4,393 research outputs found
Towards Closed World Reasoning in Dynamic Open Worlds (Extended Version)
The need for integration of ontologies with nonmonotonic rules has been
gaining importance in a number of areas, such as the Semantic Web. A number of
researchers addressed this problem by proposing a unified semantics for hybrid
knowledge bases composed of both an ontology (expressed in a fragment of
first-order logic) and nonmonotonic rules. These semantics have matured over
the years, but only provide solutions for the static case when knowledge does
not need to evolve. In this paper we take a first step towards addressing the
dynamics of hybrid knowledge bases. We focus on knowledge updates and,
considering the state of the art of belief update, ontology update and rule
update, we show that current solutions are only partial and difficult to
combine. Then we extend the existing work on ABox updates with rules, provide a
semantics for such evolving hybrid knowledge bases and study its basic
properties. To the best of our knowledge, this is the first time that an update
operator is proposed for hybrid knowledge bases.Comment: 40 pages; an extended version of the article published in Theory and
Practice of Logic Programming, 10 (4-6): 547 - 564, July. Copyright 2010
Cambridge University Pres
Hyper Hoare Logic: (Dis-)Proving Program Hyperproperties (extended version)
Hoare logics are proof systems that allow one to formally establish
properties of computer programs. Traditional Hoare logics prove properties of
individual program executions (so-called trace properties, such as functional
correctness). Hoare logic has been generalized to prove also properties of
multiple executions of a program (so-called hyperproperties, such as
determinism or non-interference). These program logics prove the absence of
(bad combinations of) executions. On the other hand, program logics similar to
Hoare logic have been proposed to disprove program properties (e.g.,
Incorrectness Logic), by proving the existence of (bad combinations of)
executions. All of these logics have in common that they specify program
properties using assertions over a fixed number of states, for instance, a
single pre- and post-state for functional properties or pairs of pre- and
post-states for non-interference.
In this paper, we present Hyper Hoare Logic, a generalization of Hoare logic
that lifts assertions to properties of arbitrary sets of states. The resulting
logic is simple yet expressive: its judgments can express arbitrary trace- and
hyperproperties over the terminating executions of a program. By allowing
assertions to reason about sets of states, Hyper Hoare Logic can reason about
both the absence and the existence of (combinations of) executions, and,
thereby, supports both proving and disproving program (hyper-)properties within
the same logic. In fact, we prove that Hyper Hoare Logic subsumes the
properties handled by numerous existing correctness and incorrectness logics,
and can express hyperproperties that no existing Hoare logic can. We also prove
that Hyper Hoare Logic is sound and complete, and admits powerful
compositionality rules. All our technical results have been proved in
Isabelle/HOL
Disjunctive Logic Programs with Inheritance
The paper proposes a new knowledge representation language, called DLP<,
which extends disjunctive logic programming (with strong negation) by
inheritance. The addition of inheritance enhances the knowledge modeling
features of the language providing a natural representation of default
reasoning with exceptions.
A declarative model-theoretic semantics of DLP< is provided, which is shown
to generalize the Answer Set Semantics of disjunctive logic programs.
The knowledge modeling features of the language are illustrated by encoding
classical nonmonotonic problems in DLP<.
The complexity of DLP< is analyzed, proving that inheritance does not cause
any computational overhead, as reasoning in DLP< has exactly the same
complexity as reasoning in disjunctive logic programming. This is confirmed by
the existence of an efficient translation from DLP< to plain disjunctive logic
programming. Using this translation, an advanced KR system supporting the DLP<
language has been implemented on top of the DLV system and has subsequently
been integrated into DLV.Comment: 28 pages; will be published in Theory and Practice of Logic
Programmin
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