Applications of Preferences using Answer Set Programming

Schlipf proved that the Stable Logic Programming solves all NP decision problems. We extend Schlipf's result to all search problems in the class NP.

Theory and Practice of Logic Programming, 2011

Preference handling and optimization are indispensable means for addressing non-trivial applications in Answer Set Programming (ASP). However, their implementation becomes difficult whenever they bring about a significant increase in computational complexity. As a consequence, existing ASP systems do not offer complex optimization capacities, supporting, for instance, inclusion-based minimization or Pareto efficiency. Rather, such complex criteria are typically addressed by resorting to dedicated modeling techniques, like saturation. Unlike the ease of common ASP modeling, however, these techniques are rather involved and hardly usable by ASP laymen. We address this problem by developing a general implementation technique by means of meta-programming, thus reusing existing ASP systems to capture various forms of qualitative preferences among answer sets. In this way, complex preferences and optimization capacities become readily available for ASP applications. * Affiliated with Simon Fraser University, Canada, and Griffith University, Australia. the form ⋄ w J for priority levels J, weights w, and ⋄ ∈ {≤, ⊆, }, an answer set Y of Π dominates an answer set X of Π wrt M if there are a priority level J and a weight w such that

2011

We elaborate upon new strategies and heuristics for solving multi-criteria optimization problems via Answer Set Programming (ASP). In particular, we conceive a new solving algorithm, based on conflict-driven learning, allowing for non-uniform descents during optimization. We apply these techniques to solve realistic Linux package configuration problems. To this end, we describe the Linux package configuration tool aspcud and compare its performance with systems pursuing alternative approaches.

2004

Ordered Choice Logic Programming (OCLP) allows for dynamic preference-based decision-making with multiple alternatives without the need for any form of negation. This complete absence of negation does not weaken the language as both forms (classical and as-failure) can be intuitively simulated in the language and eliminated using a simple pre-processor, making it also an easy language for users less familiar with logic programming.

… Engineering for Answer …, 2009

Over the last ten years, answer set programming (ASP) has grown from a pure theoretical knowledge representation and reasoning formalism to a computational approach with a very strong formal backing. At present, ASP is seen as the computational embodiment of non-monotonic reasoning incorporating techniques of databases, knowledge representation, logic and constraint programming. ASP has become an appealing tool for knowledge representation and reasoning and thanks to the increasing efficiency of the implementations of ASP solvers, the field has now started to tackle many industrially-relevant applications.

2003

Abstract. Ordered Choice Logic Programming (OCLP) allows for preferencebased decision-making with multiple alternatives without the burden of any form of negation. This complete absence of negation does not weaken the language as both forms (classical and as-failure) can be intuitively simulated in the language. The semantics of the language is based on the preference between alternatives, yielding both a skeptical and a credulous approach.

Answer Set Programming, 2001

We are interested in semantical underpinnings for existing ap- proaches to preference handling in extended logic program- ming (within the framework of answer set programming). As a starting point, we explore three different approaches that have been recently proposed in the literature. Because these approaches use rather different formal means, we furnish a series of uniform characterizations that allow us

This paper describes a doctoral research in three areas: Hybrid ASP -an extension of Answer Set Programming for reasoning about dynamical systems, an extension of Set Constraint atoms for reasoning about preferences, computing stable models of logic programs using Metropolis type algorithms. The paper discusses a possible application of all three areas to the problem of maximizing total expected reward.

Theory and Practice of Logic Programming, 2006

We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a "best" answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure, disjunction and some other formalisms such as logic programs with ordered disjunction. The approach is shown to be useful in several application areas, e.g. repairing database, where minimal repairs correspond to preferred answer sets. 5 of X that are not ordinary literals, i.e. X − = {l | not l ∈ X}. We say that X is consistent iff the set of ordinary literals ¬X − ∪ (X \not X − ) is consistent.

The Journal of Logic and Algebraic Programming, 2008

Preference logic programming (PLP) is an extension of logic programming for declaratively specifying problems requiring optimization or comparison and selection among alternative solutions to a query. PLP essentially separates the programming of a problem itself from the criteria specification of its solution selection. In this paper we present a declarative method for specifying preference logic programs. The method introduces a precise formalization for the syntax and semantics of PLP. The syntax of a preference logic program contains two disjoint sets of definite clauses, separating a core program specifying a general computational problem from its preference rules for optimization; the semantics of PLP is given based on the Herbrand model and fixed point theory, where how preferences affects the least Herbrand model of a logic program is interpreted as a sequence of meta-level mapping operations. In addition, we present an operational semantics based on a new resolution strategy and a memoized recursive algorithm for computing strictly stratified logic programs with well-formed preferences, and further show that the operational semantics of such a preference logic program is consistent to its declarative semantics.