Computing most probable worlds of action probabilistic logic programs: scalable estimation for 1030,000 worlds

The semantics of probabilistic logic programs (PLPs) is usually given through a possible worlds semantics. We propose a variant of PLPs called action probabilistic logic programs or -programs that use a two-sorted alphabet to describe the conditions under which certain real-world entities take certain actions. In such applications, worlds correspond to sets of actions these entities might take. Thus, there is a need to find the most probable world (MPW) for -programs. In contrast, past work on PLPs has primarily focused on the problem of entailment. This paper quickly presents the syntax and semantics of -programs and then shows a naive algorithm to solve the MPW problem using the linear program formulation commonly used for PLPs. As such linear programs have an exponential number of variables, we present two important new algorithms, called and to solve the MPW problem exactly. Both these algorithms can significantly reduce the number of variables in the linear programs. Subsequently, we present a “binary” algorithm that applies a binary search style heuristic in conjunction with the Naive, and algorithms to quickly find worlds that may not be “most probable.” We experimentally evaluate these algorithms both for accuracy (how much worse is the solution found by these heuristics in comparison to the exact solution) and for scalability (how long does it take to compute). We show that the results of are very accurate and also very fast: more than 10^30,000 worlds can be handled in a few minutes. Subsequently, we develop parallel versions of these algorithms and show that they provide further speedups.      

Learning hierarchical probabilistic logic programs

Machine Learning - Probabilistic logic programming (PLP) combines logic programs and probabilities. Due to its expressiveness and simplicity, it has been considered as a powerful tool for learning...     

Reasoning about probabilistic sequential programs in a probabilistic logic

We introduce a notion of strong monotonicity of probabilistic predicate transformers. This notion enables us to establish a normal form theorem for monotone probabilistic predicate transformers. Three other healthiness conditions, namely, conjunctivity, disjunctivity and continuity for probabilistic predicate transformers are also examined, and they are linked to strong monotonicity. A notion of probabilistic refinement index is proposed, and it provides us with a continuous strength spectrum of refinement relations which may be used to describe more flexible refinement between probabilistic programs. A notion of probabilistic correctness is introduced too. We give a probabilistic weakest-precondition, choice and game semantics to the contract language, and present a probabilistic generalization of the winning strategy theorem. Received: 16 April 2002 / 20 January 2003 RID="a" ID="a" This work was partly supported by the National Key Project for Fundamental Research of China (Grant No: 1998030905) and the National Foundation of Natural Sciences of China (Grant No: 60273003)     

Lifted discriminative learning of probabilistic logic programs

Machine Learning - Probabilistic logic programming (PLP) provides a powerful tool for reasoning with uncertain relational models. However, learning probabilistic logic programs is expensive due to...     

A new approach to hybrid probabilistic logic programs

This paper presents a novel revision of the framework of Hybrid Probabilistic Logic Programming, along with a complete semantics characterization, to enable the encoding of and reasoning about real-world applications. The language of Hybrid Probabilistic Logic Programs framework is extended to allow the use of non-monotonic negation, and two alternative semantical characterizations are defined: stable probabilistic model semantics and probabilistic well-founded semantics. These semantics generalize the stable model semantics and well-founded semantics of traditional normal logic programs, and they reduce to the semantics of Hybrid Probabilistic Logic programs for programs without negation. It is the first time that two different semantics for Hybrid Probabilistic Programs with non-monotonic negation as well as their relationships are described. This proposal provides the foundational grounds for developing computational methods for implementing the proposed semantics. Furthermore, it makes it clearer how to characterize non-monotonic negation in probabilistic logic programming frameworks for commonsense reasoning. An erratum to this article can be found at     

Learning probabilistic logic models from probabilistic examples

We revisit an application developed originally using abductive Inductive Logic Programming (ILP) for modeling inhibition in metabolic networks. The example data was derived from studies of the effects of toxins on rats using Nuclear Magnetic Resonance (NMR) time-trace analysis of their biofluids together with background knowledge representing a subset of the Kyoto Encyclopedia of Genes and Genomes (KEGG). We now apply two Probabilistic ILP (PILP) approaches—abductive Stochastic Logic Programs (SLPs) and PRogramming In Statistical modeling (PRISM) to the application. Both approaches support abductive learning and probability predictions. Abductive SLPs are a PILP framework that provides possible worlds semantics to SLPs through abduction. Instead of learning logic models from non-probabilistic examples as done in ILP, the PILP approach applied in this paper is based on a general technique for introducing probability labels within a standard scientific experimental setting involving control and treated data. Our results demonstrate that the PILP approach provides a way of learning probabilistic logic models from probabilistic examples, and the PILP models learned from probabilistic examples lead to a significant decrease in error accompanied by improved insight from the learned results compared with the PILP models learned from non-probabilistic examples.     

N-tuple algebra-based probabilistic logic

The concept of “probabilistic logic” known in artificial intelligence needs a more through substantiation. A new approach to constructing probabilistic logic based on the n-tuple algebra developed by the author is proposed. A brief introduction is given to the n-tuple algebra and its properties that provide efficient paralleling of algorithms for solving problems of logical analysis of systems in computer implementation are generalized. Methods for solving direct and inverse problems of probabilistic simulation of logical systems are considered.     

Parallelism in logic programs

There is a tension between the objectives of avoiding irrelevant computation and extracting parallelism, in that a computational step used to restrict another must precede the latter. Our thesis, following [3], is that evaluation methods can be viewed as implementing a choice ofsideways information propagation graphs, or sips, which determines the set of goals and facts that must be evaluated. Two evaluation methods that implement the same sips can then be compared to see which obtains a greater degree of parallelism, and we provide a formal measure of parallelism to make this comparison.Using this measure, we prove that transforming a program using the Magic Templates algorithm and then evaluating the fixpoint bottom-up provides a most parallel implementation for a given choice of sips, without taking resource constraints into account. This result, taken in conjunction with earlier results from [3,27], which show that bottom-up evaluation performs no irrelevant computation and is sound and complete, suggests that a bottom-up approach to parallel evaluation of logic programs is very promising. A more careful analysis of the relative overheads in the top-down and bottom-up evaluation paradigms is needed, however, and we discuss some of the issues.The abstract model allows us to establish several results comparing other proposed parallel evaluation methods in the logic programming and deductive database literature, thereby showing some natural, and sometimes surprising, connections. We consider the limitations of the abstract model and of the proposed bottom-up evaluation method, including the inability of sips to describe certain evaluation methods, and the effect of resource constraints. Our results shed light on the limits of the sip paradigm of computation, which we extend in the process.     

概率逻辑、不确定逻辑和模糊逻辑之比较

通过一个实例分析比较了概率逻辑、主观概率逻辑、不确定逻辑和模糊逻辑的思想方法。提出了自己的观点：基于数据统计的概率逻辑是最科学的。不确定逻辑比主观概率逻辑更科学。当具有不确定性的原子命题具有独立性时,不确定逻辑和模糊逻辑的观点是一致的。而对于处理带有不确定性的相关性命题,不确定逻辑比模糊逻辑更科学。但是模糊逻辑在建立推理理论方面见长。     

Canonical logic programs

Consider the class of programs P where the greatest fixpoint of T_P is equal to the complement of the finite failure set of P. Programs in this calss possess some important properties which others do not. The main result in this paper proves that this class is representative of all programs. Specifically, we call the programs in this class canonical and we prove that for any program P₁, there exists a semantically equivalent program P₂ which is canonical.     

Compressing probabilistic Prolog programs

ProbLog is a recently introduced probabilistic extension of Prolog (De Raedt, et al. in Proceedings of the 20th international joint conference on artificial intelligence, pp. 2468–2473, 2007). A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is then defined by the success probability of a query in a randomly sampled program. This paper introduces the theory compression task for ProbLog, which consists of selecting that subset of clauses of a given ProbLog program that maximizes the likelihood w.r.t. a set of positive and negative examples. Experiments in the context of discovering links in real biological networks demonstrate the practical applicability of the approach. Editors: Stephen Muggleton, Ramon Otero, Simon Colton.     

Fuzzy and probabilistic programs

In this paper, a general formulation of fuzzy programs or fuzzy algorithms is introduced. The relationship between this formulation and other existing formulations is studied.     

Borel型概率计量逻辑

视全体赋值之集为通常乘积拓扑空间,利用该空间上的Borel概率测度在二值命题逻辑中引入了公式的概率真度概念.该方法既克服了计量逻辑学要求赋值集上的概率测度必须为均匀概率测度的无穷可数乘积的局限,又弥补了概率逻辑学只讲局部而缺乏整体性的不足;证明了计量逻辑学中公式的真度、随机真度以及概率逻辑学中公式的概率等概念都可作为本文提出的概率真度的特例而纳入到统一的框架中,从而实现了计量逻辑学与概率逻辑学的融合与统一;证明了逻辑闭理论与赋值空间中的拓扑闭集是一一对应的以及概率真度函数与赋值空间上的Borel概率测度是一样多的等若干结论;本文的第4节给出了公式的概率真度的公理化定义,证明了公式集上满足Kolmogorov公理的任一[0,1]值函数均可由赋值空间上的某Borel概率测度按本文的方法所表出,从而建立了二值命题逻辑框架下的概率计量逻辑的理论体系.     

Fuzzy and probabilistic programs

In this paper, a general formulation of fuzzy programs or fuzzy algorithms is introduced. The relationship between this formulation and other existing formulations is studied.