arXiv subjects

Maurice Bruynooghe

Publications and source records attributed to Maurice Bruynooghe.

At least 19 recordsLinked to original sources

arXiv2024

Simulating dynamic systems using Linear Time Calculus theories

To appear in Theory and Practice of Logic Programming (TPLP). Dynamic systems play a central role in fields such as planning, verification, and databases. Fragmented throughout these fields, we find a multitude of languages to formally specify dynamic systems and a multitude of systems to reason on such specifications. Often, such systems are bound to one specific language and one specific inference task. It is troublesome that performing several inference tasks on the same knowledge requires translations of your specification to other languages. In this paper we study whether it is possible to perform a broad set of well-studied inference tasks on one specification. More concretely, we extend IDP3 with several inferences from fields concerned with dynamic specifications.

cs.LO↗

arXiv2023

Using Symmetries to Lift Satisfiability Checking

We analyze how symmetries can be used to compress structures (also known as interpretations) onto a smaller domain without loss of information. This analysis suggests the possibility to solve satisfiability problems in the compressed domain for better performance. Thus, we propose a 2-step novel method: (i) the sentence to be satisfied is automatically translated into an equisatisfiable sentence over a ``lifted'' vocabulary that allows domain compression; (ii) satisfiability of the lifted sentence is checked by growing the (initially unknown) compressed domain until a satisfying structure is found. The key issue is to ensure that this satisfying structure can always be expanded into an uncompressed structure that satisfies the original sentence to be satisfied. We present an adequate translation for sentences in typed first-order logic extended with aggregates. Our experimental evaluation shows large speedups for generative configuration problems. The method also has applications in the verification of software operating on complex data structures. Our results justify further research in automatic translation of sentences for symmetry reduction.

cs.LO↗

arXiv2022

Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory

Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalisation of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of Approximation Fixpoint Theory (AFT). We introduce an AFT formalisation equivalent with the Gelfond-Lifschitz reduct for basic ASP programs and we extend it to handle aggregates. We analyse how existing approaches relate to our framework. We hope this work sheds some new light on the issue of a proper formalisation of aggregates. This paper is under consideration for acceptance in TPLP.

cs.AI↗

arXiv2021

Justifications and a Reconstruction of Parity Game Solving Algorithms

Parity games are infinite two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification. This paper defines parametrized parity games and introduces an operation, Justify, that determines a winning strategy for a single node. By carefully ordering Justify steps, we reconstruct three algorithms well known from the literature.

cs.LO↗

arXiv2018

Predicate Logic as a Modelling Language: The IDP System

With the technology of the time, Kowalski's seminal 1974 paper {\em Predicate Logic as a Programming Language} was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the use of the Horn clause logic fragment of classical logic, which was soon extended with negation as failure, on the procedural side the procedural interpretation which made it possible to write algorithms in the formalism. Since then, strong progress was made both on the declarative understanding of the logic programming formalism and in automated reasoning technologies, particularly in SAT solving, Constraint Programming and Answer Set Programming. This has paved the way for the development of an extension of logic programming that embodies a more pure view of logic as a modelling language and its role for problem solving. In this paper, we present the \idp language and system. The language is essentially classical logic extended with one of logic programmings most important contributions to knowledge representation: the representation of complex definitions as rule sets under well-founded semantics. The system is a knowledge base system: a system in which complex declarative information is stored in a knowledge base which can be used to solve different computational problems by applying multiple forms of inference. In this view, theories are declarative modellings, bags of information, descriptions of possible states of affairs. They are neither procedures nor descriptions of computational problems. As such, the \idp language and system preserve the fundamental idea of a declarative reading of logic programs, while they break with the fundamental idea of the procedural interpretation of logic programs.

cs.LO↗

arXiv2016

A MIP Backend for the IDP System

The IDP knowledge base system currently uses MiniSAT(ID) as its backend Constraint Programming (CP) solver. A few similar systems have used a Mixed Integer Programming (MIP) solver as backend. However, so far little is known about when the MIP solver is preferable. This paper explores this question. It describes the use of CPLEX as a backend for IDP and reports on experiments comparing both backends.

cs.AI↗

arXiv2016

On Local Domain Symmetry for Model Expansion

Symmetry in combinatorial problems is an extensively studied topic. We continue this research in the context of model expansion problems, with the aim of automating the workflow of detecting and breaking symmetry. We focus on local domain symmetry, which is induced by permutations of domain elements, and which can be detected on a first-order level. As such, our work is a continuation of the symmetry exploitation techniques of model generation systems, while it differs from more recent symmetry breaking techniques in answer set programming which detect symmetry on ground programs. Our main contributions are sufficient conditions for symmetry of model expansion problems, the identification of local domain interchangeability, which can often be broken completely, and efficient symmetry detection algorithms for both local domain interchangeability as well as local domain symmetry in general. Our approach is implemented in the model expansion system IDP, and we present experimental results showcasing the strong and weak points of our approach compared to SBASS , a symmetry breaking technique for answer set programming.

cs.LO↗

arXiv2015

Mining Rooted Ordered Trees under Subtree Homeomorphism

Mining frequent tree patterns has many applications in different areas such as XML data, bioinformatics and World Wide Web. The crucial step in frequent pattern mining is frequency counting, which involves a matching operator to find occurrences (instances) of a tree pattern in a given collection of trees. A widely used matching operator for tree-structured data is subtree homeomorphism, where an edge in the tree pattern is mapped onto an ancestor-descendant relationship in the given tree. Tree patterns that are frequent under subtree homeomorphism are usually called embedded patterns. In this paper, we present an efficient algorithm for subtree homeomorphism with application to frequent pattern mining. We propose a compact data-structure, called occ, which stores only information about the rightmost paths of occurrences and hence can encode and represent several occurrences of a tree pattern. We then define efficient join operations on the occ data-structure, which help us count occurrences of tree patterns according to occurrences of their proper subtrees. Based on the proposed subtree homeomorphism method, we develop an effective pattern mining algorithm, called TPMiner. We evaluate the efficiency of TPMiner on several real-world and synthetic datasets. Our extensive experiments confirm that TPMiner always outperforms well-known existing algorithms, and in several cases the improvement with respect to existing algorithms is significant.

cs.DB↗

arXiv2015

Lazy Model Expansion: Interleaving Grounding with Search

Finding satisfying assignments for the variables involved in a set of constraints can be cast as a (bounded) model generation problem: search for (bounded) models of a theory in some logic. The state-of-the-art approach for bounded model generation for rich knowledge representation languages, like ASP, FO(.) and Zinc, is ground-and-solve: reduce the theory to a ground or propositional one and apply a search algorithm to the resulting theory. An important bottleneck is the blowup of the size of the theory caused by the reduction phase. Lazily grounding the theory during search is a way to overcome this bottleneck. We present a theoretical framework and an implementation in the context of the FO(.) knowledge representation language. Instead of grounding all parts of a theory, justifications are derived for some parts of it. Given a partial assignment for the grounded part of the theory and valid justifications for the formulas of the non-grounded part, the justifications provide a recipe to construct a complete assignment that satisfies the non-grounded part. When a justification for a particular formula becomes invalid during search, a new one is derived; if that fails, the formula is split in a part to be grounded and a part that can be justified. The theoretical framework captures existing approaches for tackling the grounding bottleneck such as lazy clause generation and grounding-on-the-fly, and presents a generalization of the 2-watched literal scheme. We present an algorithm for lazy model expansion and integrate it in a model generator for FO(ID), a language extending first-order logic with inductive definitions. The algorithm is implemented as part of the state-of-the-art FO(ID) Knowledge-Base System IDP. Experimental results illustrate the power and generality of the approach.

cs.LO↗

arXiv2014

Predicate Logic as a Modeling Language: Modeling and Solving some Machine Learning and Data Mining Problems with IDP3

This paper provides a gentle introduction to problem solving with the IDP3 system. The core of IDP3 is a finite model generator that supports first order logic enriched with types, inductive definitions, aggregates and partial functions. It offers its users a modeling language that is a slight extension of predicate logic and allows them to solve a wide range of search problems. Apart from a small introductory example, applications are selected from problems that arose within machine learning and data mining research. These research areas have recently shown a strong interest in declarative modeling and constraint solving as opposed to algorithmic approaches. The paper illustrates that the IDP3 system can be a valuable tool for researchers with such an interest. The first problem is in the domain of stemmatology, a domain of philology concerned with the relationship between surviving variant versions of text. The second problem is about a somewhat related problem within biology where phylogenetic trees are used to represent the evolution of species. The third and final problem concerns the classical problem of learning a minimal automaton consistent with a given set of strings. For this last problem, we show that the performance of our solution comes very close to that of a state-of-the art solution. For each of these applications, we analyze the problem, illustrate the development of a logic-based model and explore how alternatives can affect the performance.

cs.LO↗

arXiv2011

The Magic of Logical Inference in Probabilistic Programming

Today, many different probabilistic programming languages exist and even more inference mechanisms for these languages. Still, most logic programming based languages use backward reasoning based on SLD resolution for inference. While these methods are typically computationally efficient, they often can neither handle infinite and/or continuous distributions, nor evidence. To overcome these limitations, we introduce distributional clauses, a variation and extension of Sato's distribution semantics. We also contribute a novel approximate inference method that integrates forward reasoning with importance sampling, a well-known technique for probabilistic inference. To achieve efficiency, we integrate two logic programming techniques to direct forward sampling. Magic sets are used to focus on relevant parts of the program, while the integration of backward reasoning allows one to identify and avoid regions of the sample space that are inconsistent with the evidence.

cs.LO↗

arXiv2011

Constraint Propagation for First-Order Logic and Inductive Definitions

Constraint propagation is one of the basic forms of inference in many logic-based reasoning systems. In this paper, we investigate constraint propagation for first-order logic (FO), a suitable language to express a wide variety of constraints. We present an algorithm with polynomial-time data complexity for constraint propagation in the context of an FO theory and a finite structure. We show that constraint propagation in this manner can be represented by a datalog program and that the algorithm can be executed symbolically, i.e., independently of a structure. Next, we extend the algorithm to FO(ID), the extension of FO with inductive definitions. Finally, we discuss several applications.

cs.LO↗

arXiv2009

CP-logic: A Language of Causal Probabilistic Events and Its Relation to Logic Programming

This papers develops a logical language for representing probabilistic causal laws. Our interest in such a language is twofold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.

cs.AI↗

arXiv2007

Functional Equivalence Checking for Verification of Algebraic Transformations on Array-Intensive Source Code

Development of energy and performance-efficient embedded software is increasingly relying on application of complex transformations on the critical parts of the source code. Designers applying such nontrivial source code transformations are often faced with the problem of ensuring functional equivalence of the original and transformed programs. Currently they have to rely on incomplete and time-consuming simulation. Formal automatic verification of the transformed program against the original is instead desirable. This calls for equivalence checking tools similar to the ones available for comparing digital circuits. We present such a tool to compare array-intensive programs related through a combination of important global transformations like expression propagations, loop and algebraic transformations. When the transformed program fails to pass the equivalence check, the tool provides specific feedback on the possible locations of errors.

cs.LO↗

arXiv2006

Well-founded and Stable Semantics of Logic Programs with Aggregates

In this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valued immediate consequence operator of an aggregate program. Such an operator approximates the standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs between precision and tractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

cs.LO↗

arXiv2003

Enhancing a Search Algorithm to Perform Intelligent Backtracking

This paper illustrates how a Prolog program, using chronological backtracking to find a solution in some search space, can be enhanced to perform intelligent backtracking. The enhancement crucially relies on the impurity of Prolog that allows a program to store information when a dead end is reached. To illustrate the technique, a simple search program is enhanced. To appear in Theory and Practice of Logic Programming. Keywords: intelligent backtracking, dependency-directed backtracking, backjumping, conflict-directed backjumping, nogood sets, look-back.

cs.AI↗

arXiv2002

Offline Specialisation in Prolog Using a Hand-Written Compiler Generator

The so called ``cogen approach'' to program specialisation, writing a compiler generator instead of a specialiser, has been used with considerable success in partial evaluation of both functional and imperative languages. This paper demonstrates that the cogen approach is also applicable to the specialisation of logic programs (also called partial deduction) and leads to effective specialisers. Moreover, using good binding-time annotations, the speed-ups of the specialised programs are comparable to the speed-ups obtained with online specialisers. The paper first develops a generic approach to offline partial deduction and then a specific offline partial deduction method, leading to the offline system LIX for pure logic programs. While this is a usable specialiser by itself, it is used to develop the cogen system LOGEN. Given a program, a specification of what inputs will be static, and an annotation specifying which calls should be unfolded, LOGEN generates a specialised specialiser for the program at hand. Running this specialiser with particular values for the static inputs results in the specialised program. While this requires two steps instead of one, the efficiency of the specialisation process is improved in situations where the same program is specialised multiple times. The paper also presents and evaluates an automatic binding-time analysis that is able to derive the annotations. While the derived annotations are still suboptimal compared to hand-crafted ones, they enable non-expert users to use the LOGEN system in a fully automated way. Finally, LOGEN is extended so as to directly support a large part of Prolog's declarative and non-declarative features and so as to be able to perform so called mixline specialisations.

cs.PL↗

arXiv2002

Repairing Inconsistent Databases: A Model-Theoretic Approach and Abductive Reasoning

In this paper we consider two points of views to the problem of coherent integration of distributed data. First we give a pure model-theoretic analysis of the possible ways to `repair' a database. We do so by characterizing the possibilities to `recover' consistent data from an inconsistent database in terms of those models of the database that exhibit as minimal inconsistent information as reasonably possible. Then we introduce an abductive application to restore the consistency of a given database. This application is based on an abductive solver (A-system) that implements an SLDNFA-resolution procedure, and computes a list of data-facts that should be inserted to the database or retracted from it in order to keep the database consistent. The two approaches for coherent data integration are related by soundness and completeness results.

cs.LO↗