112,437 research outputs found
Normal forms for Answer Sets Programming
Normal forms for logic programs under stable/answer set semantics are
introduced. We argue that these forms can simplify the study of program
properties, mainly consistency. The first normal form, called the {\em kernel}
of the program, is useful for studying existence and number of answer sets. A
kernel program is composed of the atoms which are undefined in the Well-founded
semantics, which are those that directly affect the existence of answer sets.
The body of rules is composed of negative literals only. Thus, the kernel form
tends to be significantly more compact than other formulations. Also, it is
possible to check consistency of kernel programs in terms of colorings of the
Extended Dependency Graph program representation which we previously developed.
The second normal form is called {\em 3-kernel.} A 3-kernel program is composed
of the atoms which are undefined in the Well-founded semantics. Rules in
3-kernel programs have at most two conditions, and each rule either belongs to
a cycle, or defines a connection between cycles. 3-kernel programs may have
positive conditions. The 3-kernel normal form is very useful for the static
analysis of program consistency, i.e., the syntactic characterization of
existence of answer sets. This result can be obtained thanks to a novel
graph-like representation of programs, called Cycle Graph which presented in
the companion article \cite{Cos04b}.Comment: 15 pages, To appear in Theory and Practice of Logic Programming
(TPLP
Towards the implementation of a preference-and uncertain-aware solver using answer set programming
Logic programs with possibilistic ordered disjunction (or LPPODs) are a recently defined logic-programming framework based on logic programs with ordered disjunction and possibilistic logic. The framework inherits the properties of such formalisms and merging them, it supports a reasoning which is nonmonotonic, preference-and uncertain-aware. The LPPODs syntax allows to specify 1) preferences in a qualitative way, and 2) necessity values about the certainty of program clauses. As a result at semantic level, preferences and necessity values can be used to specify an order among program solutions. This class of program therefore fits well in the representation of decision problems where a best option has to be chosen taking into account both preferences and necessity measures about information. In this paper we study the computation and the complexity of the LPPODs semantics and we describe the algorithm for its implementation following on Answer Set Programming approach. We describe some decision scenarios where the solver can be used to choose the best solutions by checking whether an outcome is possibilistically preferred over another considering preferences and uncertainty at the same time.Postprint (published version
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,
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