Following the recent trend of studying the theory of belief revision under the Horn fragment of propo- sitional logic this paper develops a fully charac- terised Horn contraction which is analogous to the traditional transitively relational partial meet contraction [Alchourron et al., 1985]. This Horn con- traction extends the partial meet Horn contraction studied in [Delgrande and Wassermann, 2010] so that it is guided by a transitive relation that models the ordering of plausibility over sets of beliefs.

This paper presents an approach to belief revision in which revision is a function from a belief state and a finite set of formulas to a new belief state. In the interesting case, the set for revision S may be inconsistent but individual members of S are consistent. We argue that S will still contain interesting information regarding revision; in particular, maximum consistent subsets of S will determine candidate formulas for the revision process, and the agent's associated faithful ranking will determine the plausibility of such candidate formulas. Postulates and semantic conditions characterizing this approach are given, and representation results are provided. As a consequence of this approach, we argue that revision by a sequence of formulas, usually considered as a problem of iterated revision, is more appropriately regarded as revision by the possibly-inconsistent set of these formulas. Hence we suggest that revision by a sequence of formulas is foremost a problem of (uniterated) set revision.

We address the issue, in cognitive agents, of possible loss of previous information, which later might turn out to be correct when new information becomes available. To this aim, we propose a framework for changing the agent's mind without erasing forever previous information, thus allowing its recovery in case the change turns out to be wrong. In this new framework, a piece of information is represented as an argument which can be more or less accepted depending on the trustworthiness of the agent who proposes it. We adopt possibility theory to represent uncertainty about the information, and to model the fact that information sources can be only partially trusted. The originality of the proposed framework lies in the following two points: (i) argument reinstatement is mirrored in belief reinstatement in order to avoid the loss of previous information; (ii) new incoming information is represented under the form of arguments and it is associated with a plausibility degree depending on the trustworthiness of the information source.

Existing belief merging operators take advantage of all the models from the bases, including those contradicting the integrity constraints. In this paper, we show that this is not suited to every merging scenario. We study the case when the bases are "rationalized" with respect to the integrity constraints during the merging process. We define in formal terms several independence conditions for merging operators and show how they interact with the standard IC postulates for belief merging. Especially, we give an independence-based axiomatic characterization of a distance-based operator.

As a doxastic counterpart to epistemic logic based on S5 we study the modal logic KSD that can be viewed as an approach to modelling a kind of objective and fair belief. We apply KSD to the problem of minimal belief and develop an alterna- tive approach to nonmonotonic modal logic using a weaker concept of expansion. This corresponds to a certain minimal kind of KSD model and yields a new type of nonmonotonic doxastic reasonin

Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections.

Recent years have seen a lot of work towards extending the established AGM belief revision theory with respect to iterating revision, preserving conditional beliefs, and handling sets of propositions as new information. In particular, novel postulates like independence and evidence retainment have been brought forth as new standards for revising epistemic states by (sets of) propositional information. In this paper, we propose a constructive approach for revising epistemic states by sets of (propositional and conditional) beliefs that combines ideas from nonmonotonic reasoning with conditional belief revision. We also propose a novel principle called enforcement that covers both independence and evidence retainment, and we show our revision operator to comply with major postulates from the literature. Moreover, we point out the relevance of our approach for default reasoning.

This paper investigates belief revision where the underlying logic is that governing Horn clauses. It proves to be the case that classical (AGM) belief revision doesn’t immediately generalise to the Horn case. In particular, a standard construction based on a total preorder over possible worlds may violate the accepted (AGM) postulates. Conversely, Horn revision functions in the obvious extension to the AGM approach are not captured by total preorders over possible worlds. We address these difficulties by first restricting the semantic construction to "well behaved" orderings; and second, by augmenting the revision postulates by an additional postulate. This additional postulate is redundant in the AGM approach but not in the Horn case. In a representation result we show that these two approaches coincide. Arguably this work is interesting for several reasons. It extends AGM revision to inferentially-weaker Horn theories; hence it sheds light on the theoretical underpinnings of belief change, as well as generalising the AGM paradigm. Thus, this work is relevant to revision in areas that employ Horn clauses, such as deductive databases and logic programming, as well as areas in which inference is weaker than classical logic, such as in description logic.

Multi-context systems (MCS) are a powerful framework for interlinking heterogeneous knowledge sources. They model the flow of information among different reasoning components (called contexts) in a declarative way, using so-called bridge rules, where contexts and bridge rules may be nonmonotonic. We considerably generalize MCS to managed MCS (mMCS): while the original bridge rules can only add information to contexts, our generalization allows arbitrary operations on context knowledge bases to be freely defined, e.g., deletion or revision operators. The paper motivates and introduces the generalized framework and presents several interesting instances. Furthermore, we consider inconsistency management in mMCS and complexity issues.

Planning under uncertainty is one of the most general and hardest problems considered in the area of planning. Uncertainty can take the form of incomplete information, wrong information, multiple action outcomes, and varying action durations. My doctoral thesis concentrates on planning with incomplete knowledge and multiple action outcomes, specifically conformant planning and contingent planning. These problems have attracted the attention of many researchers, resulting in numerous sophisticated planners of different approaches. However, those planners cannot scale up well on the size of problems, mostly due to the representation methods employed in the planners. The doctoral research work provides a systematic methodology for dealing with planning under uncertainty, focusing on the representation of belief states that can be used in a forward search paradigm in the belief space for solutions. A good representation should be compact so that a planner implementing it can perform and scale up well as the larger the formulae, the more the computation and the more the memory consumption (i.e., the slower the system and the less the scalability). On the other hand, it should also have properties that allow for definition of an efficient transition function for computing successor belief states, e.g., checking satisfaction in a DNF formula is easy. Defining a direct complete transition function in presence of incomplete information for a general representation, other than the belief state, is particularly hard due to conditional action effects. To address this, I propose a generic abstract algorithm, called GAA, for defining such function given an arbitrary representation. Using the GAA algorithm, my doctoral thesis investigates the properties of different logical formulae and their applicability in planning under uncertainty as a belief state representation. The results obtained so far are very promissing as the research work developed several highly competitive planners which outperform other state-of-the-art planners in most benchmarks available in the literature.