ABSTRACT. In this paper, we investigate the use of event models for automated planning. Event models are the action defining structures used to define a semantics for dynamic epistemic logic. Using event models, two issues in planning can be addressed: Partial observability of the environment and knowledge. In planning, partial observability gives rise to an uncertainty about the world. For single-agent domains, this uncertainty can come from incomplete knowledge of the starting situation and from the nondeterminism of actions. In multi-agent domains, an additional uncertainty arises from the fact that other agents can act in the world, causing changes that are not instigated by the agent itself. For an agent to successfully construct and execute plans in an uncertain environment, the most widely used formalism in the literature on automated planning is "belief states": sets of different alternatives for the current state of the world. Epistemic logic is a significantly more expressive and theoretically better founded method for representing knowledge and ignorance about the world. Further, epistemic logic allows for planning according to the knowledge (and iterated knowledge) of other agents, allowing the specification of a more complex class of planning domains, than those simply concerned with simple facts about the world. We show how to model multi-agent planning problems using Kripke-models for representing world states, and event models for representing actions. Our mechanism makes use of slight modifications to these concepts, in order to model the internal view of agents, rather than that of an external observer. We define a type of planning domain called epistemic planning domains, a generalisation of classical planning domains, and show how epistemic planning can successfully deal with partial observability, nondeterminism, knowledge and multiple agents. Finally, we show epistemic planning to be decidable in the single-agent case, but only semi-decidable in the multi-agent case.

Abstract. This article extends and improves work on tableau-based decision methods for hybrid logic by Bolander and Braüner [5]. Their paper gives tableau-based decision procedures for basic hybrid logic (with unary modalities) and the basic logic extended with the global modality. All their proof procedures make use of loop-checks to ensure termination.Here we take a closer look at termination for hybrid tableaus. We cover both types of system used in hybrid logic: prefixed tableaus and internalised tableaus. We first treat prefixed tableaus. We prove a termination result for the basic language (with n-ary operators) that does not involve loop-checks. We then successively add the global modality and n-ary inverse modalities, show why various different types of loop-check are required in these cases, and then re-prove termination. Following this we consider internalised tableaus. At first sight, such systems seem to be more complex. However we define a internalised system which terminates without loop-checks. It is simpler than previously known internalised systems (all of which require loopchecks to terminate) and simpler than our prefix systems (no non-local side conditions on rules are required).

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

Abstract. Hybrid logics are a principled generalization of both modal logics and description logics. It is well-known that various hybrid logics without binders are decidable, but decision procedures are usually not based on tableau systems, a kind of formal proof procedure that lends itself towards computer implementation. In this paper we give four different tableaubased decision procedures for a very expressive hybrid logic including the universal modality; three of the procedures are based on different tableau systems, and one procedure is based on a Gentzen system. The decision procedures make use of so-called loop-checks which is a technique standardly used in connection with tableau systems for other logics, namely prefixed tableau systems for transitive modal logics, as well as prefixed tableau systems for certain description logics. The loop-checks used in our four decision procedures are similar, but the four proof systems on which the procedures are based constitute a spectrum of different systems: prefixed and internalized systems, tableau and Gentzen systems.

In this paper we show how to formalise false-belief tasks like the Sally-Anne task and the second-order chocolate task in Dynamic Epistemic Logic (DEL). False-belief tasks are used to test the strength of the Theory of Mind (ToM) of humans, that is, a human's ability to attribute mental states to other agents. Having a ToM is known to be essential to human social intelligence, and hence likely to be essential to social intelligence of artificial agents as well. It is therefore important to find ways of implementing a ToM in artificial agents, and to show that such agents can then solve false-belief tasks. In this paper, the approach is to use DEL as a formal framework for representing ToM, and use reasoning in DEL to solve false-belief tasks. In addition to formalising several false-belief tasks in DEL, the paper introduces some extensions of DEL itself: edge-conditioned event models and observability propositions. These extensions are introduced to provide better formalisations of the false-belief tasks, but expected to have independent future interest.

Abstract. Recent work has shown that Dynamic Epistemic Logic (DEL) offers a solid foundation for automated planning under partial observability and non-determinism. Under such circumstances, a plan must branch if it is to guarantee achieving the goal under all contingencies (strong planning). Without branching, plans can offer only the possibility of achieving the goal (weak planning). We show how to formulate planning in uncertain domains using DEL and give a language of conditional plans. Translating this language to standard DEL gives verification of both strong and weak plans via model checking. In addition to plan verification, we provide a tableau-inspired algorithm for synthesising plans, and show this algorithm to be terminating, sound and complete.

In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic. We give an axiomatization of the logic and prove that complexity of satisfiability is the same as that of public announcement logic, and therefore lower than that of action model logic. An attention-based announcement can also be described as an action model. We extend our logic by integrating attention change. Finally, we add the notion of common belief to the language, we exploit this to formalize the concept of joint attention, that has been widely discussed in the philosophical and cognitive science literature, and we provide a corresponding axiomatization. This axiomatization also employs the auxiliary notion of attention-based relativized common belief.

Epistemic planning can be used for decision making in multi-agent situations with distributed knowledge and capabilities. Dynamic Epistemic Logic (DEL) has been shown to provide a very natural and expressive framework for epistemic planning. In this paper, we aim to give an accessible introduction to DEL-based epistemic planning. The paper starts with the most classical framework for planning, STRIPS, and then moves towards epistemic planning in a number of smaller steps, where each step is motivated by the need to be able to model more complex planning scenarios.