Reasoning about Emergence of Collective Memory

We offer a very simple model of how collective memory may form. Agents keep signalling within neighbourhoods, and depending on how many support each signal, some signals win in that neighbourhood. By agents interacting between different neighbourhoods, influence spreads and sometimes, a collective signal emerges. We propose a logic in which we can reason about such emergence of memory and present preliminary technical results on the logic.

Reasoning about Social Choice and Games in Monadic Fixed-Point Logic

Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a new one. This induces a natural graph structure that we call the improvement graph on the strategy space of these systems. We suggest that the monadic fixed-point logic with counting, an extension of monadic first-order logic on graphs with fixed-point and counting quantifiers, is a natural specification language on improvement graphs, and thus for a class of properties that can be interpreted across these domains. The logic has an efficient model checking algorithm (in the size of the improvement graph).

Two variable fragment of Term Modal Logic

Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form $exists y. forall x. (Box_x P(x,y) supsetDiamond_y P(y,x))$. Like First order modal logic, TML is also notoriously undecidable, in the sense that even very simple fragments are undecidable. In this paper, we show the decidability of one interesting fragment, that of two variable TML. This is in contrast to two-variable First order modal logic, which is undecidable.

Bundled fragments of first-order modal logic: (un)decidability

Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are undecidable, over many model classes. Over the years, only a few fragments (such as the monodic) have been shown to be decidable. In this paper, we study fragments that bundle quantifiers and modalities together, inspired by earlier work on epistemic logics of know-how/why/what. As always with quantified modal logics, it makes a significant difference whether the domain stays the same across worlds, or not. In particular, we show that the bundle $forall Box$ is undecidable over constant domain interpretations, even with only monadic predicates, whereas $exists Box$ bundle is decidable. On the other hand, over increasing domain interpretations, we get decidability with both $forall Box$ and $exists Box$ bundles with unrestricted predicates. In these cases, we also obtain tableau based procedures that run in PSPACE. We further show that the $exists Box$ bundle cannot distinguish between constant domain and increasing domain interpretations.

Deviator Detection under Imperfect Monitoring

Grim-trigger strategies are a fundamental mechanism for sustaining equilibria in iterated games: the players cooperate along an agreed path, and as soon as one player deviates, the others form a coalition to play him down to his minmax level. A precondition to triggering such a strategy is that the identity of the deviating player becomes common knowledge among the other players. This can be difficult or impossible to attain in games where the information structure allows only imperfect monitoring of the played actions or of the global state. We study the problem of synthesising finite-state strategies for detecting the deviator from an agreed strategy profile in games played on finite graphs with different information structures. We show that the problem is undecidable in the general case where the global state cannot be monitored. On the other hand, we prove that under perfect monitoring of the global state and imperfect monitoring of actions, the problem becomes decidable, and we present an effective synthesis procedure that covers infinitely repeated games with private monitoring.

Proceedings of the Ninth Workshop on Methods for Modalities

Methods for Modalities is a series aimed at bringing together researchers interested in developing proof methods, verification methods, algorithms and tools based on modal logic. Here the term modal logics is conceived broadly, including description logic, guarded fragments, conditional logic, temporal and hybrid logic, dynamic logic, etc. The first workshop was held in May 1999 in Amsterdam, and since then it has travelled the world. Please see https://cs.famaf.unc.edu.ar/~careces/M4M for information on past editions of M4M. The 9th Methods for Modalities Workshop is being held at the Indian Institute of Technology (IIT) Kanpur, from January 8 to 10, 2017, co-located with the Indian Conference on Logic and its Applications (ICLA), January 5 to 7, 2017. For details, see https://www.cse.iitk.ac.in/users/icla/M4M/ This volume constitutes the proceedings of the workshop and given the substantial instructional content, should be of interest especially to young researchers and students looking for tools and techniques as well as exciting problems related to logics and computation.

Existential Assertions for Voting Protocols

In earlier work, we extend the Dolev-Yao model with assertions. We build on that work and add existential abstraction to the language, which allows us to translate common constructs used in voting protocols into proof properties. We also give an equivalence-based definition of anonymity in this model, and prove anonymity for the FOO voting protocol.

A Retraction Theorem for Distributed Synthesis

We present a general theorem for distributed synthesis problems in coordination games with $omega$-regular objectives of the form: If there exists a winning strategy for the coalition, then there exists an essential winning strategy, that is obtained by a retraction of the given one. In general, this does not lead to finite-state winning strategies, but when the knowledge of agents remains bounded, we can solve the synthesis problem. Our study is carried out in a setting where objectives are expressed in terms of events that may emph{not} be observable. This is natural in games of imperfect information, rather than the common assumption that objectives are expressed in terms of events that are observable to all agents. We characterise decidable distributed synthesis problems in terms of finiteness of knowledge states and finite congruence classes induced by them.

A Local Logic for Realizability in Web Service Choreographies

Web service choreographies specify conditions on observable interactions among the services. An important question in this regard is realizability: given a choreography C, does there exist a set of service implementations I that conform to C ? Further, if C is realizable, is there an algorithm to construct implementations in I ? We propose a local temporal logic in which choreographies can be specified, and for specifications in the logic, we solve the realizability problem by constructing service implementations (when they exist) as communicating automata. These are nondeterministic finite state automata with a coupling relation. We also report on an implementation of the realizability algorithm and discuss experimental results.