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When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…

Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…

While most approaches to automatically recognizing entailment relations have used classifiers employing hand engineered features derived from complex natural language processing pipelines, in practice their performance has been only…

Currently used metrics for assessing summarization algorithms do not account for whether summaries are factually consistent with source documents. We propose a weakly-supervised, model-based approach for verifying factual consistency and…

Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…

Written language is complex. A written text can be considered an attempt to convey a meaningful message which ends up being constrained by language rules, context dependence and highly redundant in its use of resources. Despite all these…

The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In this paper, we argue that to apply rationality result of belief dynamics theory to…

This paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency…

In this paper, we present a new corpus of entailment problems. This corpus combines the following characteristics: 1. it is precise (does not leave out implicit hypotheses) 2. it is based on "real-world" texts (i.e. most of the premises…

Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…

We introduce a sequence of numerical tests that can determine the entanglement or separability of a state even when there is not enough information to completely determine its density matrix. Given partial information about the state in the…

Similar to a tree grammar, a Horn theory can be used to describe an infinite set of terms. In this paper, we present a class of Horn theories such that the set of definable predicates is closed wrt. conjunction and such that the…

Recent success of Bayesian methods in neuroscience and artificial intelligence gives rise to the hypothesis that the brain is a Bayesian machine. Since logic, as the laws of thought, is a product and practice of the human brain, it leads to…

In this paper we give an overview of partial orders on the space of probability distributions that carry a notion of information content and serve as a generalisation of the Bayesian order given in (Coecke and Martin, 2011). We investigate…

In this paper we study the uses and the semantics of non-monotonic negation in probabilistic deductive data bases. Based on the stable semantics for classical logic programming, we introduce the notion of stable formula, functions. We show…

In mathematics information is a number that measures uncertainty (entropy) based on a probabilistic distribution, often of an obscure origin. In real life language information is a datum, a statement, more precisely, a formula. But such a…

We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…

Efficient consistency maintenance of incomplete and dynamic real-life databases is a quality label for further data analysis. In prior work, we tackled the generic problem of database updating in the presence of tuple generating constraints…

In large scale systems such as the Internet, replicating data is an essential feature in order to provide availability and fault-tolerance. Attiya and Welch proved that using strong consistency criteria such as atomicity is costly as each…

Web Service is one of the most significant current discussions in information sharing technologies and one of the examples of service oriented processing. To ensure accurate execution of web services operations, it must be adaptable with…