.harzing.com, based on Google Scholar scholar.google.com) are standardly consulted by job selection committees prior to interviewing candidates. 1 Individuals and journals post their h-indices online, and they compare their h-indices with those of their peers. (The h-index of an individual is the largest number n such that n of its publications are all cited at least n times. The definition also applies to research institutes, journals, etc.) We think it is important to be aware of these developments. It is particularly important for researchers at the start of their career that they are aware of how successful researchers operate in this changing academic environment. Logicians work across the spectrum of faculties and departments. They are found in philosophy, linguistics, computer science, cognitive science and mathematics departments. A development particularly affecting logicians with positions in science faculties is the strong trend in those faculties to select and promote personnel on the basis of quantitative measures, chiefly the h-index based on Web of Knowledge. One of the consequences is that in many science faculties in the Netherlands and abroad, researchers are actively discouraged to submit their work to journals without Web of Knowledge impact factor, such as (in 2010) Studia Logica, Journal of Logic, Language and Information and Journal of Philosophical Logic. This makes some logicians turn to journals of neighbouring fields (such as artificial intelligence, cognitive science and computer science) that do have Web of Knowledge journals, even if their papers would be very interesting for a logic journal. Is this a desirable development? It seemed wise to step back and consider the background, the facts and the strategies. We quickly recall what the h-index is and purports. We then discuss answers to a questionnaire on publication strategies sent out to seven well-known logicians, trying to determine whether the issue ‘lives’ among the community, and whether the tricks of the trade are quantitative or not. Following is an overview of h-indices of some well-known logicians (other than the interviewees), and as further reference material the h-indices of the 2009 Vidi grant winners, a recognition in the Netherlands of successful early-career logicians. Finally, we come with several recommendations and suggestions.

We propose a formal semantics of intention and plan dynamics based on the notion of local assignment. The function of a local assignment is to change the truth value of a given proposition at a specific time point along a history. We combine a static modal logic including a temporal modality and modal operators for mental attitudes belief and choice, with three kinds of dynamic modalities and corresponding three kinds of local assignments operating on agent's beliefs, on agent's choices and on the physical world. An agent's intention is defined in our approach as the agent's choice to perform a given action at a certain time point in the future and two operations called intention generation and intention reconsideration are defined as specific kinds of local assignments on choices. In Section 1 we introduce a static logic of time, action, and mental attitudes. In Section 2 we add the dynamic notion of local assignment to the logic of Section 1. In Section 3, we focus on two specific kinds of local assignment on choice which allow to model the processes of intention and plan generation and reconsideration.

Public announcement logic extends multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. In this article, we propose a labelled tableau calculus for this logic, and show that it decides satisfiability of formulas in deterministic polynomial space. Since this problem is known to be PSPACE-complete, it follows that our proof method is optimal.

The Sum-and-Product riddle was first published in the reference H. Freudenthal (1969, Nieuw Archief voor Wiskunde 3, 152) [6]. We provide an overview on the history of the dissemination of this riddle through the academic and puzzle-math community. This includes some references to precursors of the riddle, that were previously (as far as we know) unknown. We then model the Sum-and-Product riddle in a modal logic called public announcement logic. This logic contains operators for knowledge, but also operators for the informational consequences of public announcements. The logic is interpreted on multi-agent Kripke models. The information in the riddle can be represented in the traditional way by number pairs, so that Sum knows their sum and Product their product, but also as an interpreted system, so that Sum and Product at least know their local state. We show that the different representations are isomorphic. We also provide characteristic formulas of the initial epistemic state of the riddle. We analyse one of the announcements towards the solution of the riddle as a so-called unsuccessful update: a formula that becomes false because it is announced. The riddle is then implemented and its solution verified in the epistemic model checker DEMO. This can be done, we think, surprisingly elegantly. The results are compared with other work in epistemic model checking and the complexity is experimentally investigated for several representations and parameter settings.

Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: □φ expresses that φ is true after an arbitrary announcement ψ. As this includes the trivial announcement ⊤, one might as well say that □φ expresses what remains true after any announcement: it therefore corresponds to truth persistence after (definable) relativisation. The dual operation ⋄φ expresses that there is an announcement after which φ. This gives a perspective on Fitch's knowability issues: for which formulas φ does it hold that φ → ⋄Kφ? We give various semantic results, and we show completeness for a Hilbert-style axiomatisation of this logic.