31,829 research outputs found
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
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
Characterizing and Extending Answer Set Semantics using Possibility Theory
Answer Set Programming (ASP) is a popular framework for modeling
combinatorial problems. However, ASP cannot easily be used for reasoning about
uncertain information. Possibilistic ASP (PASP) is an extension of ASP that
combines possibilistic logic and ASP. In PASP a weight is associated with each
rule, where this weight is interpreted as the certainty with which the
conclusion can be established when the body is known to hold. As such, it
allows us to model and reason about uncertain information in an intuitive way.
In this paper we present new semantics for PASP, in which rules are interpreted
as constraints on possibility distributions. Special models of these
constraints are then identified as possibilistic answer sets. In addition,
since ASP is a special case of PASP in which all the rules are entirely
certain, we obtain a new characterization of ASP in terms of constraints on
possibility distributions. This allows us to uncover a new form of disjunction,
called weak disjunction, that has not been previously considered in the
literature. In addition to introducing and motivating the semantics of weak
disjunction, we also pinpoint its computational complexity. In particular,
while the complexity of most reasoning tasks coincides with standard
disjunctive ASP, we find that brave reasoning for programs with weak
disjunctions is easier.Comment: 39 pages and 16 pages appendix with proofs. This article has been
accepted for publication in Theory and Practice of Logic Programming,
Copyright Cambridge University Pres
Complexity of fuzzy answer set programming under Ćukasiewicz semantics
Fuzzy answer set programming (FASP) is a generalization of answer set programming (ASP) in which propositions are allowed to be graded. Little is known about the computational complexity of FASP and almost no techniques are available to compute the answer sets of a FASP program. In this paper, we analyze the computational complexity of FASP under Ćukasiewicz semantics. In particular we show that the complexity of the main reasoning tasks is located at the first level of the polynomial hierarchy, even for disjunctive FASP programs for which reasoning is classically located at the second level. Moreover, we show a reduction from reasoning with such FASP programs to bilevel linear programming, thus opening the door to practical applications. For definite FASP programs we can show P-membership. Surprisingly, when allowing disjunctions to occur in the body of rules â a syntactic generalization which does not affect the expressivity of ASP in the classical case â the picture changes drastically. In particular, reasoning tasks are then located at the second level of the polynomial hierarchy, while for simple FASP programs, we can only show that the unique answer set can be found in pseudo-polynomial time. Moreover, the connection to an existing open problem about integer equations suggests that the problem of fully characterizing the complexity of FASP in this more general setting is not likely to have an easy solution
Communicating answer set programs
Answer set programming i s a form of declarative programming that has proven very successful in succinctly formulating and solving complex problems. Although mechanisms for representing and reasoning with the combined answer set programs of multiple agents have already been proposed, the actual gain in expressivity when adding communication has not been thoroughly studied. We show that allowing simple programs to talk to each other results in the same expressivity as adding negation-as-failure. Furthermore, we show that the ability to focus on one program in a network of simple programs results in the same expressivity as adding disjunction in the head of the rules
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
The DLV System for Knowledge Representation and Reasoning
This paper presents the DLV system, which is widely considered the
state-of-the-art implementation of disjunctive logic programming, and addresses
several aspects. As for problem solving, we provide a formal definition of its
kernel language, function-free disjunctive logic programs (also known as
disjunctive datalog), extended by weak constraints, which are a powerful tool
to express optimization problems. We then illustrate the usage of DLV as a tool
for knowledge representation and reasoning, describing a new declarative
programming methodology which allows one to encode complex problems (up to
-complete problems) in a declarative fashion. On the foundational
side, we provide a detailed analysis of the computational complexity of the
language of DLV, and by deriving new complexity results we chart a complete
picture of the complexity of this language and important fragments thereof.
Furthermore, we illustrate the general architecture of the DLV system which
has been influenced by these results. As for applications, we overview
application front-ends which have been developed on top of DLV to solve
specific knowledge representation tasks, and we briefly describe the main
international projects investigating the potential of the system for industrial
exploitation. Finally, we report about thorough experimentation and
benchmarking, which has been carried out to assess the efficiency of the
system. The experimental results confirm the solidity of DLV and highlight its
potential for emerging application areas like knowledge management and
information integration.Comment: 56 pages, 9 figures, 6 table
- âŠ