In order to properly regulate iterated belief revision, Darwiche and Pearl (1997) model belief revision as revising epistemic states by propositions. An epistemic state in their sense consists of a belief set and a set of conditional beliefs. Although the denotation of an epistemic state can be indirectly captured by a total preorder on the set of worlds, it is unclear how to directly capture the structure in terms of the beliefs and conditional beliefs it contains. In this paper, we first provide an axiomatic characterisation for epistemic states by using nine rules about beliefs and conditional beliefs, and then argue that the last two rules are too strong and should be eliminated for characterising the belief state of an agent. We call a structure which satisfies the first seven rules a general epistemic state (GEP). To provide a semantical characterisation of GEPs, we introduce a mathematical structure called belief algebra, which is in essence a certain binary relation defined on the power set of worlds.We then establish a 1-1 correspondence between GEPs and belief algebras, and show that total preorders on worlds are special cases of belief algebras. Furthermore, using the notion of belief algebras, we extend the classical iterated belief revision rules of Darwiche and Pearl to our setting of general epistemic states.

This paper proposes an alternative definition of elementary loops and extends the notion of proper loops for disjunctive logic programs. Different from normal logic programs, the computational complexities of recognizing elementary loops and proper loops for disjunctive programs are coNP-complete. To address this problem, we introduce weaker versions of both elementary loops and proper loops and provide polynomial time algorithms for identifying them respectively. On the other hand, based on the notion of elementary loops, the class of Head-Elementary-loop-Free (HEF) programs was presented, which can be turned into equivalent normal logic programs by shifting head atoms into bodies. However, the problem of recognizing an HEF program is coNP-complete. Then we present a subclass of HEF programs which generalizes the class of Head-Cycle-Free programs and provide a polynomial time algorithm to identify them. At last, some experiments show that both elementary loops and proper loops could be replaced by their weak versions in practice.

Lifschitz and Turner introduced the notion of the splitting set and provided a method to divide a logic program into two parts. They showed that the task of computing the answer sets of the program can be converted into the tasks of computing the answer sets of these parts. However, the empty set and the set of all atoms are the only two splitting sets for many programs, then these programs cannot be divided by the splitting method. In this paper, we extend Lifschitz and Turner's splitting set theorem to allow the program to be split by an arbitrary set of atoms, while some new atoms may be introduced in the process. To illustrate the usefulness of the result, we show that for some typical programs the splitting process is efficient and the program simplification problem can be investigated using the concept of splitting.

We provide a logical representation of Pearl's structural causal models in the causal calculus of McCain and Turner (1997) and its first-order generalization by Lifschitz. It will be shown that, under this representation, the nonmonotonic semantics of the causal calculus describes precisely the solutions of the structural equations (the causal worlds of the causal model), while the causal logic from Bochman (2004) is adequate for describing the behavior of causal models under interventions (forming submodels).

Action languages are formal models of parts of natural language that are designed to describe effects of actions. Many of these languages can be viewed as high level notations of answer set programs structured to represent transition systems. However, the form of answer set programs considered in the earlier work is quite limited in comparison with the modern Answer Set Programming (ASP) language, which allows several useful constructs for knowledge representation, such as choice rules, aggregates, and abstract constraint atoms. We propose a new action language called BC+, which closes the gap between action languages and the modern ASP language. Language BC+ is defined as a high level notation of propositional formulas under the stable model semantics. Due to the generality of the underlying language, BC+ is expressive enough to encompass many modern ASP language constructs and the best features of several other action languages, such as B, C, C+ and BC. Computational methods available in ASP solvers are readily applicable to compute BC+, which led us to implement the language by extending system Cplus2ASP.

We design a tractable Horn fragment of the Halpern-Shoham temporal logic and extend it to interval-based temporal description logics, instance checking in which is P-complete for both combined and data complexity.

This paper represents a paradigm shift in what advice agents should provide people. Contrary to what was previously thought, we empirically show that agents that dispense optimal advice will not necessary facilitate the best improvement in people's strategies. Instead, we claim that agents should at times suboptimally advise. We provide results demonstrating the effectiveness of a suboptimal advising approach in extensive experiments in two canonical mixed agent-human advice-giving domains. Our proposed guideline for suboptimal advising is to rely on the level of intuitiveness of the optimal advice as a measure for how much the suboptimal advice presented to the user should drift from the optimal value.

Reputation-based approaches allow a crowdsourcing system to identify reliable workers to whom tasks can be delegated. In crowdsourcing systems that can be modeled as multi-agent trust networks consist of resource constrained trustee agents (i.e., workers), workers may need to further sub-delegate tasks to others if they determine that they cannot complete all pending tasks before the stipulated deadlines. Existing reputation-based decision-making models cannot help workers decide when and to whom to sub-delegate tasks. In this paper, we proposed a reputation aware task sub-delegation (RTS) approach to bridge this gap. By jointly considering a worker's reputation, workload, the price of its effort and its trust relationships with others, RTS can be implemented as an intelligent agent to help workers make sub-delegation decisions in a distributed manner. The resulting task allocation maximizes social welfare through efficient utilization of the collective capacity of a crowd, and provides provable performance guarantees. Experimental comparisons with state-of-the-art approaches based on the Epinions trust network demonstrate significant advantages of RTS under high workload conditions.

We consider the problem of task allocation in crowdsourcing systems with multiple complex workflows, each of which consists of a set of inter-dependent micro-tasks.We propose Budgeteer, an algorithm to solve this problem under a budget constraint. In particular, our algorithm first calculates an efficient way to allocate budget to each workflow. It then determines the number of inter-dependent micro-tasks and the price to pay for each task within each workflow, given the corresponding budget constraints. We empirically evaluate it on a well-known crowdsourcing-based text correction workflow using Amazon Mechanical Turk, and show that Budgeteer can achieve similar levels of accuracy to current benchmarks, but is on average 45 % cheaper.

In a basic economic system, each participant receives a (financial) reward according to his own contribution to the system. In this work, we study an alternative approach — Incentive Networks — in which a participant's reward depends not only on his own contribution; but also in part on the contributions made by his social contacts or friends. We show that the key parameter effecting the efficiency of such an Incentive Network-based economic system depends on the participant's degree of directed altruism. Directed altruism is the extent to which someone is willing to work if his work results in a payment to his friend, rather than to himself. Specifically, we characterize the condition under which an Incentive Network-based economy is more efficient than the basic "pay-for-your-contribution" economy. We quantify by how much incentive networks can reduce the total reward that needs to be paid to the participants in order to achieve a certain overall contribution. Finally, we study the impact of the network topology and various exogenous parameters on the efficiency of incentive networks. Our results suggest that in many practical settings, Incentive Network-based reward systems or compensation structures could be more efficient than the ubiquitous 'pay-for-your-contribution' schemes.