Kim Bauters

Weak and strong disjunction in possibilistic ASP

Possibilistic answer set programming (PASP) unites answer set programming (ASP) and possibilistic logic (PL) by associating certainty values with rules. The resulting framework allows to combine both non-monotonic reasoning and reasoning under uncertainty in a single framework. While PASP has been well-studied for possibilistic definite and possibilistic normal programs, we argue that the current semantics of possibilistic disjunctive programs are not entirely satisfactory. The problem is twofold. First, the treatment of negation-as-failure in existing approaches follows an all-or-nothing scheme that is hard to match with the graded notion of proof underlying PASP. Second, we advocate that the notion of disjunction can be interpreted in several ways. In particular, in addition to the view of ordinary ASP where disjunctions are used to induce a non-deterministic choice, the possibilistic setting naturally leads to a more epistemic view of disjunction. In this paper, we propose a semantics for possibilistic disjunctive programs, discussing both views on disjunction. Extending our earlier work, we interpret such programs as sets of constraints on possibility distributions, whose least specific solutions correspond to answer sets.

Possible and Necessary Answer Sets of Possibilistic Answer Set Programs

Answer set programming (ASP) and possibility theory can be combined to form possibilistic answer set programming (PASP), a framework for non-monotonic reasoning under uncertainty. Existing proposals view answer sets of PASP programs as weighted epistemic states, in which the strength by which different literals are believed to hold may vary. In contrast, in this paper we propose an approach in which epistemic states remain Boolean, but some epistemic states may be considered more plausible than others. A PASP program is then a representation of an incomplete description of these epistemic states where certainties are associated with each rule which is interpreted in terms of a necessity measure. The main contribution of this paper is the introduction of a new semantics for PASP as well as a study of the resulting complexity.

Semantics for possibilistic answer set programs: Uncertain rules versus rules with uncertain conclusions

Although Answer Set Programming (ASP) is a powerful framework for declarative problem solving, it cannot in an intuitive way handle situations in which some rules are uncertain, or in which it is more important to satisfy some constraints than others. Possibilistic ASP (PASP) is a natural extension of ASP in which certainty weights are associated with each rule. In this paper we contrast two different views on interpreting the weights attached to rules. Under the first view, weights reflect the certainty with which we can conclude the head of a rule when its body is satisfied. Under the second view, weights reflect the certainty that a given rule restricts the considered epistemic states of an agent in a valid way, i.e. it is the certainty that the rule itself is correct. The first view gives rise to a set of weighted answer sets, whereas the second view gives rise to a weighted set of classical answer sets.

Risk-aware Planning in BDI Agents

The ability of an autonomous agent to select rational actions is vital in enabling it to achieve its goals. To do so effectively in a high-stakes setting, the agent must be capable of considering the risk and potential reward of both immediate and future actions. In this paper we provide a novel method for calculating risk alongside utility in online planning algorithms. We integrate such a risk-aware planner with a BDI agent, allowing us to build agents that can set their risk aversion levels dynamically based on their changing beliefs about the environment. To guide the design of a risk-aware agent we propose a number of principles which such an agent should adhere to and show how our proposed framework satisfies these principles. Finally, we evaluate our approach and demonstrate that a dynamically risk-averse agent is capable of achieving a higher success rate than an agent that ignores risk, while obtaining a higher utility than an agent with a static risk attitude.

Communicating ASP and the polynomial hierarchy

Communicating answer set programming is a framework to represent and reason about the combined knowledge of multiple agents using the idea of stable models. The semantics and expressiveness of this framework crucially depends on the nature of the communication mechanism that is adopted. The communication mechanism we introduce in this paper allows us to focus on a sequence of programs, where each program in the sequence may successively eliminate some of the remaining models. The underlying intuition is that of leaders and followers: each agents decisions are limited by what its leaders have previously decided. We show that extending answer set programs in this way allows us to capture the entire polynomial hierarchy.

COMMUNICATING ANSWER SET PROGRAMS

Answer set programming is a form of declarative programming that has proven very successful in succinctly formulating and solving complex problems. Although mecha- nisms for representing and reasoning with the combined answer set programs of multiple agents have already been proposed, the actual gain in expressivity when adding commu- nication has not been thoroughly studied. We show that allowing simple programs to talk to each other results in the same expressivity as adding negation-as-failure. Furthermore, we show that the ability to focus on one program in a network of simple programs results in the same expressivity as adding disjunction in the head of the rules.

Anytime Algorithms for Solving Possibilistic MDPs and Hybrid MDPs

The ability of an agent to make quick, rational decisions in an uncertain environment is paramount for its applicability in realistic settings. Markov Decision Processes MDP provide such a framework, but can only model uncertainty that can be expressed as probabilities. Possibilistic counterparts of MDPs allow to model imprecise beliefs, yet they cannot accurately represent probabilistic sources of uncertainty and they lack the efficient online solvers found in the probabilistic MDP community. In this paper we advance the state of the art in three important ways. Firstly, we propose the first online planner for possibilistic MDP by adapting the Monte-Carlo Tree Search MCTS algorithm. A key component is the development of efficient search structures to sample possibility distributions based on the DPY transformation as introduced by Dubois, Prade, and Yager. Secondly, we introduce a hybrid MDP model that allows us to express both possibilistic and probabilistic uncertainty, where the hybrid model is a proper extension of both probabilistic and possibilistic MDPs. Thirdly, we demonstrate that MCTS algorithms can readily be applied to solve such hybrid models.

Probabilistic Planning in AgentSpeak using the POMDP framework.

AgentSpeak is a logic-based programming language, based on the Belief-Desire-Intention paradigm, suitable for building complex agent-based systems. To limit the computational complexity, agents in AgentSpeak rely on a plan library to reduce the planning problem to the much simpler problem of plan selection. However, such a plan library is often inadequate when an agent is situated in an uncertain environment. In this work, we propose the \(\text {AgentSpeak}^+\) framework, which extends AgentSpeak with a mechanism for probabilistic planning. The beliefs of an \(\text {AgentSpeak}^+\) agent are represented using epistemic states to allow an agent to reason about its uncertain observations and the uncertain effects of its actions. Each epistemic state consists of a POMDP, used to encode the agent’s knowledge of the environment, and its associated probability distribution (or belief state). In addition, the POMDP is used to select the optimal actions for achieving a given goal, even when faced with uncertainty.

A Collaborative Multiagent Framework Based on Online Risk-Aware Planning and Decision-Making

Planning is an essential process in teams of multiple agents pursuing a common goal. When the effects of actions undertaken by agents are uncertain, evaluating the potential risk of such actions alongside their utility might lead to more rational decisions upon planning. This challenge has been recently tackled for single agent settings, yet domains with multiple agents that present diverse viewpoints towards risk still necessitate comprehensive decision making mechanisms that balance the utility and risk of actions. In this work, we propose a novel collaborative multi-agent planning framework that integrates (i) a team-level online planner under uncertainty that extends the classical UCT approximate algorithm, and (ii) a preference modeling and multicriteria group decision making approach that allows agents to find accepted and rational solutions for planning problems, predicated on the attitude each agent adopts towards risk. When utilised in risk-pervaded scenarios, the proposed framework can reduce the cost of reaching the common goal sought and increase effectiveness, before making collective decisions by appropriately balancing risk and utility of actions.

Managing Different Sources of Uncertainty in a BDI Framework in a Principled way with Tractable Fragments

The Belief-Desire-Intention (BDI) architecture is a practical approach for modelling large-scale intelligent systems. In the BDI setting, a complex system is represented as a network of interacting agents – or components – each one modelled based on its beliefs, desires and intentions. However, current BDI implementations are not well-suited for modelling more realistic intelligent systems which operate in environments pervaded by different types of uncertainty. Furthermore, existing approaches for dealing with uncertainty typically do not offer syntactical or tractable ways of reasoning about uncertainty. This complicates their integration with BDI implementations, which heavily rely on fast and reactive decisions. In this paper, we advance the state-of-the-art w.r.t. handling different types of uncertainty in BDI agents. The contributions of this paper are, first, a new way of modelling the beliefs of an agent as a set of epistemic states. Each epistemic state can use a distinct underlying uncertainty theory and revision strategy, and commensurability between epistemic states is achieved through a stratification approach. Second, we present a novel syntactic approach to revising beliefs given unreliable input. We prove that this syntactic approach agrees with the semantic definition, and we identify expressive fragments that are particularly useful for resource-bounded agents. Third, we introduce full operational semantics that extend Can, a popular semantics for BDI, to establish how reasoning about uncertainty can be tightly integrated into the BDI framework. Fourth, we provide comprehensive experimental results to highlight the usefulness and feasibility of our approach, and explain how the generic epistemic state can be instantiated into various representations.