Preferential Default Reasoning on the Semantic Web

Proc. of APPIA-GULP-PRODE Joint …, 2003

The Semantic Web (SW) can be seen as abstract representation and exchange of data and metadata. Metadata is given in terms of data mark-up and reference to shared, Web-accessible ontologies. Several interesting languages are now available for the Semantic Web. They exploit XML allowing data/metadata communication, yet are endowed with a logical semantics. Such languages allow compact descriptions by means of inheritance mechanisms that permit one to describe an object as belonging to one or more classes whose hierarchy is already described on the Web. With few exceptions, SW logical languages are designed to be monotonic, thus they cannot employ the closed-world assumption i) to make object description compact and most importantly ii) to prevent large ontologies from admitting inconsistency resulting from multiple inheritance. We address these problems by proposing a version of Local Closed-World Assumption that fits SW purposes. Its extent is itself the subject of negotiation between communicating agents. In this light, we give a new default semantics to RDF type inheritance primitives and show that Answer Set Programming seems a promising tool for the automation of consistency maintenance over Semantic Web annotations. This work has been supported by i) MIUR COFIN project Aggregate-and numberreasoning for computing: from decision algorithms to constraint programming with multisets, sets, and maps. and ii) the Information Society Technologies programme of the European Commission, Future and Emerging Technologies under the IST-2001-37004 WASP and IST-2001-33058 PANDA projects.

Computational Intelligence, 1994

Default logic has been introduced for handling reasoning with incomplete knowledge. It has been widely studied, and various definitions have been proposed for it. Most of the variants have been defined by means of fixed points of some operator. We propose here another approach, which is based on a study of the way in which general rules with exceptions, used in a default reasoning process, can contradict one another. We then isolate sets of noncontradicting rules, as large as possible in order to exploit as much information as possible, and construct, for each of these sets of rules, the set of conclusions that can be deduced from it. We show that our framework encompasses most of the existing variants of default logic, allowing those variants to be compared from a knowledge representation point of view. Our approach also enables us to provide an operational definition of extensions in some interesting cases. Proof-theoretical and semantical aspects are investigated.

1995

Terminological Logics (TLs) are knowledge representation formalisms of considerable applicative interest, as they are speci cally oriented to the vast class of application domains that are describable by means of taxonomic organizations of complex objects. Although the eld of TLs has lately been an active area of investigation, only few researchers have addressed the problem of extending these logics with the ability to perform default reasoning. Such extensions would prove of paramount applicative value, as many application domains may be formalized by means of monotonic TLs only at the price of oversimpli cation. In this paper we show how we can e ectively integrate terminological reasoning and default reasoning, yielding a terminological default logic. The kind of default reasoning we embed in our TL is reminiscent of Reiter's Default Logic, but overcomes some of its drawbacks by subscribing to the \implicit" handling of exceptions typical of the Multiple Inheritance Networks with Exceptions proposed by Touretzky and others.

1991

A class of default reasoning systems based on the notion of "model-preference" have recently been proposed by Selman and Kautz. These systems are similar in spirit to Shoham's "preferential" logics; however, unlike the latter, they are not generalpurpose reasoning tools, but are specially designed for the task of knowledge base vivification, i.e. the generation of a complete, vivid knowledge base from an incomplete one and a set of default implications. Vivid knowledge bases are "pictorial-like" representations of the domain of discourse, and reasoning on them is provably efficient. Research on model-preference systems attempts to define systems that be at the same time expressively powerful (thus allowing the representation of rich forms of default and categorical knowledge), computationally tractable (thus allowing vivid knowledge bases to be generated in polynomial time) and semantically well-founded. In this paper we review the current state of research on model-preference default systems, and discuss some open problems relating either to their epistemological adequacy or to their computational complexity.

Artificial Intelligence, 2000

We address the problem of reasoning about preferences among properties (outcomes, desiderata, etc.) in Reiter's default logic. Preferences are expressed using an ordered default theory, consisting of default rules, world knowledge, and an ordering, reflecting preference, on the default rules. In contrast with previous work in the area, we do not rely on prioritised versions of default logic, but rather we transform an ordered default theory into a second, standard default theory wherein the preferences are respected, in that defaults are applied in the prescribed order. This translation is accomplished via the naming of defaults, so that reference may be made to a default rule from within a theory. In an elaboration of the approach, we allow an ordered default theory where preference information is specified within a default theory. Here one may specify preferences that hold by default, in a particular context, or give preferences among preferences. In the approach, one essentially axiomatises how different orderings interact within a theory and need not rely on metatheoretic characterisations. As well, we can immediately use existing default logic theorem provers for an implementation. From a theoretical point of view, this shows that the explicit representation of priorities among defaults adds nothing to the overall expressibility of default logic.

Lecture Notes in Computer Science, 2004

Attempto Controlled English (ACE)-a subset of English that can be unambiguously translated into first-order logic-is a knowledge representation language. To support automatic reasoning in ACE we have developed the Attempto Reasoner RACE (Reasoning in ACE). RACE proves that one ACE text is the logical consequence of another one, and gives a justification for the proof in ACE. Variations of the basic proof procedure permit query answering and consistency checking. Reasoning in RACE is supported by auxiliary first-order axioms and by evaluable functions. The current implementation of RACE is based on the model generator Satchmo.

The need to make default assumptions is frequently encountered in reasoning'about incompletely specified worlds. Inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations. It is this property which leads to the non.monotonJcity of any logic of defaults. In this paper we propose a logic for default reasoning. We then specialize our treatment to a very large class of commonly occurring defaults. For this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover. Finally, we provide criteria under which the revision of derived beliefs must be effected.

Lecture Notes in Computer Science, 2006

Ranking is an important concept to avoid empty or overfull and unordered result sets. However, such scoring can only express total orders, which restricts its usefulness when several factors influence result relevance. A more flexible way to express relevance is the notion of preferences. Users state which kind of answers they 'prefer' by adding soft constraints to their queries.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2007

Recently, the logics of minimal knowledge and negation as failure MKNF [12] was used to introduce hybrid MKNF knowledge bases [14], a powerful formalism for combining open and closed world reasoning for the Semantic Web. We present an extension based on a new three-valued framework including an alternating fixpoint, the well-founded MKNF model. This approach, the well-founded MKNF semantics, derives its name from the very close relation to the corresponding semantics known from logic programming. We show that the well-founded MKNF model is the least model among all (three-valued) MKNF models, thus soundly approximating also the two-valued MKNF models from [14]. Furthermore, its computation yields better complexity results (up to polynomial) than the original semantics where models usually have to be guessed. 9 See e.g. the W3C member submission on tractable fragments of OWL 1.

2006

We introduce conditional preference bases as a means for ranking objects in ontologies. Conditional preference bases consist of a description logic knowledge base and a finite set of variable-strength conditional preferences. They are inspired by Goldszmidt and Pearl’s approach to default reasoning from conditional knowledge bases in System Z + . We define a notion of consistency for conditional preference bases, and show how consistent conditional preference bases can be used for ranking objects in ontologies. We also provide algorithms for computing the rankings. To give evidence of the usefulness of this approach in practice, we describe an application in the area of literature search.