arXiv subjects

Jia-Huai You

Publications and source records attributed to Jia-Huai You.

At least 19 recordsLinked to original sources

arXiv2026

A New Well-Supported Semantics for Description Logic Programs

Description logic programs are a powerful formalism for combining rules with ontologies. The well-supported semantics for description logic programs ensures that no answer sets rely on cyclic dependencies. Most popular semantics for logic programming have this property of well-supportedness. We recognize two limitations of the current well-supported semantics for DL programs: its increased computational complexity for the consistency problem and its lack of a reduct transformation characterization. In this work, we present a new semantics which evaluates ontological atoms more strictly than the current semantics. This keeps the complexity of its consistency problem NP-complete, rather than increasing it to the second level of the polynomial hierarchy. Additionally, we identify a syntactic class of description logic programs for which our new semantics is equivalent to the current semantics. We characterize our semantics using a fixpoint operator and a reduct-based transformation. Our new semantics is a strict subset of the current well-supported semantics, so it maintains the prior notion of well-supportedness while inducing its own stricter notion. We prefer our new notion of well-supportedness due to its similarities with logic programming.

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arXiv2024

On the Foundations of Conflict-Driven Solving for Hybrid MKNF Knowledge Bases

Hybrid MKNF Knowledge Bases (HMKNF-KBs) constitute a formalism for tightly integrated reasoning over closed-world rules and open-world ontologies. This approach allows for accurate modeling of real-world systems, which often rely on both categorical and normative reasoning. Conflict-driven solving is the leading approach for computationally hard problems, such as satisfiability (SAT) and answer set programming (ASP), in which MKNF is rooted. This paper investigates the theoretical underpinnings required for a conflict-driven solver of HMKNF-KBs. The approach defines a set of completion and loop formulas, whose satisfaction characterizes MKNF models. This forms the basis for a set of nogoods, which in turn can be used as the backbone for a conflict-driven solver.

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arXiv2023

Eliminating Unintended Stable Fixpoints for Hybrid Reasoning Systems

A wide variety of nonmonotonic semantics can be expressed as approximators defined under AFT (Approximation Fixpoint Theory). Using traditional AFT theory, it is not possible to define approximators that rely on information computed in previous iterations of stable revision. However, this information is rich for semantics that incorporate classical negation into nonmonotonic reasoning. In this work, we introduce a methodology resembling AFT that can utilize priorly computed upper bounds to more precisely capture semantics. We demonstrate our framework's applicability to hybrid MKNF (minimal knowledge and negation as failure) knowledge bases by extending the state-of-the-art approximator.

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arXiv2022

A Fixpoint Characterization of Three-Valued Disjunctive Hybrid MKNF Knowledge Bases

The logic of hybrid MKNF (minimal knowledge and negation as failure) is a powerful knowledge representation language that elegantly pairs ASP (answer set programming) with ontologies. Disjunctive rules are a desirable extension to normal rule-based reasoning and typically semantic frameworks designed for normal knowledge bases need substantial restructuring to support disjunctive rules. Alternatively, one may lift characterizations of normal rules to support disjunctive rules by inducing a collection of normal knowledge bases, each with the same body and a single atom in its head. In this work, we refer to a set of such normal knowledge bases as a head-cut of a disjunctive knowledge base. The question arises as to whether the semantics of disjunctive hybrid MKNF knowledge bases can be characterized using fixpoint constructions with head-cuts. Earlier, we have shown that head-cuts can be paired with fixpoint operators to capture the two-valued MKNF models of disjunctive hybrid MKNF knowledge bases. Three-valued semantics extends two-valued semantics with the ability to express partial information. In this work, we present a fixpoint construction that leverages head-cuts using an operator that iteratively captures three-valued models of hybrid MKNF knowledge bases with disjunctive rules. This characterization also captures partial stable models of disjunctive logic programs since a program can be expressed as a disjunctive hybrid MKNF knowledge base with an empty ontology. We elaborate on a relationship between this characterization and approximators in AFT (approximation fixpoint theory) for normal hybrid MKNF knowledge bases.

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arXiv2021

Unfounded Sets for Disjunctive Hybrid MKNF Knowledge Bases

Combining the closed-world reasoning of answer set programming (ASP) with the open-world reasoning of ontologies broadens the space of applications of reasoners. Disjunctive hybrid MKNF knowledge bases succinctly extend ASP and in some cases without increasing the complexity of reasoning tasks. However, in many cases, solver development is lagging behind. As the result, the only known method of solving disjunctive hybrid MKNF knowledge bases is based on guess-and-verify, as formulated by Motik and Rosati in their original work. A main obstacle is understanding how constraint propagation may be performed by a solver, which, in the context of ASP, centers around the computation of \textit{unfounded atoms}, the atoms that are false given a partial interpretation. In this work, we build towards improving solvers for hybrid MKNF knowledge bases with disjunctive rules: We formalize a notion of unfounded sets for these knowledge bases, identify lower complexity bounds, and demonstrate how we might integrate these developments into a solver. We discuss challenges introduced by ontologies that are not present in the development of solvers for disjunctive logic programs, which warrant some deviations from traditional definitions of unfounded sets. We compare our work with prior definitions of unfounded sets.

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arXiv2020

Restricted Chase Termination for Existential Rules: a Hierarchical Approach and Experimentation

The chase procedure for existential rules is an indispensable tool for several database applications, where its termination guarantees the decidability of these tasks. Most previous studies have focused on the skolem chase variant and its termination analysis. It is known that the restricted chase variant is a more powerful tool in termination analysis provided a database is given. But all-instance termination presents a challenge since the critical database and similar techniques do not work. In this paper, we develop a novel technique to characterize the activeness of all possible cycles of a certain length for the restricted chase, which leads to the formulation of a parameterized class of the finite restricted chase, called $k$-$\mathsf{safe}(Φ)$. This approach applies to any class of finite skolem chase identified with a condition of acyclicity. More generally, we show that the approach can be applied to the hierarchy of bounded rule sets previously only defined for the skolem chase. Experiments on a collection of ontologies from the web show the applicability of the proposed methods on real-world ontologies. Under consideration in Theory and Practice of Logic Programming (TPLP).

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arXiv2019

Towards Universal Languages for Tractable Ontology Mediated Query Answering

An ontology language for ontology mediated query answering (OMQA-language) is universal for a family of OMQA-languages if it is the most expressive one among this family. In this paper, we focus on three families of tractable OMQA-languages, including first-order rewritable languages and languages whose data complexity of the query answering is in AC0 or PTIME. On the negative side, we prove that there is, in general, no universal language for each of these families of languages. On the positive side, we propose a novel property, the locality, to approximate the first-order rewritability, and show that there exists a language of disjunctive embedded dependencies that is universal for the family of OMQA-languages with locality. All of these results apply to OMQA with query languages such as conjunctive queries, unions of conjunctive queries and acyclic conjunctive queries.

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arXiv2019

Mutex Graphs and Multicliques: Reducing Grounding Size for Planning

We present an approach to representing large sets of mutual exclusions, also known as mutexes or mutex constraints. These are the types of constraints that specify the exclusion of some properties, events, processes, and so on. They are ubiquitous in many areas of applications. The size of these constraints for a given problem can be overwhelming enough to present a bottleneck for the solving efficiency of the underlying solver. In this paper, we propose a novel graph-theoretic technique based on multicliques for a compact representation of mutex constraints and apply it to domain-independent planning in ASP. As computing a minimum multiclique covering from a mutex graph is NP-hard, we propose an efficient approximation algorithm for multiclique covering and show experimentally that it generates substantially smaller grounding size for mutex constraints in ASP than the previously known work in SAT.

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arXiv2019

Domain-Independent Cost-Optimal Planning in ASP

We investigate the problem of cost-optimal planning in ASP. Current ASP planners can be trivially extended to a cost-optimal one by adding weak constraints, but only for a given makespan (number of steps). It is desirable to have a planner that guarantees global optimality. In this paper, we present two approaches to addressing this problem. First, we show how to engineer a cost-optimal planner composed of two ASP programs running in parallel. Using lessons learned from this, we then develop an entirely new approach to cost-optimal planning, stepless planning, which is completely free of makespan. Experiments to compare the two approaches with the only known cost-optimal planner in SAT reveal good potentials for stepless planning in ASP. The paper is under consideration for acceptance in TPLP.

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arXiv2019

Characterization of Glue Variables in CDCL SAT Solving

A state-of-the-art criterion to evaluate the importance of a given learned clause is called Literal Block Distance (LBD) score. It measures the number of distinct decision levels in a given learned clause. The lower the LBD score of a learned clause, the better is its quality. The learned clauses with LBD score of 2, called glue clauses, are known to possess high pruning power which are never deleted from the clause databases of the modern CDCL SAT solvers. In this work, we relate glue clauses to decision variables. We call the variables that appeared in at least one glue clause up to the current search state Glue Variables. We first show experimentally, by running the state-of-the-art CDCL SAT solver MapleLCMDist on benchmarks from SAT Competition-2017 and 2018, that branching decisions with glue variables are categorically more inference and conflict efficient than nonglue variables. Based on this observation, we develop a structure aware CDCL variable bumping scheme, which bumps the activity score of a glue variable based on its appearance count in the glue clauses that are learned so far by the search. Empirical evaluation shows effectiveness of the new method over the main track instances from SAT Competition 2017 and 2018.

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arXiv2017

Well-Founded Operators for Normal Hybrid MKNF Knowledge Bases

Hybrid MKNF knowledge bases have been considered one of the dominant approaches to combining open world ontology languages with closed world rule-based languages. Currently, the only known inference methods are based on the approach of guess-and-verify, while most modern SAT/ASP solvers are built under the DPLL architecture. The central impediment here is that it is not clear what constitutes a constraint propagator, a key component employed in any DPLL-based solver. In this paper, we address this problem by formulating the notion of unfounded sets for nondisjunctive hybrid MKNF knowledge bases, based on which we propose and study two new well-founded operators. We show that by employing a well-founded operator as a constraint propagator, a sound and complete DPLL search engine can be readily defined. We compare our approach with the operator based on the alternating fixpoint construction by Knorr et al [2011] and show that, when applied to arbitrary partial partitions, the new well-founded operators not only propagate more truth values but also circumvent the non-converging behavior of the latter. In addition, we study the possibility of simplifying a given hybrid MKNF knowledge base by employing a well-founded operator, and show that, out of the two operators proposed in this paper, the weaker one can be applied for this purpose and the stronger one cannot. These observations are useful in implementing a grounder for hybrid MKNF knowledge bases, which can be applied before the computation of MKNF models. The paper is under consideration for acceptance in TPLP.

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arXiv2016

Expressive Completeness of Existential Rule Languages for Ontology-based Query Answering

Existential rules, also known as data dependencies in Databases, have been recently rediscovered as a promising family of languages for Ontology-based Query Answering. In this paper, we prove that disjunctive embedded dependencies exactly capture the class of recursively enumerable ontologies in Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness result does not rely on any built-in linear order on the database. To establish the expressive completeness, we introduce a novel semantic definition for OCQA ontologies. We also show that neither the class of disjunctive tuple-generating dependencies nor the class of embedded dependencies is expressively complete for recursively enumerable OCQA ontologies.

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arXiv2015

Existential Rule Languages with Finite Chase: Complexity and Expressiveness

Finite chase, or alternatively chase termination, is an important condition to ensure the decidability of existential rule languages. In the past few years, a number of rule languages with finite chase have been studied. In this work, we propose a novel approach for classifying the rule languages with finite chase. Using this approach, a family of decidable rule languages, which extend the existing languages with the finite chase property, are naturally defined. We then study the complexity of these languages. Although all of them are tractable for data complexity, we show that their combined complexity can be arbitrarily high. Furthermore, we prove that all the rule languages with finite chase that extend the weakly acyclic language are of the same expressiveness as the weakly acyclic one, while rule languages with higher combined complexity are in general more succinct than those with lower combined complexity.

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arXiv2014

A Well-Founded Semantics for FOL-Programs

An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with description logics. In this paper, we define a well-founded semantics for FOL-programs based on a new notion of unfounded sets on consistent as well as inconsistent sets of literals, and study some of its properties. The semantics is defined for all FOL-programs, including those where it is necessary to represent inconsistencies explicitly. The semantics supports a form of combined reasoning by rules under closed world as well as open world assumptions, and it is a generalization of the standard well-founded semantics for normal logic programs. We also show that the well-founded semantics defined here approximates the well-supported answer set semantics for normal DL programs.

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arXiv2011

Embedding Description Logic Programs into Default Logic

Description logic programs (dl-programs) under the answer set semantics formulated by Eiter {\em et al.} have been considered as a prominent formalism for integrating rules and ontology knowledge bases. A question of interest has been whether dl-programs can be captured in a general formalism of nonmonotonic logic. In this paper, we study the possibility of embedding dl-programs into default logic. We show that dl-programs under the strong and weak answer set semantics can be embedded in default logic by combining two translations, one of which eliminates the constraint operator from nonmonotonic dl-atoms and the other translates a dl-program into a default theory. For dl-programs without nonmonotonic dl-atoms but with the negation-as-failure operator, our embedding is polynomial, faithful, and modular. In addition, our default logic encoding can be extended in a simple way to capture recently proposed weakly well-supported answer set semantics, for arbitrary dl-programs. These results reinforce the argument that default logic can serve as a fruitful foundation for query-based approaches to integrating ontology and rules. With its simple syntax and intuitive semantics, plus available computational results, default logic can be considered an attractive approach to integration of ontology and rules.

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arXiv2011

Relating Weight Constraint and Aggregate Programs: Semantics and Representation

Weight constraint and aggregate programs are among the most widely used logic programs with constraints. In this paper, we relate the semantics of these two classes of programs, namely the stable model semantics for weight constraint programs and the answer set semantics based on conditional satisfaction for aggregate programs. Both classes of programs are instances of logic programs with constraints, and in particular, the answer set semantics for aggregate programs can be applied to weight constraint programs. We show that the two semantics are closely related. First, we show that for a broad class of weight constraint programs, called strongly satisfiable programs, the two semantics coincide. When they disagree, a stable model admitted by the stable model semantics may be circularly justified. We show that the gap between the two semantics can be closed by transforming a weight constraint program to a strongly satisfiable one, so that no circular models may be generated under the current implementation of the stable model semantics. We further demonstrate the close relationship between the two semantics by formulating a transformation from weight constraint programs to logic programs with nested expressions which preserves the answer set semantics. Our study on the semantics leads to an investigation of a methodological issue, namely the possibility of compact representation of aggregate programs by weight constraint programs. We show that almost all standard aggregates can be encoded by weight constraints compactly. This makes it possible to compute the answer sets of aggregate programs using the ASP solvers for weight constraint programs. This approach is compared experimentally with the ones where aggregates are handled more explicitly, which show that the weight constraint encoding of aggregates enables a competitive approach to answer set computation for aggregate programs.

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arXiv2010

Loop Formulas for Description Logic Programs

Description Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the {\em canonical answer set semantics}, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.

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arXiv2009

Characterizations of Stable Model Semantics for Logic Programs with Arbitrary Constraint Atoms

This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond-Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al., which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.

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