90,484 research outputs found
Comprehending nulls
The Nested Relational Calculus (NRC) has been an influential high-level query
language, providing power and flexibility while still allowing translation to
standard SQL queries. It has also been used as a basis for language-integrated
query in programming languages such as F#, Scala, and Links. However, SQL's
treatment of incomplete information, using nulls and three-valued logic, is not
compatible with `standard' NRC based on two-valued logic. Nulls are widely used
in practice for incomplete data, but the question of how to accommodate
SQL-style nulls and incomplete information in NRC, or integrate such queries
into a typed programming language, appears not to have been studied thoroughly.
In this paper we consider two approaches: an explicit approach in which option
types are used to represent (possibly) nullable primitive types, and an
implicit approach in which types are treated as possibly-null by default. We
give translations relating the implicit and explicit approaches, discuss
handling nulls in language integration, and sketch extensions of normalization
and conservativity results
Efficient paraconsistent reasoning with rules and ontologies for the semantic web
Ontologies formalized by means of Description Logics (DLs) and rules in the form of Logic Programs (LPs) are two prominent formalisms in the field of Knowledge Representation and Reasoning. While DLs adhere to the OpenWorld Assumption and are suited for taxonomic reasoning, LPs implement reasoning under the Closed World Assumption, so that default knowledge can be expressed. However, for many applications it is useful to have a means that allows reasoning over an open domain and expressing rules with exceptions at the same time. Hybrid MKNF knowledge bases make such a means available by formalizing DLs and LPs in a common logic, the Logic of Minimal Knowledge and Negation as Failure (MKNF).
Since rules and ontologies are used in open environments such as the Semantic Web,
inconsistencies cannot always be avoided. This poses a problem due to the Principle of Explosion, which holds in classical logics. Paraconsistent Logics offer a solution to this issue by assigning meaningful models even to contradictory sets of formulas. Consequently, paraconsistent semantics for DLs and LPs have been investigated intensively. Our goal is to apply the paraconsistent approach to the combination of DLs and LPs in hybrid MKNF knowledge bases.
In this thesis, a new six-valued semantics for hybrid MKNF knowledge bases is introduced, extending the three-valued approach by Knorr et al., which is based on the wellfounded semantics for logic programs. Additionally, a procedural way of computing paraconsistent well-founded models for hybrid MKNF knowledge bases by means of an alternating fixpoint construction is presented and it is proven that the algorithm is sound and complete w.r.t. the model-theoretic characterization of the semantics. Moreover, it is shown that the new semantics is faithful w.r.t. well-studied paraconsistent semantics for DLs and LPs, respectively, and maintains the efficiency of the approach it extends
Lazy Model Expansion: Interleaving Grounding with Search
Finding satisfying assignments for the variables involved in a set of
constraints can be cast as a (bounded) model generation problem: search for
(bounded) models of a theory in some logic. The state-of-the-art approach for
bounded model generation for rich knowledge representation languages, like ASP,
FO(.) and Zinc, is ground-and-solve: reduce the theory to a ground or
propositional one and apply a search algorithm to the resulting theory.
An important bottleneck is the blowup of the size of the theory caused by the
reduction phase. Lazily grounding the theory during search is a way to overcome
this bottleneck. We present a theoretical framework and an implementation in
the context of the FO(.) knowledge representation language. Instead of
grounding all parts of a theory, justifications are derived for some parts of
it. Given a partial assignment for the grounded part of the theory and valid
justifications for the formulas of the non-grounded part, the justifications
provide a recipe to construct a complete assignment that satisfies the
non-grounded part. When a justification for a particular formula becomes
invalid during search, a new one is derived; if that fails, the formula is
split in a part to be grounded and a part that can be justified.
The theoretical framework captures existing approaches for tackling the
grounding bottleneck such as lazy clause generation and grounding-on-the-fly,
and presents a generalization of the 2-watched literal scheme. We present an
algorithm for lazy model expansion and integrate it in a model generator for
FO(ID), a language extending first-order logic with inductive definitions. The
algorithm is implemented as part of the state-of-the-art FO(ID) Knowledge-Base
System IDP. Experimental results illustrate the power and generality of the
approach
A Program-Level Approach to Revising Logic Programs under the Answer Set Semantics
An approach to the revision of logic programs under the answer set semantics
is presented. For programs P and Q, the goal is to determine the answer sets
that correspond to the revision of P by Q, denoted P * Q. A fundamental
principle of classical (AGM) revision, and the one that guides the approach
here, is the success postulate. In AGM revision, this stipulates that A is in K
* A. By analogy with the success postulate, for programs P and Q, this means
that the answer sets of Q will in some sense be contained in those of P * Q.
The essential idea is that for P * Q, a three-valued answer set for Q,
consisting of positive and negative literals, is first determined. The positive
literals constitute a regular answer set, while the negated literals make up a
minimal set of naf literals required to produce the answer set from Q. These
literals are propagated to the program P, along with those rules of Q that are
not decided by these literals. The approach differs from work in update logic
programs in two main respects. First, we ensure that the revising logic program
has higher priority, and so we satisfy the success postulate; second, for the
preference implicit in a revision P * Q, the program Q as a whole takes
precedence over P, unlike update logic programs, since answer sets of Q are
propagated to P. We show that a core group of the AGM postulates are satisfied,
as are the postulates that have been proposed for update logic programs
- …