arXiv subjects

Bart Bogaerts

Publications and source records attributed to Bart Bogaerts.

48 records · Page 3Linked to original sources

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.

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arXiv2017

Propagators and Solvers for the Algebra of Modular Systems

To appear in the proceedings of LPAR 21. Solving complex problems can involve non-trivial combinations of distinct knowledge bases and problem solvers. The Algebra of Modular Systems is a knowledge representation framework that provides a method for formally specifying such systems in purely semantic terms. Formally, an expression of the algebra defines a class of structures. Many expressive formalism used in practice solve the model expansion task, where a structure is given on the input and an expansion of this structure in the defined class of structures is searched (this practice overcomes the common undecidability problem for expressive logics). In this paper, we construct a solver for the model expansion task for a complex modular systems from an expression in the algebra and black-box propagators or solvers for the primitive modules. To this end, we define a general notion of propagators equipped with an explanation mechanism, an extension of the alge- bra to propagators, and a lazy conflict-driven learning algorithm. The result is a framework for seamlessly combining solving technology from different domains to produce a solver for a combined system.

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arXiv2017

A Logical Study of Some Common Principles of Inductive Definition and its Implications for Knowledge Representation

The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification languages and systems. This paper is a formal study of some of the most common forms of inductive definitions found in scientific text: monotone inductive definition, definition by induction over a well-founded order and iterated inductive definitions. We define a logic of definitions offering a uniform formal syntax to express definitions of the different sorts, and we define its semantics by a faithful formalization of the induction process. Several fundamental properties of definition by induction emerge: the non-determinism of the induction process, the confluence of induction processes, the role of the induction order and its relation to the inductive rules, how the induction order constrains the induction process and, ultimately, that the induction order is irrelevant: the defined set does not depend on the induction order. We propose an inductive construction capable of constructing the defined set without using the induction order. We investigate borderline definitions of the sort that appears in definitional paradoxes.

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arXiv2016

BreakID: Static Symmetry Breaking for ASP (System Description)

Symmetry breaking has been proven to be an efficient preprocessing technique for satisfiability solving (SAT). In this paper, we port the state-of-the-art SAT symmetry breaker BreakID to answer set programming (ASP). The result is a lightweight tool that can be plugged in between the grounding and the solving phases that are common when modelling in ASP. We compare our tool with sbass, the current state-of-the-art symmetry breaker for ASP.

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arXiv2016

Implementing a Relevance Tracker Module

PC(ID) extends propositional logic with inductive definitions: rule sets under the well-founded semantics. Recently, a notion of relevance was introduced for this language. This notion determines the set of undecided literals that can still influence the satisfiability of a PC(ID) formula in a given partial assignment. The idea is that the PC(ID) solver can make decisions only on relevant literals without losing soundness and thus safely ignore irrelevant literals. One important insight that the relevance of a literal is completely determined by the current solver state. During search, the solver state changes have an effect on the relevance of literals. In this paper, we discuss an incremental, lightweight implementation of a relevance tracker module that can be added to and interact with an out-of-the-box SAT(ID) solver.

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arXiv2016

Stable-Unstable Semantics: Beyond NP with Normal Logic Programs

Standard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic programs offers the most prominent way of reaching the second level of the PH, but encoding respective hard problems as disjunctive programs typically requires sophisticated techniques such as saturation or meta-interpretation. The application of such techniques easily leads to encodings that are inaccessible to non-experts. Furthermore, while disjunctive ASP solvers often rely on calls to a (co-)NP oracle, it may be difficult to detect from the input program where the oracle is being accessed. In other formalisms, such as Quantified Boolean Formulas (QBFs), the interface to the underlying oracle is more transparent as it is explicitly recorded in the quantifier prefix of a formula. On the other hand, ASP has advantages over QBFs from the modeling perspective. The rich high-level languages such as ASP-Core-2 offer a wide variety of primitives that enable concise and natural encodings of search problems. In this paper, we present a novel logic programming--based modeling paradigm that combines the best features of ASP and QBFs. We develop so-called combined logic programs in which oracles are directly cast as (normal) logic programs themselves. Recursive incarnations of this construction enable logic programming on arbitrarily high levels of the PH. We develop a proof-of-concept implementation for our new paradigm. This paper is under consideration for acceptance in TPLP.

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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.

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arXiv2015

Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory

To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 2015 Recent advances in knowledge compilation introduced techniques to compile \emph{positive} logic programs into propositional logic, essentially exploiting the constructive nature of the least fixpoint computation. This approach has several advantages over existing approaches: it maintains logical equivalence, does not require (expensive) loop-breaking preprocessing or the introduction of auxiliary variables, and significantly outperforms existing algorithms. Unfortunately, this technique is limited to \emph{negation-free} programs. In this paper, we show how to extend it to general logic programs under the well-founded semantics. We develop our work in approximation fixpoint theory, an algebraical framework that unifies semantics of different logics. As such, our algebraical results are also applicable to autoepistemic logic, default logic and abstract dialectical frameworks.

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arXiv2014

FO(C): A Knowledge Representation Language of Causality

Cause-effect relations are an important part of human knowledge. In real life, humans often reason about complex causes linked to complex effects. By comparison, existing formalisms for representing knowledge about causal relations are quite limited in the kind of specifications of causes and effects they allow. In this paper, we present the new language C-Log, which offers a significantly more expressive representation of effects, including such features as the creation of new objects. We show how C-Log integrates with first-order logic, resulting in the language FO(C). We also compare FO(C) with several related languages and paradigms, including inductive definitions, disjunctive logic programming, business rules and extensions of Datalog.

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arXiv2014

Inference in the FO(C) Modelling Language

Recently, FO(C), the integration of C-Log with classical logic, was introduced as a knowledge representation language. Up to this point, no systems exist that perform inference on FO(C), and very little is known about properties of inference in FO(C). In this paper, we study both of the above problems. We define normal forms for FO(C), one of which corresponds to FO(ID). We define transformations between these normal forms, and show that, using these transformations, several inference tasks for FO(C) can be reduced to inference tasks for FO(ID), for which solvers exist. We implemented a prototype of this transformation, and thus present the first system to perform inference in FO(C). We also provide results about the complexity of reasoning in FO(C).

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arXiv2014

FO(C) and Related Modelling Paradigms

Recently, C-Log was introduced as a language for modelling causal processes. Its formal semantics has been defined together with introductory examples, but the study of this language is far from finished. In this paper, we compare C-Log to other declarative modelling languages. More specifically, we compare to first-order logic (FO), and argue that C-Log and FO are orthogonal and that their integration, FO(C), is a knowledge representation language that allows for clear and succinct models. We compare FO(C) to E-disjunctive logic programming with the stable semantics, and define a fragment on which both semantics coincide. Furthermore, we discuss object-creation in FO(C), relating it to mathematics, business rules systems, and data base systems.

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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.

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