Target Compilation Language Research Articles

Conditioning in First-Order Knowledge Compilation and Lifted Probabilistic Inference

Knowledge compilation is a powerful technique for compactly representing and efficiently reasoning about logical knowledge bases. It has been successfully applied to numerous problems in artificial intelligence, such as probabilistic inference and conformant planning. Conditioning, which updates a knowledge base with observed truth values for some propositions, is one of the fundamental operations employed for reasoning. In the propositional setting, conditioning can be efficiently applied in all cases. Recently, people have explored compilation for first-order knowledge bases. The majority of this work has centered around using first-order d-DNNF circuits as the target compilation language. However, conditioning has not been studied in this setting. This paper explores how to condition a first-order d-DNNF circuit. We show that it is possible to efficiently condition these circuits on unary relations. However, we prove that conditioning on higher arity relations is #P-hard. We study the implications of these findings on the application of performing lifted inference for first-order probabilistic models.This leads to a better understanding of which types of queries lifted inference can address.

A generic approach to planning in the presence of incomplete information: Theory and implementation

This paper proposes a generic approach to planning in the presence of incomplete information. The approach builds on an abstract notion of a belief state representation, along with an associated set of basic operations. These operations facilitate the development of a sound and complete transition function, for reasoning about effects of actions in the presence of incomplete information, and a set of abstract algorithms for planning. The paper demonstrates how the abstract definitions and algorithms can be instantiated in three concrete representations—minimal-DNF, minimal-CNF, and prime implicates—resulting in three highly competitive conformant planners: Dnf, Cnf, and PIP. The paper relates the notion of a representation to that of ordered binary decision diagrams, a well-known belief state representation employed by many conformant planners, and several target compilation languages that have been presented in the literature. The paper also includes an experimental evaluation of the planners Dnf, Cnf, and PIP and proposes a new set of conformant planning benchmarks that are challenging for state-of-the-art conformant planners.

Reduced ordered binary decision diagram with implied literals: a new knowledge compilation approach

Knowledge compilation is an approach to tackle the computational intractability of general reasoning problems. According to this approach, knowledge bases are converted off-line into a target compilation language which is tractable for on-line querying. Reduced ordered binary decision diagram (ROBDD) is one of the most influential target languages. We generalize ROBDD by associating some implied literals in each node and the new language is called reduced ordered binary decision diagram with implied literals (ROBDD-L). Then we discuss a kind of subsets of ROBDD-L called ROBDD-i with precisely i implied literals (0 \leq i \leq \infty). In particular, ROBDD-0 is isomorphic to ROBDD; ROBDD-\infty requires that each node should be associated by the implied literals as many as possible. We show that ROBDD-i has uniqueness over some specific variables order, and ROBDD-\infty is the most succinct subset in ROBDD-L and can meet most of the querying requirements involved in the knowledge compilation map. Finally, we propose an ROBDD-i compilation algorithm for any i and a ROBDD-\infty compilation algorithm. Based on them, we implement a ROBDD-L package called BDDjLu and then get some conclusions from preliminary experimental results: ROBDD-\infty is obviously smaller than ROBDD for all benchmarks; ROBDD-\infty is smaller than the d-DNNF the benchmarks whose compilation results are relatively small; it seems that it is better to transform ROBDDs-\infty into FBDDs and ROBDDs rather than straight compile the benchmarks.

Knowledge Compilation Meets Database Theory: Compiling Queries to Decision Diagrams

The goal of Knowledge Compilation is to represent a Boolean expression in a format in which it can answer a range of “online-queries” in PTIME. The online-query of main interest to us is model counting, because of its application to query evaluation on probabilistic databases, but other online-queries can be supported as well such as testing for equivalence, testing for implication, etc. In this paper we study the following problem: given a database query q, decide whether its lineage can be compiled efficiently into a given target language. We consider four target languages, of strictly increasing expressive power (when the size of compilation is restricted to be polynomial in the data size): read-once Boolean formulae, OBDD, FBDD and d-DNNF. For each target, we study the class of database queries that admit polynomial size representation: these queries can also be evaluated in PTIME over probabilistic databases. When queries are restricted to conjunctive queries without self-joins, it was known that these four classes collapse to the class of hierarchical queries, which is also the class of PTIME queries over probabilistic databases. Our main result in this paper is that, in the case of Unions of Conjunctive Queries (UCQ), these classes form a strict hierarchy. Thus, unlike conjunctive queries without self-joins, the expressive power of UCQ differs considerably with respect to these target compilation languages. Moreover, we give a complete characterization of the first two target languages, based on the query’s syntax.

A New Default Theories Compilation for MSP-Entailment

Handling exceptions represents one of the most important problems in Artificial Intelligence. Several approaches have been proposed for reasoning on default theories. This paper focuses on a possibilistic approach, and more precisely on the MSP-entailment (where MSP stands for Minimum Specificity Principle) from default theories which is equivalent to System P augmented by rational monotony. In order to make this entailment tractable from a computational point of view, we propose here a compilation of default theories with respect to a target compilation language. This allows us to provide polynomial algorithms to derive efficiently the MSP-conclusions of a compiled default theory. Moreover, the proposed compilation is qualified to be flexible since it efficiently takes advantage of any classical compiler and generally provides a low recompilation cost when updating a compiled default theory.

A Knowledge Compilation Map

We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. We then provide a knowledge compilation map, which analyzes a large number of existing target compilation languages according to their succinctness and their polytime transformations and queries. We argue that such analysis is necessary for placing new compilation approaches within the context of existing ones. We also go beyond classical, flat target compilation languages based on CNF and DNF, and consider a richer, nested class based on directed acyclic graphs (such as OBDDs), which we show to include a relatively large number of target compilation languages.

A knowledge compilation map

We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, an...

Decomposable negation normal form

Knowledge compilation has been emerging recently as a new direction of research for dealing with the computational intractability of general propositional reasoning. According to this approach, the reasoning process is split into two phases: an off-line compilation phase and an on-line query-answering phase. In the off-line phase, the propositional theory is compiled into some target language, which is typically a tractable one. In the on-line phase, the compiled target is used to efficiently answer a (potentially) exponential number of queries. The main motivation behind knowledge compilation is to push as much of the computational overhead as possible into the off-line phase, in order to amortize that overhead over all on-line queries. Another motivation behind compilation is to produce very simple on-line reasoning systems, which can be embedded cost-effectively into primitive computational platforms, such as those found in consumer electronics.One of the key aspects of any compilation approach is the target language into which the propositional theory is compiled. Previous target languages included Horn theories, prime implicates/implicants and ordered binary decision diagrams (OBDDs). We propose in this paper a new target compilation language, known as decomposable negation normal form (DNNF), and present a number of its properties that make it of interest to the broad community. Specifically, we show that DNNF is universal; supports a rich set of polynomial--time logical operations; is more space-efficient than OBDDs; and is very simple as far as its structure and algorithms are concerned. Moreover, we present an algorithm for converting any propositional theory in clausal form into a DNNF and show that if the clausal form has a bounded treewidth, then its DNNF compilation has a linear size and can be computed in linear time (treewidth is a graph-theoretic parameter that measures the connectivity of the clausal form). We also propose two techniques for approximating the DNNF compilation of a theory when the size of such compilation is too large to be practical. One of the techniques generates a sound but incomplete compilation, while the other generates a complete but unsound compilation. Together, these approximations bound the exact compilation from below and above in terms of their ability to answer clausal entailment queries. Finally, we show that the class of polynomial--time DNNF operations is rich enough to support relatively complex AI applications, by proposing a specific framework for compiling model-based diagnosis systems.