Independent Choice Logic Research Articles

Repairing errors in probabilistic databases models using probabilistic abduction reasoning

This paper presents a technique to diagnose probabilistic counter examples that are generated when model checking probabilistic databases models against probabilistic properties formulating queries on probabilistic databases. In probabilistic model checking (PMC), a counterexample is a set of paths that satisfies a path formula, whose cumulative probability mass violates the probability bound. The diagnosis is to repair errors in probabilistic PRISM programs of probabilistic databases models using the probabilistic abduction reasoning on independent choice logic (ICL) programs describing the generated probabilistic counterexamples.

Repairing errors in probabilistic databases models using probabilistic abduction reasoning

This paper presents a technique to diagnose probabilistic counter examples that are generated when model checking probabilistic databases models against probabilistic properties formulating queries on probabilistic databases. In probabilistic model checking (PMC), a counterexample is a set of paths that satisfies a path formula, whose cumulative probability mass violates the probability bound. The diagnosis is to repair errors in probabilistic PRISM programs of probabilistic databases models using the probabilistic abduction reasoning on independent choice logic (ICL) programs describing the generated probabilistic counterexamples.

Well–definedness and efficient inference for probabilistic logic programming under the distribution semantics

AbstractDistribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs), and ProbLog. When a program contains functions symbols, the distribution semantics is well–defined only if the set of explanations for a query is finite and so is each explanation. Well–definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper, we identify a larger class of programs for which the semantics is well–defined together with an efficient procedure for computing the probability of queries. Since Logic Programs with Annotated Disjunctions offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint, and CVE. PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.

The PITA system: Tabling and answer subsumption for reasoning under uncertainty

AbstractMany real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM, and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability.Each of these approaches—general PLP, restricted PLP, and Possibilistic Logic Programming—can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of the problems to be solved. In this paper, we show how the PITA system, which originally supported the general PLP language of LPADs, can also efficiently support restricted PLP and Possibilistic Logic Programs. PITA relies on tabling with answer subsumption and consists of a transformation along with an API for library functions that interface with answer subsumption. We show that, by adapting its transformation and library functions, PITA can be parameterized to PITA(IND, EXC) which supports the restricted PLP of PRISM, including optimizations that reduce non-discriminating arguments and the computation of Viterbi paths. Furthermore, we show PITA to be competitive with PRISM for complex queries to Hidden Markov Model examples, and sometimes much faster. We further show how PITA can be parameterized to PITA(COUNT) which computes the number of different explanations for a subgoal, and to PITA(POSS) which scalably implements Possibilistic Logic Programming. PITA is a supported package in version 3.3 of XSB.

SLGAD Resolution for Inference on Logic Programs with Annotated Disjunctions

Logic Programs with Annotated Disjunctions (LPADs) allow to express probabilistic information in logic programming. The semantics of an LPAD is given in terms of the well-founded models of the normal logic programs obtained by selecting one disjunct from each ground LPAD clause. Inference on LPADs can be performed using either the system Ailog2, that was developed for the Independent Choice Logic, or SLDNFAD, an algorithm based on SLDNF. However, both of these algorithms run the risk of going into infinite loops and of performing redundant computations. In order to avoid these problems, we present SLGAD resolution that computes the (conditional) probability of a ground query from a range-restricted LPAD and is based on SLG resolution for normal logic programs. As SLG, it uses tabling to avoid some infinite loops and to avoid redundant computations. The performances of SLGAD are evaluated on classical benchmarks for normal logic programs under the well-founded semantics, namely a 2-person game and the ancestor relation, and on games of dice. SLGAD is compared with Ailog2 and SLDNFAD on the problems in which they do not go into infinite loops, namely those that are described by a modularly acyclic program. The results show that SLGAD is sometimes slower than Ailog2 and SLDNFAD but, if the program requires the repeated computations of the same goals, as for the dice games, then SLGAD is faster than both.

Extended semantics and inference for the Independent Choice Logic

Extended semantics and inference for the Independent Choice Logic

Probabilistic description logic programs

Towards sophisticated representation and reasoning techniques that allow for probabilistic uncertainty in the Rules, Logic, and Proof layers of the Semantic Web, we present probabilistic description logic programs (or pdl-programs), which are a combination of description logic programs (or dl-programs) under the answer set semantics and the well-founded semantics with Poole’s independent choice logic. We show that query processing in such pdl-programs can be reduced to computing all answer sets of dl-programs and solving linear optimization problems, and to computing the well-founded model of dl-programs, respectively. Moreover, we show that the answer set semantics of pdl-programs is a refinement of the well-founded semantics of pdl-programs. Furthermore, we also present an algorithm for query processing in the special case of stratified pdl-programs, which is based on a reduction to computing the canonical model of stratified dl-programs.

Abducing through negation as failure: stable models within the independent choice logic

The independent choice logic (ICL) is part of a project to combine logic and decision/game theory into a coherent framework. The ICL has a simple possible-worlds semantics characterised by independent choices and an acyclic logic program that specifies the consequences of these choices. This paper gives an abductive characterization of the ICL. The ICL is defined model-theoretically, but we show that it is naturally abductive: the set of explanations of a proposition g is a concise description of the worlds in which g is true. We give an algorithm for computing explanations and show it is sound and complete with respect to the possible-worlds semantics. What is unique about this approach is that the explanations of the negation of g can be derived from the explanations of g. The use of probabilities over choices in this framework and going beyond acyclic logic programs are also discussed.

The independent choice logic for modelling multiple agents under uncertainty

Inspired by game theory representations, Bayesian networks, influence diagrams, structured Markov decision process models, logic programming, and work in dynamical systems, the independent choice logic (ICL) is a semantic framework that allows for independent choices (made by various agents, including nature) and a logic program that gives the consequence of choices. This representation can be used as a specification for agents that act in a world, make observations of that world and have memory, as well as a modelling tool for dynamic environments with uncertainty. The rules specify the consequences of an action, what can be sensed and the utility of outcomes. This paper presents a possible-worlds semantics for ICL, and shows how to embed influence diagrams, structured Markov decision processes, and both the strategic (normal) form and extensive (game-tree) form of games within the ICL. It is argued that the ICL provides a natural and concise representation for multi-agent decision-making under uncertainty that allows for the representation of structured probability tables, the dynamic construction of networks (through the use of logical variables) and a way to handle uncertainty and decisions in a logical representation.