4,945 research outputs found
On the Relative Expressiveness of Argumentation Frameworks, Normal Logic Programs and Abstract Dialectical Frameworks
We analyse the expressiveness of the two-valued semantics of abstract
argumentation frameworks, normal logic programs and abstract dialectical
frameworks. By expressiveness we mean the ability to encode a desired set of
two-valued interpretations over a given propositional signature using only
atoms from that signature. While the computational complexity of the two-valued
model existence problem for all these languages is (almost) the same, we show
that the languages form a neat hierarchy with respect to their expressiveness.Comment: Proceedings of the 15th International Workshop on Non-Monotonic
Reasoning (NMR 2014
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
Disjunctive ASP with Functions: Decidable Queries and Effective Computation
Querying over disjunctive ASP with functions is a highly undecidable task in
general. In this paper we focus on disjunctive logic programs with stratified
negation and functions under the stable model semantics (ASP^{fs}). We show
that query answering in this setting is decidable, if the query is finitely
recursive (ASP^{fs}_{fr}). Our proof yields also an effective method for query
evaluation. It is done by extending the magic set technique to ASP^{fs}_{fr}.
We show that the magic-set rewritten program is query equivalent to the
original one (under both brave and cautious reasoning). Moreover, we prove that
the rewritten program is also finitely ground, implying that it is decidable.
Importantly, finitely ground programs are evaluable using existing ASP solvers,
making the class of ASP^{fs}_{fr} queries usable in practice.Comment: 16 pages, 1 figur
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
Bounded Refinement Types
We present a notion of bounded quantification for refinement types and show
how it expands the expressiveness of refinement typing by using it to develop
typed combinators for: (1) relational algebra and safe database access, (2)
Floyd-Hoare logic within a state transformer monad equipped with combinators
for branching and looping, and (3) using the above to implement a refined IO
monad that tracks capabilities and resource usage. This leap in expressiveness
comes via a translation to "ghost" functions, which lets us retain the
automated and decidable SMT based checking and inference that makes refinement
typing effective in practice.Comment: 14 pages, International Conference on Functional Programming, ICFP
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