Semiring-based constraint logic programming

Abstract

We extend the Constraint Logic Programming (CLP) formalism in order to handle semiringbased constraints. This allows us to perform in the same language both constraint solving and optimization. In fact, constraints based on semirings are able to model both classical constraint solving and more sophisticated features like uncertainty, probability, fuzziness, and optimization. We then provide this class of languages with three equivalent semantics: model-theoretic, fix-point, and proof-theoretic, in the style of classical CLP programs.

Ordering based decision making – A survey

“…The first five are preference based alternative ordering methods, and the rest three are mainly for qualitative information processing. [94] Difficult on global combination of quantitative preferences [95] CP-nets Elicitation of CP-nets from users is very intuitive [96] The complexity of reasoning with them [54,95] Borda count and other Social Choice approaches Take all the opinions into account, intuitive and easy to implement [54] Can only be used for total order, and absolute scores are usually difficult to decide [106] Cohen's method It can obtain an approximately optimal total order [106] It can only deal with preferences in total ordering [46] Wang's method Intuitive and easy to use [46] It is not expressive under situations where some alternatives can be equally ranked [107] Fuzzy ordinal linguistic approach Easy to use by manipulating directly on linguistic labels with indexes without underlying numerical approximation [32] It can only deal with totally ordered information [5] Hedge algebra Expressive for modelling the semantic ordering relation among linguistic terms [43] No further steps made into logic and information processing methods [5] Logic based method Strict theoretical foundation and direct reasoning about information without numerical approximation [111] Complexity of the theoretical results makes it somewhat difficult for non-specialist users [98] All the methods in Table 1 can deal with qualitative information except Soft constraints, but Borda's Rule, Cohen's method and Wang's method deal with qualitative information by assigning numerical score or transforming it into quantitative value. Fuzzy ordinal linguistic approach, Borda's rule and Cohen's method can only deal with totally ordered information as shown in Example 1, and Hedge algebra mainly focuses on the algebraic representation of ordinal linguistic information.…”

“…Soft constraints [93][94][95] are one of the popular methods for representing and aggregating quantitative preferences. Soft constraints were originally proposed to overcome the limitations of classical methods for constraint satisfaction problems (CSPs) under fuzzy or incomplete situations.…”

A Life Cycle for the Development of Autonomic Systems: The E-mobility Showcase

“…However, only classical constraints can be handled. So, in [11], a further extension has been proposed to also handle soft constraints. This has led to a high-level and flexible declarative programming formalism, called Soft CLP (SCLP), allowing to easily model and solve real-life problems.…”

Managing Quality of Service with Soft Constraints

“…In this model we describe how to represent a network configuration in its corresponding and-or graph, mapping network nodes to andor graph nodes and links to graph connectors. Afterwards, we propose the Soft Constraint Logic Programming (SCLP) (Bistarelli and Rossi 2001) framework as a convenient declarative programming environment in which to specify and solve such problem. In particular, we show how to represent an and-or graph as an SCLP program, and how the semantics of such a program computes the best tree in the corresponding weighted and-or graph.…”