arXiv subjects

Bart Bogaerts

Publications and source records attributed to Bart Bogaerts.

At least 37 records · Page 2Linked to original sources

arXiv2023

Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking are easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes XOR and cardinality reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

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arXiv2023

Distributed Autoepistemic Logic: Semantics, Complexity, and Applications to Access Control

In this paper we define and study a multi-agent extension of autoepistemic logic (AEL) called distributed autoepistemic logic (dAEL). We define the semantics of dAEL using approximation fixpoint theory, an abstract algebraic framework that unifies different knowledge representation formalisms by describing their semantics as fixpoints of semantic operators. We define 2- and 3-valued semantic operators for dAEL. Using these operators, approximation fixpoint theory allows us to define a class of semantics for dAEL, each based on different intuitions that are well-studied in the context of AEL. We define a mapping from dAEL to AEL and identify the conditions under which the mapping preserves semantics, and furthermore argue that when it does not, the dAEL semantics is more desirable than the AEL-induced semantics since dAEL manages to contain inconsistencies. The development of dAEL has been motivated by an application in the domain of access control. We explain how dAEL can be fruitfully applied to this domain and discuss how well-suited the different semantics are for the application in access control.

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arXiv2023

Mathematical Foundations for Joining Only Knowing and Common Knowledge (Extended Version)

Common knowledge and only knowing capture two intuitive and natural notions that have proven to be useful in a variety of settings, for example to reason about coordination or agreement between agents, or to analyse the knowledge of knowledge-based agents. While these two epistemic operators have been extensively studied in isolation, the approaches made to encode their complex interplay failed to capture some essential properties of only knowing. We propose a novel solution by defining a notion of $μ$-biworld for countable ordinals $μ$, which approximates not only the worlds that an agent deems possible, but also those deemed impossible. This approach allows us to define a multi-agent epistemic logic with common knowledge and only knowing operators, and a three-valued model semantics for it. Moreover, we show that we only really need biworlds of depth at most $ω^2+1$. Based on this observation, we define a Kripke semantics on a canonical Kripke structure and show that this semantics coincides with the model semantics. Finally, we discuss issues arising when combining negative introspection or truthfulness with only knowing and show how positive introspection can be integrated into our logic.

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arXiv2023

Interactive Model Expansion in an Observable Environment

Many practical problems can be understood as the search for a state of affairs that extends a fixed partial state of affairs, the \emph{environment}, while satisfying certain conditions that are formally specified. Such problems are found in, e.g., engineering, law or economics. We study this class of problems in a context where some of the relevant information about the environment is not known by the user at the start of the search. During the search, the user may consider tentative solutions that make implicit hypotheses about these unknowns. To ensure that the solution is appropriate, these hypotheses must be verified by observing the environment. Furthermore, we assume that, in addition to knowledge of what constitutes a solution, knowledge of general laws of the environment is also present. We formally define partial solutions with enough verified facts to guarantee the existence of complete and appropriate solutions. Additionally, we propose an interactive system to assist the user in their search by determining 1) which hypotheses implicit in a tentative solution must be verified in the environment, and 2) which observations can bring useful information for the search. We present an efficient method to over-approximate the set of relevant information, and evaluate our implementation.

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arXiv2023

Non-deterministic approximation operators: ultimate operators, semi-equilibrium semantics and aggregates (full version)

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e.\ operators whose range are sets of elements rather than single elements. In this paper, we make three further contributions to non-deterministic AFT: (1) we define and study ultimate approximations of non-deterministic operators, (2) we give an algebraic formulation of the semi-equilibrium semantics by Amendola, et al., and (3) we generalize the characterisations of disjunctive logic programs to disjunctive logic programs with aggregates.

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arXiv2023

Distributed Subweb Specifications for Traversing the Web

Link Traversal-based Query Processing (ltqp), in which a sparql query is evaluated over a web of documents rather than a single dataset, is often seen as a theoretically interesting yet impractical technique. However, in a time where the hypercentralization of data has increasingly come under scrutiny, a decentralized Web of Data with a simple document-based interface is appealing, as it enables data publishers to control their data and access rights. While ltqp allows evaluating complex queries over such webs, it suffers from performance issues (due to the high number of documents containing data) as well as information quality concerns (due to the many sources providing such documents). In existing ltqp approaches, the burden of finding sources to query is entirely in the hands of the data consumer. In this paper, we argue that to solve these issues, data publishers should also be able to suggest sources of interest and guide the data consumer towards relevant and trustworthy data. We introduce a theoretical framework that enables such guided link traversal and study its properties. We illustrate with a theoretic example that this can improve query results and reduce the number of network requests. We evaluate our proposal experimentally on a virtual linked web with specifications and indeed observe that not just the data quality but also the efficiency of querying improves. Under consideration in Theory and Practice of Logic Programming (TPLP).

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arXiv2022

Non-Deterministic Approximation Fixpoint Theory and Its Application in Disjunctive Logic Programming

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

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arXiv2022

Inputs, Outputs, and Composition in the Logic of Information Flows

The logic of information flows (LIF) is a general framework in which tasks of a procedural nature can be modeled in a declarative, logic-based fashion. The first contribution of this paper is to propose semantic and syntactic definitions of inputs and outputs of LIF expressions. We study how the two relate and show that our syntactic definition is optimal in a sense that is made precise. The second contribution is a systematic study of the expressive power of sequential composition in LIF. Our results on composition tie in the results on inputs and outputs, and relate LIF to first-order logic (FO) and bounded-variable LIF to bounded-variable FO.

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arXiv2022

Tree-Like Justification Systems are Consistent

Justification theory is an abstract unifying formalism that captures semantics of various non-monotonic logics. One intriguing problem that has received significant attention is the consistency problem: under which conditions are justifications for a fact and justifications for its negation suitably related. Two variants of justification theory exist: one in which justifications are trees and one in which they are graphs. In this work we resolve the consistency problem once and for all for the tree-like setting by showing that all reasonable tree-like justification systems are consistent.

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arXiv2022

SHACL: A Description Logic in Disguise

SHACL is a W3C-proposed language for expressing structural constraints on RDF graphs. In recent years, SHACL's popularity has risen quickly. This rise in popularity comes with questions related to its place in the semantic web, particularly about its relation to OWL (the de facto standard for expressing ontological information on the web) and description logics (which form the formal foundations of OWL). We answer these questions by arguing that SHACL is in fact a description logic. On the one hand, our answer is surprisingly simple, some might even say obvious. But, on the hand, our answer is also controversial. By resolving this issue once and for all, we establish the field of description logics as the solid formal foundations of SHACL.

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arXiv2022

On Nested Justification Systems (full version)

Justification theory is a general framework for the definition of semantics of rule-based languages that has a high explanatory potential. Nested justification systems, first introduced by Denecker et al. (2015), allow for the composition of justification systems. This notion of nesting thus enables the modular definition of semantics of rule-based languages, and increases the representational capacities of justification theory. As we show in this paper, the original semantics for nested justification systems lead to the loss of information relevant for explanations. In view of this problem, we provide an alternative characterization of semantics of nested justification systems and show that this characterization is equivalent to the original semantics. Furthermore, we show how nested justification systems allow representing fixpoint definitions (Hou and Denecker 2009).

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arXiv2021

Fixpoint Semantics for Recursive SHACL

SHACL is a W3C-proposed language for expressing structural constraints on RDF graphs. The recommendation only specifies semantics for non-recursive SHACL; recently, some efforts have been made to allow recursive SHACL schemas. In this paper, we argue that for defining and studying semantics of recursive SHACL, lessons can be learned from years of research in non-monotonic reasoning. We show that from a SHACL schema, a three-valued semantic operator can directly be obtained. Building on Approximation Fixpoint Theory (AFT), this operator immediately induces a wide variety of semantics, including a supported, stable, and well-founded semantics, related in the expected ways. By building on AFT, a rich body of theoretical results becomes directly available for SHACL. As such, the main contribution of this short paper is providing theoretical foundations for the study of recursive SHACL, which can later enable an informed decision for an extension of the W3C recommendation.

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arXiv2021

Proceedings 37th International Conference on Logic Programming (Technical Communications)

ICLP is the premier international event for presenting research in logic programming. Contributions to ICLP 2021 were sought in all areas of logic programming, including but not limited to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages issues: Concurrency, Objects, Coordination, Mobility, Higher order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming techniques. Programming support: Program analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing, Execution visualization. Implementation: Compilation, Virtual machines, Memory management, Parallel and Distributed execution, Constraint handling rules, Tabling, Foreign interfaces, User interfaces. Related Paradigms and Synergies: Inductive and coinductive logic programming, Constraint logic programming, Answer set programming, Interaction with SAT, SMT and CSP solvers, Theorem proving, Argumentation, Probabilistic programming, Machine learning. Applications: Databases, Big data, Data integration and federation, Software engineering, Natural language processing, Web and semantic web, Agents, Artificial intelligence, Computational life sciences, Cyber-security, Robotics, Education.

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arXiv2021

Efficiently Explaining CSPs with Unsatisfiable Subset Optimization

We build on a recently proposed method for explaining solutions of constraint satisfaction problems. An explanation here is a sequence of simple inference steps, where the simplicity of an inference step is measured by the number and types of constraints and facts used, and where the sequence explains all logical consequences of the problem. We build on these formal foundations and tackle two emerging questions, namely how to generate explanations that are provably optimal (with respect to the given cost metric) and how to generate them efficiently. To answer these questions, we develop 1) an implicit hitting set algorithm for finding optimal unsatisfiable subsets; 2) a method to reduce multiple calls for (optimal) unsatisfiable subsets to a single call that takes constraints on the subset into account, and 3) a method for re-using relevant information over multiple calls to these algorithms. The method is also applicable to other problems that require finding cost-optimal unsatiable subsets. We specifically show that this approach can be used to effectively find sequences of optimal explanation steps for constraint satisfaction problems like logic grid puzzles.

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arXiv2020

LP2PB: Translating Answer Set Programs into Pseudo-Boolean Theories

Answer set programming (ASP) is a well-established knowledge representation formalism. Most ASP solvers are based on (extensions of) technology from Boolean satisfiability solving. While these solvers have shown to be very successful in many practical applications, their strength is limited by their underlying proof system, resolution. In this paper, we present a new tool LP2PB that translates ASP programs into pseudo-Boolean theories, for which solvers based on the (stronger) cutting plane proof system exist. We evaluate our tool, and the potential of cutting-plane-based solving for ASP on traditional ASP benchmarks as well as benchmarks from pseudo-Boolean solving. Our results are mixed: overall, traditional ASP solvers still outperform our translational approach, but several benchmark families are identified where the balance shifts the other way, thereby suggesting that further investigation into a stronger proof system for ASP is valuable.

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arXiv2020

Exploiting Game Theory for Analysing Justifications

Justification theory is a unifying semantic framework. While it has its roots in non-monotonic logics, it can be applied to various areas in computer science, especially in explainable reasoning; its most central concept is a justification: an explanation why a property holds (or does not hold) in a model. In this paper, we continue the study of justification theory by means of three major contributions. The first is studying the relation between justification theory and game theory. We show that justification frameworks can be seen as a special type of games. The established connection provides the theoretical foundations for our next two contributions. The second contribution is studying under which condition two different dialects of justification theory (graphs as explanations vs trees as explanations) coincide. The third contribution is establishing a precise criterion of when a semantics induced by justification theory yields consistent results. In the past proving that such semantics were consistent took cumbersome and elaborate proofs. We show that these criteria are indeed satisfied for all common semantics of logic programming. This paper is under consideration for acceptance in Theory and Practice of Logic Programming (TPLP).

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arXiv2020

A framework for step-wise explaining how to solve constraint satisfaction problems

We explore the problem of step-wise explaining how to solve constraint satisfaction problems, with a use case on logic grid puzzles. More specifically, we study the problem of explaining the inference steps that one can take during propagation, in a way that is easy to interpret for a person. Thereby, we aim to give the constraint solver explainable agency, which can help in building trust in the solver by being able to understand and even learn from the explanations. The main challenge is that of finding a sequence of simple explanations, where each explanation should aim to be as cognitively easy as possible for a human to verify and understand. This contrasts with the arbitrary combination of facts and constraints that the solver may use when propagating. We propose the use of a cost function to quantify how simple an individual explanation of an inference step is, and identify the explanation-production problem of finding the best sequence of explanations of a CSP. Our approach is agnostic of the underlying constraint propagation mechanisms, and can provide explanations even for inference steps resulting from combinations of constraints. In case multiple constraints are involved, we also develop a mechanism that allows to break the most difficult steps up and thus gives the user the ability to zoom in on specific parts of the explanation. Our proposed algorithm iteratively constructs the explanation sequence by using an optimistic estimate of the cost function to guide the search for the best explanation at each step. Our experiments on logic grid puzzles show the feasibility of the approach in terms of the quality of the individual explanations and the resulting explanation sequences obtained.

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arXiv2019

Proceedings 35th International Conference on Logic Programming (Technical Communications)

Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. Contributions are sought in all areas of logic programming, including but not restricted to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages: Concurrency, Objects, Coordination, Mobility, Higher Order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming Techniques. Declarative programming: Declarative program development, Analysis, Type and mode inference, Partial evaluation, Abstract interpretation, Transformation, Validation, Verification, Debugging, Profiling, Testing, Execution visualization Implementation: Virtual machines, Compilation, Memory management, Parallel/distributed execution, Constraint handling rules, Tabling, Foreign interfaces, User interfaces. Related Paradigms and Synergies: Inductive and Co-inductive Logic Programming, Constraint Logic Programming, Answer Set Programming, Interaction with SAT, SMT and CSP solvers, Logic programming techniques for type inference and theorem proving, Argumentation, Probabilistic Logic Programming, Relations to object-oriented and Functional programming. Applications: Databases, Big Data, Data integration and federation, Software engineering, Natural language processing, Web and Semantic Web, Agents, Artificial intelligence, Computational life sciences, Education, Cybersecurity, and Robotics.

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