45,138 research outputs found
Nominal Logic Programming
Nominal logic is an extension of first-order logic which provides a simple
foundation for formalizing and reasoning about abstract syntax modulo
consistent renaming of bound names (that is, alpha-equivalence). This article
investigates logic programming based on nominal logic. We describe some typical
nominal logic programs, and develop the model-theoretic, proof-theoretic, and
operational semantics of such programs. Besides being of interest for ensuring
the correct behavior of implementations, these results provide a rigorous
foundation for techniques for analysis and reasoning about nominal logic
programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as
of July 23, 200
A Polynomial Translation of Logic Programs with Nested Expressions into Disjunctive Logic Programs: Preliminary Report
Nested logic programs have recently been introduced in order to allow for
arbitrarily nested formulas in the heads and the bodies of logic program rules
under the answer sets semantics. Nested expressions can be formed using
conjunction, disjunction, as well as the negation as failure operator in an
unrestricted fashion. This provides a very flexible and compact framework for
knowledge representation and reasoning. Previous results show that nested logic
programs can be transformed into standard (unnested) disjunctive logic programs
in an elementary way, applying the negation as failure operator to body
literals only. This is of great practical relevance since it allows us to
evaluate nested logic programs by means of off-the-shelf disjunctive logic
programming systems, like DLV. However, it turns out that this straightforward
transformation results in an exponential blow-up in the worst-case, despite the
fact that complexity results indicate that there is a polynomial translation
among both formalisms. In this paper, we take up this challenge and provide a
polynomial translation of logic programs with nested expressions into
disjunctive logic programs. Moreover, we show that this translation is modular
and (strongly) faithful. We have implemented both the straightforward as well
as our advanced transformation; the resulting compiler serves as a front-end to
DLV and is publicly available on the Web.Comment: 10 pages; published in Proceedings of the 9th International Workshop
on Non-Monotonic Reasonin
Introducing Dynamic Behavior in Amalgamated Knowledge Bases
The problem of integrating knowledge from multiple and heterogeneous sources
is a fundamental issue in current information systems. In order to cope with
this problem, the concept of mediator has been introduced as a software
component providing intermediate services, linking data resources and
application programs, and making transparent the heterogeneity of the
underlying systems. In designing a mediator architecture, we believe that an
important aspect is the definition of a formal framework by which one is able
to model integration according to a declarative style. To this purpose, the use
of a logical approach seems very promising. Another important aspect is the
ability to model both static integration aspects, concerning query execution,
and dynamic ones, concerning data updates and their propagation among the
various data sources. Unfortunately, as far as we know, no formal proposals for
logically modeling mediator architectures both from a static and dynamic point
of view have already been developed. In this paper, we extend the framework for
amalgamated knowledge bases, presented by Subrahmanian, to deal with dynamic
aspects. The language we propose is based on the Active U-Datalog language, and
extends it with annotated logic and amalgamation concepts. We model the sources
of information and the mediator (also called supervisor) as Active U-Datalog
deductive databases, thus modeling queries, transactions, and active rules,
interpreted according to the PARK semantics. By using active rules, the system
can efficiently perform update propagation among different databases. The
result is a logical environment, integrating active and deductive rules, to
perform queries and update propagation in an heterogeneous mediated framework.Comment: Other Keywords: Deductive databases; Heterogeneous databases; Active
rules; Update
Reasoning about Minimal Belief and Negation as Failure
We investigate the problem of reasoning in the propositional fragment of
MBNF, the logic of minimal belief and negation as failure introduced by
Lifschitz, which can be considered as a unifying framework for several
nonmonotonic formalisms, including default logic, autoepistemic logic,
circumscription, epistemic queries, and logic programming. We characterize the
complexity and provide algorithms for reasoning in propositional MBNF. In
particular, we show that entailment in propositional MBNF lies at the third
level of the polynomial hierarchy, hence it is harder than reasoning in all the
above mentioned propositional formalisms for nonmonotonic reasoning. We also
prove the exact correspondence between negation as failure in MBNF and negative
introspection in Moore's autoepistemic logic
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
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