Forexample, constraint-based methods exploit conditional independence relations between the variables in order to estimate the Markov equivalence classoftheunderlying causal graph [Spirtesetal.,2000;

We address the problem of supporting empirical probabilities in monadic logic databases. Though the semantics of multivalued logic programs has been studied extensively, the treatment of probabilities as results of statistical findings has not been studied in logic programming/deductive databases. We develop a model-theoretic characterization of logic databases that facilitates such a treatment. We present an algorithm for checking consistency of such databases and prove its total correctness. We develop a sound and complete query processing procedure for handling queries to such databases.

Paul Bernays and David Hilbert carefully avoided overspecification of Hilbert's epsilon-operator and axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the epsilon-operator underspecified. In the meanwhile, there have been several suggestions for semantics of the epsilon as a choice operator. After reviewing the literature on semantics of Hilbert's epsilon operator, we propose a new semantics with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the epsilon supports proof search optimally and is natural in the sense that it does not only mirror some cases of referential interpretation of indefinite articles in natural language, but may also contribute to philosophy of language. Finally, we ask the question whether our epsilon within our free-variable framework can serve as a paradigm useful in the specification and computation of semantics of discourses in natural language.