Strong Equivalence of Qualitative Optimization Problems

by   Wolfgang Faber, et al.
University of Calabria
TU Wien

We introduce the framework of qualitative optimization problems (or, simply, optimization problems) to represent preference theories. The formalism uses separate modules to describe the space of outcomes to be compared (the generator) and the preferences on outcomes (the selector). We consider two types of optimization problems. They differ in the way the generator, which we model by a propositional theory, is interpreted: by the standard propositional logic semantics, and by the equilibrium-model (answer-set) semantics. Under the latter interpretation of generators, optimization problems directly generalize answer-set optimization programs proposed previously. We study strong equivalence of optimization problems, which guarantees their interchangeability within any larger context. We characterize several versions of strong equivalence obtained by restricting the class of optimization problems that can be used as extensions and establish the complexity of associated reasoning tasks. Understanding strong equivalence is essential for modular representation of optimization problems and rewriting techniques to simplify them without changing their inherent properties.


page 1

page 2

page 3

page 4


Algebraic characterizations of least model and uniform equivalence of propositional Krom logic programs

This research note provides algebraic characterizations of equivalence w...

Characterising equilibrium logic and nested logic programs: Reductions and complexity

Equilibrium logic is an approach to nonmonotonic reasoning that extends ...

Strong Equivalence for LPMLN Programs

LPMLN is a probabilistic extension of answer set programs with the weigh...

Strong equivalence for LP^MLN programs

Strong equivalence is a well-studied and important concept in answer set...

Geometric optimization using nonlinear rotation-invariant coordinates

Geometric optimization problems are at the core of many applications in ...

Here and There with Arithmetic

In the theory of answer set programming, two groups of rules are called ...

Logical Probability Preferences

We present a unified logical framework for representing and reasoning ab...

Please sign up or login with your details

Forgot password? Click here to reset