The Thirty-First International Florida Artificial Intelligence Research Society Conference (FLAIRS-31)

Reasoning with Doxastic Attitudes in Multi-Agent Domains

Ben Wright, Enrico Pontelli Department of Computer Science New Mexico State University { bwright, epontell} @cs.nmsu.edu

Abstract 2017; Wan et al. 2015). That is, no contextual beliefs would modify an agent’s reasoning to change its in the mo- In recent years, we have witnessed a blossoming of research proposals addressing the challenges in reasoning about ac- ment. tion and change in domains that include an agent operating This paper will introduce the concept of doxastic attitudes in a multi-agent setting. In particular, the recent emphasis has to help represent this idea of changing beliefs over time and been on dealing with domains that involve agents reasoning to address issues of false or conflicting beliefs. We intro- not only about the state of the world but also about the knowl- duce some relevant background of Kripke Structures and the edge and beliefs of other agents. An open challenge is the action language mA+ which we build on, then we define management of conflicting and incorrect beliefs. This paper the concept of Doxastic Attitudes. These are then utilized to seeks to introduce a solution to this through the use of dox- modify mA+ to handle attitudes, with intuitions of the tran- mA+ astic attitudes. Built on top of the action language ,we sition functions given. We introduce both dynamic and static extend the transition functions of an agent to include this idea versions of doxastic attitudes. Finally, we work through two of attitudes and showcase how these work in two different examples. different examples to showcase how the attitudes function. Background Introduction & Motivation Kripke Structures Reasoning about action and change has long been a field of study; more recently, a push towards reasoning about multi- A Kripke structure is a formalism commonly used to capture agent actions has been studied. In particular, researchers the possible-world semantics for Logic involving epistemic have emphasized the importance of reasoning about beliefs or doxastic operations (Ditmarsch, van der Hoek, and Kooi and of agents and the impact that epistemic ac- 2007; Fagin et al. 1995). Given a countable set of proposi- tions P and a finite set of agents A, a Kripke structure is a tions have on them. However, in many of these cases of be- A P lief reasoning, either the system is developed from the per- structure M = S, R ,V , where: spective of a single agent in the system or it is not robust • S is a set of states enough to handle beliefs that conflict or might be false. This • RA ∀a ∈ A RA(a) ⊆ S × S is illustrated in the following example: is a function where • V P : P → 2S ∀p ∈ P Light in the Room Example: There are two agents A is a valuation function, where , V P (p) ⊆ S p and B. Agents A and B are in Room2. In Room2, there is the set of states in which the proposition is a light switch. The switch turns the light on or off is true. for that room. The light cannot be seen from a different In this structure, each state in S is a possible world of our Room1. An agent can look at the light to determine if it domain. The function RA then maps equivalence between is on or not. Agents can announce to a room if the light possible worlds for each agent. That is, if an agent has a re- is on or off. lation between states s and t, then that agent cannot discern Agent A the light is on, after seeing Room2. between those two possible worlds. It then moves to Room1. After some time in Room1, Additionally, a pointed Kripke Structure (M,s) is com- Agent B enters Room1 and announces that the light in posed of a Kripke structure, M, and a distinguished state Room2 is off. Agent A now has an invalid belief (light s ∈ S—typically representing the “real” state of the wo