Answer Set Programming (ASP) is a popular framework for modelling combinatorial problems. However, ASP cannot be used easily for reasoning about uncertain information. Possibilistic ASP (PASP) is an extension of ASP that combines possibilistic logic and ASP. In PASP a weight is associated with each rule, whereas this weight is interpreted as the certainty with which the conclusion can be established when the body is known to hold. As such, it allows us to model and reason about uncertain information in an intuitive way. In this paper we present new semantics for PASP in which rules are interpreted as constraints on possibility distributions. Special models of these constraints are then identified as possibilistic answer sets. In addition, since ASP is a special case of PASP in which all the rules are entirely certain, we obtain a new characterization of ASP in terms of constraints on possibility distributions. This allows us to uncover a new form of disjunction, called weak disjunction, that has not been previously considered in the literature. In addition to introducing and motivating the semantics of weak disjunction, we also pinpoint its computational complexity. In particular, while the complexity of most reasoning tasks coincides with standard disjunctive ASP, we find that brave reasoning for programs with weak disjunctions is easier.

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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.

Abstract. 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.

Abstract: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.

Abstract. 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.

The BDI architecture, where agents are modelled based on their belief, desires, and intentions, provides a practical approach to developing intelligent agents. One of the key features of BDI agents is that they are able to pursue multiple intentions in parallel, i.e. in an interleaved manner. Most of the previous works have enabled BDI agents to avoid negative interactions between intentions to ensure the correct execution. However, to avoid execution inefficiencies, BDI agents should also capitalise on positive interactions between intentions. In this paper, we provide a theoretical framework where first-principles planning (FPP) is employed to manage the intention interleaving in an automated fashion. Our FPP approach not only guarantees the achievability of intentions, but also discovers and exploits potential common sub-intentions to reduce the overall cost of intention execution. Our results show that our approach is both theoretically sound and practically feasible. The effectiveness evaluation in a manufacturing scenario shows that our approach can significantly reduce the total number of actions by merging common sub-intentions, while still accomplishing all intentions.

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Abstract. 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 AgentSpeak + framework, which extends AgentSpeak with a mechanism for probabilistic planning. The beliefs of an 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.