On A Theory of Probabilistic Deductive Databases

This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability logic is characterized as a generalization of bivalent truth-functional propositional logic (short "logic"), as being connexive, and as being nonmonotonic. The chapter discusses selected argument forms and associated uncertainty propagation...

The purpose of this paper is to report on the most recent developments in our ongoing investigation of the representation and manipulation of uncertainty in automated reasoning systems. In our earlier studies (Tong and Shapiro, 1985) we described a series of experiments with RUBRIC (Tong et al., 1985), a system for full-text document retrieval, that generated some interesting insights into the effects of choosing among a class of scalar valued uncertainty calculi. [n order to...

Probabilistic databases (PDBs) model uncertainty in data in a quantitative way. In the established formal framework, probabilistic (relational) databases are finite probability spaces over relational database instances. This finiteness can clash with intuitive query behavior (Ceylan et al., KR 2016), and with application scenarios that are better modeled by continuous probability distributions (Dalvi et al., CACM 2009). We formally introduced infinite PDBs in (Grohe and Lin...

This paper investigates the possibility of performing automated reasoning in probabilistic logic when probabilities are expressed by means of linguistic quantifiers. Each linguistic term is expressed as a prescribed interval of proportions. Then instead of propagating numbers, qualitative terms are propagated in accordance with the numerical interpretation of these terms. The quantified syllogism, modelling the chaining of probabilistic rules, is studied in this context. It i...

Data provenance consists in bookkeeping meta information during query evaluation, in order to enrich query results with their trust level, likelihood, evaluation cost, and more. The framework of semiring provenance abstracts from the specific kind of meta information that annotates the data. While the definition of semiring provenance is uncontroversial for unions of conjunctive queries, the picture is less clear for Datalog. Indeed, the original definition might include infi...

In this paper, a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information is defined. This approach introduces the use of possibilistic disjunctive clauses which are able to capture incomplete information and incomplete states of a knowledge base at the same time. By considering a possibilistic logic program as a possibilistic logic theory, a construction of a possibilistic logic programming semantic based on answe...

To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and trapezoidal fuzzy numbers are used as the set of truth values along with traditional intervals. Preorder-based truth and knowledge ordering are defined over the set of fuzzy numbers defined over $[0,1]$. Based on this enhanced set of epistemic states...

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to account for it. The first contribution of this paper is a novel interpretation of probabilistic argumentation frameworks as probabilistic logic programs. Probabilistic logic programs are logic programs in which some of the facts are annotated...

In this paper, we introduce a novel approach to deductive databases meant to take into account the needs of current applications in the area of data integration. To this end, we extend the formalism of standard deductive databases to the context of Four-valued logic so as to account for unknown, inconsistent, true or false information under the open world assumption. In our approach, a database is a pair (E,R) where E is the extension and R the set of rules. The extension is ...

We address the problem of integrating information coming from different sources. The information consists of facts that a central server collects and tries to combine using (a) a set of logical rules, i.e. a logic program, and (b) a hypothesis representing the server's own estimates. In such a setting incomplete information from a source or contradictory information from different sources necessitate the use of many-valued logics in which programs can be evaluated and hypothe...