Probabilistic Programming Concepts

A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages employs its own probabilistic primitives, and comes with a particular syntax, semantics and inference procedure. This makes it hard to understand the underlying programming concepts and appreciate the differences between the different languages. To obtain a better understanding of probabilistic programming, we identify a number of core programming concepts underlying the primitives used by various probabilistic languages, discuss the execution mechanisms that they require and use these to position state-of-the-art probabilistic languages and their implementation. While doing so, we focus on probabilistic extensions of logic programming languages such as Prolog, which have been developed since more than 20 years

A Transformation-based Implementation for CLP with Qualification and Proximity

Uncertainty in logic programming has been widely investigated in the last decades, leading to multiple extensions of the classical LP paradigm. However, few of these are designed as extensions of the well-established and powerful CLP scheme for Constraint Logic Programming. In a previous work we have proposed the SQCLP (proximity-based qualified constraint logic programming) scheme as a quite expressive extension of CLP with support for qualification values and proximity relations as generalizations of uncertainty values and similarity relations, respectively. In this paper we provide a transformation technique for transforming SQCLP programs and goals into semantically equivalent CLP programs and goals, and a practical Prolog-based implementation of some particularly useful instances of the SQCLP scheme. We also illustrate, by showing some simple-and working-examples, how the prototype can be effectively used as a tool for solving problems where qualification values and proximity relations play a key role. Intended use of SQCLP includes flexible information retrieval applications.Comment: 49 pages, 5 figures, 1 table, preliminary version of an article of the same title, published as Technical Report SIC-4-10, Universidad Complutense, Departamento de Sistemas Inform\'aticos y Computaci\'on, Madrid, Spai

A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints

We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms.Comment: In Proceedings UNIF 2010, arXiv:1012.455