Catálogo de publicaciones - libros

Measuring inconsistency in knowledge bases has been recognized as an important problem in many research areas. Most of approaches proposed for measuring inconsistency are based on paraconsistent semantics. However, very few of them provide an algorithm for implementation. In this paper, we first give a four-valued semantics for first-order logic and then propose an approach for measuring the degree of inconsistency based on this four-valued semantics. After that, we propose an algorithm to compute the inconsistency degree by introducing a new semantics for first order logic, which is called -4 semantics.

There has been a significant amount of interest in recent years on how to reason about inconsistent knowledge bases. However, with the exception of three papers by Lozinskii, Hunter and Konieczny and by Grant and Hunter, there has been almost no work on characterizing the degree of dirtiness of a database. One can conceive of many reasonable ways of characterizing how dirty a database is. Rather than choose one of many possible measures, we present a set of axioms that any dirtiness measure must satisfy. We then present several plausible candidate dirtiness measures from the literature (including those of Hunter-Konieczny and Grant-Hunter) and identify which of these satisfy our axioms and which do not. Moreover, we define a new dirtiness measure which satisfies all of our axioms.

The Any-World Assumption (AWA) has been introduced for normal logic programs as a generalization of the well-known notions of Closed World Assumption (CWA) and the Open World Assumption (OWA). The AWA allows assignment (i.e., interpretation), over a (bilattice), to be a default assumption and, thus, the CWA and OWA are just special cases. To answer queries, we provide a novel and simple top-down procedure.

In this paper we investigate logic which is suitable for reasoning about uncertainty in different situations. A possible-world approach is used to provide semantics to formulas. Axiomatic system for our logic is given and the corresponding strong completeness theorem is proved. Relationships to other systems are discussed.

We define weak implication (“H weakly implies E under ”) through the relation = 1, where is a (coherent) conditional uncertainty measure. By considering various such measures with different levels of generality, we get different sets of “inferential rules”, that correspond to those of default logic when reduces to a conditional probability.

A sufficient condition, in terms of a de Finetti style representation, is given for a probability function in Inductive Logic (with relations of all arities) satisfying Spectrum Exchangeability to additionally satisfy Language Invariance. This condition is shown to also be necessary in the case of homogeneous probability functions. In contrast it is proved that (purely) -heterogeneous probability functions can never be members of a language invariant family satisfying Spectrum Exchangeability.

A Ruspini partition is a finite family of fuzzy sets {, ..., }, : [0, 1] →[0, 1], such that for all  ∈ [0, 1]. We analyze such partitions in the language of Gödel logic. Our main result identifies the precise degree to which the Ruspini condition is expressible in this language, and yields inter alia a constructive procedure to axiomatize a given Ruspini partition by a theory in Gödel logic.

Reasoning with qualitative and quantitative uncertainty is required in some real-world applications [6]. However, current extensions to logic programming with uncertainty support representing and reasoning with either qualitative or quantitative uncertainty. In this paper we extend the language of Hybrid Probabilistic Logic programs [29,27], originally introduced for reasoning with quantitative uncertainty, to support both qualitative and quantitative uncertainty. We propose to combine disjunctive logic programs [10,19] with Extended and Normal Hybrid Probabilistic Logic Programs (EHPP [27] and NHPP [29]) in a unified logic programming framework, to allow directly and intuitively to represent and reason in the presence of both qualitative and quantitative uncertainty. The semantics of the proposed languages are based on the answer sets semantics and stable model semantics of extended and normal disjunctive logic programs [10,19]. In addition, they also rely on the probabilistic answer sets semantics and the stable probabilistic model semantics of EHPP [27] and NHPP [29].

This paper is directed towards an infrastructure for handling both uncertainty and vagueness in the Rules, Logic, and Proof layers of the Semantic Web.More concretely, we present probabilistic fuzzy description logic programs, which combine fuzzy description logics, fuzzy logic programs (with stratified nonmonotonic negation), and probabilistic uncertainty in a uniform framework for the Semantic Web. We define important concepts dealing with both probabilistic uncertainty and fuzzy vagueness, such as the expected truth value of a crisp sentence and the probability of a vague sentence. Furthermore, we describe a shopping agent example, which gives evidence of the usefulness of probabilistic fuzzy description logic programs in realistic web applications. In the extended report, we also provide algorithms for query processing in probabilistic fuzzy description logic programs, and we delineate a special case where query processing can be done in polynomial time in the data complexity.

Dynamic epistemic logic (DEL) as viewed by Baltag et col. and propositional dynamic logic (PDL) offer different semantics of events. On the one hand, DEL adds dynamics to epistemic logic by introducing so-called epistemic action models as syntactic objects into the language. On the other hand, PDL has instead transition relations between possible worlds. This last approach allows to easily introduce converse events. We add epistemics to this, and call the resulting logic epistemic dynamic logic (EDL). We show that DEL can be translated into EDL thanks to this use of the converse operator: this device enables us to translate the structure of the action (or event) model directly within a particular axiomatization of EDL, without having to refer to a particular epistemic action (event) model in the language (as done in DEL). It follows that EDL is more expressive and general than DEL.