Francesco M. Donini

{\cal A}{\cal L} -log: Integrating Datalog and Description Logics

We present an integrated system for knowledge representation, calledAL -log, based on description logics and the deductive database language Datalog. AL-log embodies two subsystems, called structural and relational. The former allows for the definition of structural knowledge about classes of interest (concepts) and membership relation between objects and classes. The latter allows for the definition of relational knowledge about objects described in the structural component. The interaction between the two components is obtained by allowing constraints within Datalog clauses, thus requiring the variables in the clauses to range over the set of instances of a specified concept. We propose a method for query answering in AL-log based on constrained resolution, where the usual deduction procedure defined for Datalog is integrated with a method for reasoning on the structural knowledge.

The complexity of concept languages

Abstract A basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called a concept language (or description logic ), which is given a well-defined set-theoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform.

Decidable reasoning in terminological knowledge representation systems

Terminological Knowledge Representation Systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). The TKRS we consider in this paper is of practical interest since it goes beyond the capabilities of presently available TKRSs. First, our TKRS is equipped with a highly expressive concept, language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, it allows one to express inclusion statements between general concepts, in particular to express terminological cycles. We provide a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases based on the general technique of constraint systems.

Description logics of minimal knowledge and negation as failure

We present description logics of minimal knowledge and negation as failure (MKNF-DLs), which augment description logics with modal operators interpreted according to Lifschitzs nonmonotonic logic MKNF. We show the usefulness of MKNF-DLs for a formal characterization of a wide variety of nonmonotonic features that are both commonly available inframe-based systems, and needed in the development of practical knowledge-based applications: defaults, integrity constraints, role, and concept closure. In addition, we provide a correct and terminating calculus for query answering in a very expressive MKNF-DL.

A system for principled matchmaking in an electronic marketplace

More and more resources are becoming available on the Web, and there is a growing need for infrastructures that, based on advertised descriptions, are able to semantically match demands with supplies.We formalize general properties a matchmaker should have, then we present a matchmaking facilitator, compliant with desired properties.The system embeds a NeoClassic reasoner, whose structural subsumption algorithm has been modified to allow match categorization into potential and partial, and ranking of matches within categories. Experiments carried out show the good correspondence between users and system rankings.

An epistemic operator for description logics

Abstract Description logics (also called terminological logics, or concept languages) are fragments of first-order logic that provide a formal account of the basic features of frame-based systems. However, there are aspects of frame-based systems—such as nonmonotonic reasoning and procedural rules—that cannot be characterized in a standard first-order framework. Such features are needed for real applications, and a clear understanding of the logic underlying them is necessary for principled implementations. We show how description logics enriched with an epistemic operator can formalize such aspects. The logic obtained is a fragment of a first-order nonmonotonic modal logic. We show that the epistemic operator formalizes procedural rules, as provided in many knowledge representation systems, and enables sophisticated query formulation, including various forms of closed-world reasoning. We provide an effective procedure for answering epistemic queries posed to a knowledge base expressed in a description logic and extend this procedure in order to deal with rules. We also address the computational complexity of reasoning with the epistemic operator, identifying cases in which an appropriate use of the epistemic operator can help in decreasing the complexity of reasoning.

Deduction in Concept Languages: from Subsumption to Instance Checking

It is a common opinion that subsumption is the central reasoning task in frame-based knowledge representation languages (or concept languages). Intuitively, a concept C subsumes another concept D if the set of objects represented by C is a superset of the one represented by D. When individual objects are taken into account, the basic deduc-tive task for retrieving information from a knowledge base is instance checking, that amounts to checking whether the knowledge base implies that an individual is an instance of a given concept. In this paper, we address the question of whether instance checking can be solved by means of subsumption algorithms. We do so by considering several languages where subsumption belongs to diierent complexity classes. For such languages we present methods for the instance checking problem, provide a complexity analysis of this problem, and compare it with the subsumption problem. The main result of the paper is that instance checking is not always easily reducible to subsumption. In particular, there are cases where it is strictly harder than subsumption. This impacts on the design of reasoning algorithms for knowledge representation systems based on concept languages.

EXP TIME tableaux for ALC

Abstract The last years have seen two major advances in Knowledge Representation and Reasoning. First, many interesting problems (ranging from Semi-structured Data to Linguistics) were shown to be expressible in logics whose main deductive problems are EXPtime -complete. Second, experiments in automated reasoning have substantially broadened the meaning of “practical tractability”. Instances of realistic size for Pspace -complete problems are now within reach for implemented systems. Still, there is a gap between the reasoning services needed by the expressive logics mentioned above and those provided by the current systems. Indeed, the algorithms based on tree-automata, which are used to prove EXPtime -completeness, require exponential time and space even in simple cases. On the other hand, current algorithms based on tableau methods can take advantage of such cases, but require double exponential time in the worst case. We propose a tableau calculus for the description logic ALC for checking the satisfiability of a concept with respect to a TBox with general axioms, and transform it into the first simple tableau-based decision procedure working in single exponential time. To guarantee the ease of implementation, we also discuss the effects that optimizations (propositional backjumping, simplification, semantic branching, etc.) might have on our complexity result, and introduce a few optimizations ourselves.

Concept abduction and contraction for semantic-based discovery of matches and negotiation spaces in an e-marketplace

In this paper, we present a Description Logic approach - fully compliant with the Semantic web vision and technologies - to extended matchmaking between demands and supplies in a semantic-enabled Electronic Marketplace, which allows the semantic-based treatment of negotiable and strict requirements in the demand/supply descriptions. To this aim, we exploit two novel non-standard Description Logic inference services, Concept Contraction - which extends satisfiability - and Concept Abduction - which extends subsumption. Based on these services, we devise algorithms, which allow to find negotiation spaces and to determine the quality of a possible match, also in the presence of a distinction between strictly required and optional elements. Both the algorithms and the semantic-based approach are novel, and enable a mechanism to boost logic-based discovery and negotiation stages within an e-marketplace. A set of simple experiments confirm the validity of the approach.

Semantic matchmaking as non-monotonic reasoning: a description logic approach

Matchmaking arises when supply and demand meet in an electronic marketplace, or when agents search for a web service to perform some task, or even when recruiting agencies match curricula and job profiles. In such open environments, the objective of a matchmaking process is to discover best available offers to a given request. We address the problem of matchmaking from a knowledge representation perspective, with a formalization based on Description Logics. We devise Concept Abduction and Concept Contraction as non-monotonic inferences in Description Logics suitable for modeling matchmaking in a logical framework, and prove some related complexity results. We also present reasonable algorithms for semantic matchmaking based on the devised inferences, and prove that they obey to some commonsense properties. Finally, we report on the implementation of the proposed matchmaking framework, which has been used both as a mediator in e-marketplaces and for semantic web services discovery.