Thomas Bolander

Epistemic planning for single- and multi-agent systems

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.

Tableau-based Decision Procedures for Hybrid Logic

Based on tableau systems, we in this chapter prove decidability results for hybrid logic using tableau systems. The chapter is structured as follows. In the first section of the chapter we sketch the basics of tableau systems. In the second section we give a tableau-based decision procedure for a very expressive hybrid logic including the universal modality. In the third section we show how the decision procedure of the second section can be modified such that simpler tableau-based decision procedures (that is, without loop-checks) are obtained for a weaker hybrid logic where the universal modality is not included. In the fourth section we reformulate the tableau systems of the second and the third sections as Gentzen systems and we discuss how to reformulate the decision procedures. In the fifth section we discuss the results. The results of the second, fourth, and fifth sections of this chapter are taken from Bolander and Brauner (2006). The material in the third section is new (but the tableau systems considered in the third section are obtained by directly modifying the tableau system given in the second section, inspired by a tableau-based decision procedure given in Bolander and Blackburn (2007)).

Conditional epistemic planning

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.

Decidability of a Hybrid Duration Calculus

We present a logic which we call Hybrid Duration Calculus (HDC). HDC is obtained by adding the following hybrid logical machinery to the Restricted Duration Calculus (RDC): nominals, satisfaction operators, down-arrow binder, and the global modality. RDC is known to be decidable, and in this paper we show that decidability is retained when adding the hybrid logical machinery. Decidability of HDC is shown by reducing the satisfiability problem to satisfiability of Monadic Second-Order Theory of Order. We illustrate the increased expressive power obtained in hybridizing RDC by showing that HDC, in contrast to RDC, can express all of the 13 possible relations between intervals.

Seeing Is Believing: Formalising False-Belief Tasks in Dynamic Epistemic Logic

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.

Many-Valued Hybrid Logic

In this paper we define a many-valued semantics for hybrid logic and we give a sound and complete tableau system which is proof theoretically well-behaved, in particular, it gives rise to a decision procedure for the logic. This shows that many-valued hybrid logics is a natural enterprise and opens up the way for future applications.

CDIO Projects in DTU’s B.Eng. in IT Study Program

Since the fall 2008 all B.Eng. study programs at the Technical University of Denmark have been based on the CDIO concept. The adoption of the CDIO standards and principles resulted in new or significantly revised study programs. As part of this effort design-build projects have been introduced on each of the first 4 semesters, and each semester-project spans several courses. The aim of this paper is to describe the four CDIO semester projects in the B.Eng. in IT study, and – along with similar papers describing the other six B.Eng. programs – to provide documentation to accompany an exposition with stands providing additional information and with students demonstrating their projects. The paper is narrowly focused on the IT-study program. At the time of writing this paper the students enrolled in 2008 have completed all four semesters in the new CDIO-based study plan, and the students enrolled in 2009 are currently in the process of finishing the 4 th semester. Consequently, the paper is reporting on curriculum development which has been implemented, and for which experiences have gained.

Maximal Introspection of Agents

This paper concerns the representation of introspective belief and knowledge in multi-agent systems. An introspective agent is an agent that has the ability to refer to itself and reason about its own beliefs. It is well-known that representing introspective beliefs is theoretically very problematic. An agent which is given strong introspective abilities is most likely to have inconsistent beliefs, since it can use introspection to express self-referential beliefs that are paradoxical in the same way as the classical paradoxes of self-reference. In multi-agent systems these paradoxical beliefs can even be expressed as beliefs about the correctness and completeness of other agents’ beliefs, i.e., even without the presence of explicit introspection. In this paper we explore the maximal sets of introspective beliefs that an agent can consistently obtain and retain when situated in a dynamic environment, and when treating beliefs “syntactically” (that is, formalizing beliefs as axioms of first-order predicate logic rather than using modal formalisms). We generalize some previous ’ > >

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.

A Seligman-Style Tableau System

Proof systems for hybrid logic typically use @-operators to access information hidden behind modalities; this labeling approach lies at the heart of most resolution, natural deduction, and tableau systems for hybrid logic. But there is another, less well-known approach, which we have come to believe is conceptually clearer. We call this Seligman-style inference, as it was first introduced and explored by Jerry Seligman in the setting of natural deduction and sequent calculus in the late 1990s. The purpose of this paper is to introduce a Seligman-style tableau system.