Stochastic Invariants for Probabilistic Termination

Termination is one of the basic liveness properties, and we study the termination problem for probabilistic programs with real-valued variables. Previous works focused on the qualitative problem that asks whether an input program terminates with probability~1 (almost-sure termination). A powerful approach for this qualitative problem is the notion of ranking supermartingales with respect to a given set of invariants. The quantitative problem (probabilistic termination) asks for bounds on the termination probability. A fundamental and conceptual drawback of the existing approaches to address probabilistic termination is that even though the supermartingales consider the probabilistic behavior of the programs, the invariants are obtained completely ignoring the probabilistic aspect. In this work we address the probabilistic termination problem for linear-arithmetic probabilistic programs with nondeterminism. We define the notion of {\em stochastic invariants}, which are constraints along with a probability bound that the constraints hold. We introduce a concept of {\em repulsing supermartingales}. First, we show that repulsing supermartingales can be used to obtain bounds on the probability of the stochastic invariants. Second, we show the effectiveness of repulsing supermartingales in the following three ways: (1)~With a combination of ranking and repulsing supermartingales we can compute lower bounds on the probability of termination; (2)~repulsing supermartingales provide witnesses for refutation of almost-sure termination; and (3)~with a combination of ranking and repulsing supermartingales we can establish persistence properties of probabilistic programs. We also present results on related computational problems and an experimental evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page

Coalgebraic Semantics for Probabilistic Logic Programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic semantics on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a `possible worlds' interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming. Furthermore, we show that a similar approach can be used to provide a coalgebraic semantics to weighted logic programming

Expectation Maximization in Deep Probabilistic Logic Programming

Probabilistic Logic Programming (PLP) combines logic and probability for representing and reasoning over domains with uncertainty. Hierarchical probability Logic Programming (HPLP) is a recent language of PLP whose clauses are hierarchically organized forming a deep neural network or arithmetic circuit. Inference in HPLP is done by circuit evaluation and learning is therefore cheaper than any generic PLP language. We present in this paper an Expectation Maximization algorithm, called Expectation Maximization Parameter learning for HIerarchical Probabilistic Logic programs (EMPHIL), for learning HPLP parameters. The algorithm converts an arithmetic circuit into a Bayesian network and performs the belief propagation algorithm over the corresponding factor graph

Beyond the grounding bottleneck: Datalog techniques for inference in probabilistic logic programs

State-of-the-art inference approaches in probabilistic logic programming typically start by computing the relevant ground program with respect to the queries of interest, and then use this program for probabilistic inference using knowledge compilation and weighted model counting. We propose an alternative approach that uses efficient Datalog techniques to integrate knowledge compilation with forward reasoning with a non-ground program. This effectively eliminates the grounding bottleneck that so far has prohibited the application of probabilistic logic programming in query answering scenarios over knowledge graphs, while also providing fast approximations on classical benchmarks in the field

A Coalgebraic Perspective on Probabilistic Logic Programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic perspective on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a "possible worlds" interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming

Probabilistic logic programming in 2P-KT

The work introduces an elastic and platform-agnostic approach to probabilistic logic programming aimed at linking this paradigm with modern mainstream programming platforms, thus widening its usability and portability (e.g. towards the JVM, Android, Python, and JavaScript platforms). We design our solution as an extension of the 2P-Kt symbolic AI ecosystem to inherit its multi-platform and multi-paradigm nature

Coalgebraic semantics for probabilistic logic programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic semantics on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a 'possible worlds' interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming. Furthermore, we show that a similar approach can be used to provide a coalgebraic semantics to weighted logic programming

A coalgebraic perspective on probabilistic logic programming

Probabilistic logic programming is increasingly important in artificial intelligence and related fields as a formalism to reason about uncertainty. It generalises logic programming with the possibility of annotating clauses with probabilities. This paper proposes a coalgebraic perspective on probabilistic logic programming. Programs are modelled as coalgebras for a certain functor F, and two semantics are given in terms of cofree coalgebras. First, the cofree F-coalgebra yields a semantics in terms of derivation trees. Second, by embedding F into another type G, as cofree G-coalgebra we obtain a “possible worlds” interpretation of programs, from which one may recover the usual distribution semantics of probabilistic logic programming