Catálogo de publicaciones - libros

In this paper we investigate a probability logic which enriches propositional calculus with a class of conditional probability operators of de Finetti’s type. The logic allows making formulas such as (|), with the intended meaning ”the conditional probability of given is at least ”. A possible-world approach is proposed to give semantics to such formulas. An infinitary axiomatic system for our logic which is sound and complete with respect to the mentioned class of models is given. We prove decidability of the presented logic.

Towards sophisticated representation and reasoning techniques that allow for probabilistic uncertainty in the Rules, Logic, and Proof layers of the Semantic Web, we present probabilistic description logic programs (or pdl-programs), which are a combination of description logic programs (or dl-programs) under the answer set semantics and the well-founded semantics with Poole’s independent choice logic. We show that query processing in such pdl-programs can be reduced to computing all answer sets of dl-programs and solving linear optimization problems, and to computing the well-founded model of dl-programs, respectively. Furthermore, we show that the answer set semantics of pdl-programs is a refinement of the well-founded semantics of pdl-programs.

In this paper we propose a way to restrict extension bounds induced by coherent conditional lower-upper probability assessments. Such shrinkage turns out to be helpful whenever the natural bounds are too vague to be used. Since coherence of a conditional lower-upper probability assessment can be characterized through a class of conditional probability distributions, the idea is to take the intersection of the extension bounds induced by each single element of the class instead of the convex combination, as it is usually done. Coherence of such method is proved for extensions performed on both conditional events logical dependent and not-dependent on the initial domain.

This paper is part of a project to match real-world descriptions of instances of objects to models of objects. We use a rich ontology to describe instances and models at multiple levels of detail and multiple levels of abstraction. The models are described using qualitative probabilities. This paper is about the problem of type uncertainty; what if we have a qualitative distribution over the types. For example allowing a model to specify that a meeting is always scheduled in a building, usually in a civic building, and never a shopping mall can help an agent find a meeting even if it is unsure about the address.

We consider a finite family of conditional events and, among other results, we prove a connection property for the set of coherent assessments on such family. This property assures that, for every pair of coherent assessments on the family, there exists (at least) a continuous curve whose points are intermediate coherent probability assessments. We also consider the compactness property for the set of coherent assessments. Then, as a corollary of connection and closure properties, we obtain the theorem of extension for coherent conditional probabilities.

Most formal techniques of automated reasoning are either rooted in logic or in probability theory. These areas have a long tradition in science, particularly among philosophers and mathematicians. More recently, computer scientists have discovered logic and probability theory to be the two key techniques for building intelligent systems which rely on reasoning as a central component. Despite numerous attempts to link logical and probabilistic reasoning, a satisfiable unified theory of reasoning is still missing. This paper analyses the connection between logical and probabilistic reasoning, it discusses their respective similarities and differences, and proposes a new unified theory of reasoning in which both logic and probability theory are contained as special cases.

Preferences and uncertainty occur in many real-life problems. The theory of possibility is one non-probabilistic way of dealing with uncertainty, which allows for easy integration with fuzzy preferences. In this paper we consider an existing technique to perform such an integration and, while following the same basic idea, we propose various alternative semantics which allow us to observe both the preference level and the robustness w.r.t. uncertainty of the complete instantiations. We then extend this technique to other classes of soft constraints, proving that certain desirable properties still hold.

In this paper, the issue of querying databases that may contain ill-known values represented by disjunctive weighted sets (possibility or probability distributions) is considered. The queries dealt with are of the form: “to what extent is it possible (or probable, depending on the framework considered) that tuple t belongs to the result of query Q”, where Q denotes a usual relational query. In the possibilistic database framework, some previous works resulted in the definition of an evaluation method that does not entail computing the different possible worlds of the database. In this paper, we show that this method cannot be used in the probabilistic database framework in general. On the other hand, we describe an alternative evaluation method that is suitable for probabilistic queries when Q complies with certain constraints.

Conditional deduction in binary logic basically consists of deriving new statements from an existing set of statements and conditional rules. Modus Ponens, which is the classical example of a conditional deduction rule, expresses a conditional relationship between an antecedent and a consequent. A generalisation of Modus Ponens to probabilities in the form of probabilistic conditional inference is also well known. This paper describes a method for conditional deduction with beliefs which is a generalisation of probabilistic conditional inference and Modus Ponens. Meaningful conditional deduction requires a degree of relevance between the antecedent and the consequent, and this relevance can be explicitly expressed and measured with our method. Our belief representation has the advantage that it is possible to represent partial ignorance regarding the truth of statements, and is therefore suitable to model typical real life situations. Conditional deduction with beliefs thereby allows partial ignorance to be included in the analysis and deduction of statements and hypothesis.

In this article, we investigate the problem of checking consistency in a hybrid formalism, which combines two essential formalisms in qualitative spatial reasoning: topological formalism and cardinal direction formalism. Instead of using conventional composition tables, we investigate the interactions between topological and cardinal directional relations with the aid of rules that are used efficiently in many research fields such as content-based image retrieval. These rules are shown to be sound, i.e. the deductions are logically correct. Based on these rules, an improved constraint propagation algorithm is introduced to enforce the path consistency. The results of computational complexity of checking consistency for constraint satisfaction problems based on various subsets of this hybrid formalism are presented at the end of this article.