Two essential tasks in managing description logic knowledge bases are eliminating problematic axioms and incorporating newly formed ones. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change. In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach. Standard description logic semantics yields an infinite number of models for DL-Lite knowledge bases, thus it is difficult to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which can replace the standard semantics in characterising the standard inference tasks of DL-Lite.

Two essential tasks in managing description logic knowledge bases are eliminating problematic axioms and incorporating newly formed ones. Such elimination and incorporation are formalised as the operations of contraction and revision in belief change. In this paper, we deal with contraction and revision for the DL-Lite family through a model-theoretic approach. Standard description logic semantics yields an infinite number of models for DL-Lite knowledge bases, thus it is difficult to develop algorithms for contraction and revision that involve DL models. The key to our approach is the introduction of an alternative semantics called type semantics which can replace the standard semantics in characterising the standard inference tasks of DL-Lite. Type semantics has several advantages over the standard one. It is more succinct and importantly, with a finite signature, the semantics always yields a finite number of models. We then define model-based contraction and revision functions for DL-Lite knowledge bases under type semantics and provide representation theorems for them. Finally, the finiteness and succinctness of type semantics allow us to develop tractable algorithms for instantiating the functions.

Abduction is a pattern of inference in which an agent seeks an explanation for an observation or report. Iterated abduction is a variety of abduction in which evidence is acquired and explained over time. The long-term goal is to maintain highly plausible consistent explanations for as much of the evidence as possible. Some reports, at the time of acquisition, may be inconsistent with the agent's present beliefs, so some beliefs must be contracted in order to find an explanation of the new reports. Existing work in iterated belief revision only addresses how to maintain consistent beliefs in light of inconsistent observations; whether or not existing beliefs serve as explanations is not considered. What is needed to meet the goal of iterated abduction is a means of seeking new explanations for old evidence when previously-accepted explanations are contracted. We develop a logical formalism for this process as well as a computational implementation.

Merging beliefs requires the plausibility of the sources of the information to be merged. They are typically assumed equally reliable in lack of hints indicating otherwise; yet, a recent line of research spun from the idea of deriving this information from the revision process itself. In particular, the history of previous revisions and previous merging examples provide information for performing subsequent mergings. Yet, no examples or previous revisions may be available. In spite of the apparent lack of information, something can still be inferred by a try-and-check approach: a relative reliability ordering is assumed, the merging process is performed based on it, and the result is compared with the original information. The outcome of this check may be incoherent with the initial assumption, like when a completely reliable source is rejected some of the information it provided. In such cases, the reliability ordering assumed in the first place can be excluded from consideration. The first theorem of this article proves that such a scenario is indeed possible. Other results are obtained under various definition of reliability and merging.

Dynamic Bayesian networks (DBNs) are a general model for stochastic processes with partially observed states. Belief filtering in DBNs is the task of inferring the belief state (i.e. the probability distribution over process states) based on incomplete and noisy observations. This can be a hard problem in complex processes with large state spaces. In this article, we explore the idea of accelerating the filtering task by automatically exploiting causality in the process. We consider a specific type of causal relation, called passivity, which pertains to how state variables cause changes in other variables. We present the Passivity-based Selective Belief Filtering (PSBF) method, which maintains a factored belief representation and exploits passivity to perform selective updates over the belief factors. PSBF produces exact belief states under certain assumptions and approximate belief states otherwise, where the approximation error is bounded by the degree of uncertainty in the process. We show empirically, in synthetic processes with varying sizes and degrees of passivity, that PSBF is faster than several alternative methods while achieving competitive accuracy. Furthermore, we demonstrate how passivity occurs naturally in a complex system such as a multi-robot warehouse, and how PSBF can exploit this to accelerate the filtering task.

Dynamic Bayesian networks (DBNs) are a general model for stochastic processes with partially observed states. Belief filtering in DBNs is the task of inferring the belief state (i.e. the probability distribution over process states) based on incomplete and noisy observations. This can be a hard problem in complex processes with large state spaces. In this article, we explore the idea of accelerating the filtering task by automatically exploiting causality in the process. We consider a specific type of causal relation, called passivity, which pertains to how state variables cause changes in other variables. We present the Passivity-based Selective Belief Filtering (PSBF) method, which maintains a factored belief representation and exploits passivity to perform selective updates over the belief factors. PSBF produces exact belief states under certain assumptions and approximate belief states otherwise, where the approximation error is bounded by the degree of uncertainty in the process. We show empirically, in synthetic processes with varying sizes and degrees of passivity, that PSBF is faster than several alternative methods while achieving competitive accuracy. Furthermore, we demonstrate how passivity occurs naturally in a complex system such as a multi-robot warehouse, and how PSBF can exploit this to accelerate the filtering task.

In many scenarios where the integration of information into a knowledge base (KB) leads to inconsistencies there is a need to change the KB minimally. In belief revision, relevance postulates meet the minimality requirement by restricting the elimination of KB elements to those that are relevant for the incoming information. This paper focuses on two minimality postulates in an ontology revision scenario in which conflicts are caused by ambiguous use of symbols: a relevance postulate and a generalized inclusion postulate which limits the creativity of the operators. Both postulates exploit the (satisfiably) equivalent representation of a first-order logic KB by its prime implicates, which, intuitively, represent the most atomic logical components of the KB. The paper shows that reinterpretation operators (which are ontology revision operators) fulfill both postulates.

We consider the problem of obtaining coherence in a propositional knowledge base using techniques from Belief Change. Our motivation comes from the field of formal ontologies where coherence is interpreted to mean that a concept name has to be satisfiable. In the propositional case we consider here, this translates to a propositional formula being satisfiable. We define belief change operators in a framework of nonmonotonic preferential reasoning.We show how the introduction of defeasible information using contraction operators can be an effective means for obtaining coherence.

This paper tackles the problem of evaluating the degree of inconsistency in spatial and temporal qualitative reasoning. We first introduce postulates to propose a formal framework for measuring inconsistency in this context. Then, we provide two inconsistency measures that can be useful in various AI applications. The first one is based on the number of constraints that we need to relax to get a consistent qualitative constraint network. The second inconsistency measure is based on variable restrictions to restore consistency. It is defined from the minimum number of variables that we need to ignore to recover consistency. We show that our proposed measures satisfy required postulates and other appropriate properties. Finally, we discuss the impact of our inconsistency measures on belief merging in qualitative reasoning.

Preference models lie at the core of the formalization for several related notions, such as non-monotonic reasoning,obligations, goals, beliefs, etc. Recently, the interest in integrating dynamic operators in the logics of belief, preference and obligation has gained momentum.This integration sheds light on similarities among several change operations traditionally studied independently of each other. While a prolific approach, important operations, such as the well-known contraction of beliefs or derogation of norms studied in the AGM tradition,have not received proper attention in this framework.In this work, we study codifications of contraction operations, stemming from the work on iterate dbelief change, in the logic of preferences, by means of both semantically defined operations and their counterpart in syntactical priority structures.