Undecidability in Epistemic Planning

Dynamic epistemic logic (DEL) provides a very expressive framework for multi-agent planning that can deal with nondeterminism, partial observability, sensing actions, and arbitrary nesting of beliefs about other agents’ beliefs. However, as we show in this paper, this expressiveness comes at a price. The planning framework is undecidable, even if we allow only purely epistemic actions (actions that change only beliefs, not ontic facts). Undecidability holds already in the S5 setting with at least 2 agents, and even with 1 agent in S4. It shows that multi-agent planning is robustly undecidable if we assume that agents can reason with an arbitrary nesting of beliefs about beliefs. We also prove a corollary showing undecidability of the DEL model checking problem with the star operator on actions (iteration)

Undecidability and the urban: Feminist pathways through urban political economy

There is a well established body of feminist scholarship critiquing the methodological and epistemological limits of an “objective” view from nowhere in urban research and political economy frameworks. Recent developments, such as the planetary urbanization thesis, have reignited feminist efforts to counter patriarchal, colonial, and hegemonic ways of knowing. Here, we recount our frustrations with the reproduction of dominant political economic modes of “knowing” urban processes such as gentrification and culture-led regeneration in research that seeks to uncover the production of neoliberal spaces and subjectivities. We argue that this narrow approach forecloses the possibility of observing or working with radical world-making projects that stand outside of traditional understandings of the political. Thus, we heed our feminist colleagues’ call to foreground the undecidability of the urban, allowing ourselves and our subjects to express uncertainty about the causes, outcomes, and impacts of urban processes. In what follows, we share short research vignettes from our projects in Toronto and Glasgow and discuss the implications of forging unexpected solidarities, engaging in embodied, participatory knowledge production, and reading urban politics off of persistent, uncertain, under-the-radar projects. We maintain that working from a position of undecidability yields greater potential for renewing our political imaginations beyond neoliberalism

A Semantic Approach to Decidability in Epistemic Planning (Extended Version)

The use of Dynamic Epistemic Logic (DEL) in multi-agent planning has led to a widely adopted action formalism that can handle nondeterminism, partial observability and arbitrary knowledge nesting. As such expressive power comes at the cost of undecidability, several decidable fragments have been isolated, mainly based on syntactic restrictions of the action formalism. In this paper, we pursue a novel semantic approach to achieve decidability. Namely, rather than imposing syntactical constraints, the semantic approach focuses on the axioms of the logic for epistemic planning. Specifically, we augment the logic of knowledge S5$_n$ and with an interaction axiom called (knowledge) commutativity, which controls the ability of agents to unboundedly reason on the knowledge of other agents. We then provide a threefold contribution. First, we show that the resulting epistemic planning problem is decidable. In doing so, we prove that our framework admits a finitary non-fixpoint characterization of common knowledge, which is of independent interest. Second, we study different generalizations of the commutativity axiom, with the goal of obtaining decidability for more expressive fragments of DEL. Finally, we show that two well-known epistemic planning systems based on action templates, when interpreted under the setting of knowledge, conform to the commutativity axiom, hence proving their decidability

To Be Announced

In this survey we review dynamic epistemic logics with modalities for quantification over information change. Of such logics we present complete axiomatizations, focussing on axioms involving the interaction between knowledge and such quantifiers, we report on their relative expressivity, on decidability and on the complexity of model checking and satisfiability, and on applications. We focus on open problems and new directions for research

Synthesizing and executing plans in Knowledge and Action Bases

We study plan synthesis for a variant of Knowledge and Action Bases (KABs). KABs have been recently introduced as a rich, dynamic framework where states are full-fledged description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that can introduce new objects from an infinite domain. We show that, in general, plan existence over KABs is undecidable even under severe restrictions. We then focus on the class of state-bounded KABs, for which plan existence is decidable, and we provide sound and complete plan synthesis algorithms, through a novel combination of techniques based on standard planning, DL query answering, and finite-state abstractions. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning. © 2016, CEUR-WS. All rights reserved

Complexity of ITL model checking: some well-behaved fragments of the interval logic HS

Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics, while little work has been done in the interval temporal logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal logic of time intervals HS over finite Kripke structures (under the homogeneity assumption) and an EXPSPACE model checking procedure for two meaningful fragments of it have been proposed. In this paper, we show that more efficient model checking procedures can be developed for some expressive enough fragments of HS

Infinite games with finite knowledge gaps

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow. Instead, our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play. We show that it is decidable whether a given game satisfies the condition, and prove tight complexity bounds for the strategy synthesis problem under $\omega$-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio

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

Cooperative Epistemic Multi-Agent Planning for Implicit Coordination

Epistemic planning can be used for decision making in multi-agent situations with distributed knowledge and capabilities. Recently, Dynamic Epistemic Logic (DEL) has been shown to provide a very natural and expressive framework for epistemic planning. We extend the DEL-based epistemic planning framework to include perspective shifts, allowing us to define new notions of sequential and conditional planning with implicit coordination. With these, it is possible to solve planning tasks with joint goals in a decentralized manner without the agents having to negotiate about and commit to a joint policy at plan time. First we define the central planning notions and sketch the implementation of a planning system built on those notions. Afterwards we provide some case studies in order to evaluate the planner empirically and to show that the concept is useful for multi-agent systems in practice.Comment: In Proceedings M4M9 2017, arXiv:1703.0173

Plan Synthesis for Knowledge and Action Bases

We study plan synthesis for a variant of Knowledge and Action Bases (KABs), a rich, dynamic framework, where states are description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that possibly introduce new objects from an infinite domain. We show that plan existence over KABs is undecidable even under severe restrictions. We then focus on state-bounded KABs, a class for which plan existence is decidable, and provide sound and complete plan synthesis algorithms, which combine techniques based on standard planning, DL query answering, and finite-state abstraction. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning