Qualitative Choice Logic Research Articles

Sequent Calculi for Choice Logics

Choice logics constitute a family of propositional logics and are used for the representation of preferences, with especially qualitative choice logic (QCL) being an established formalism with numerous applications in artificial intelligence. While computational properties and applications of choice logics have been studied in the literature, only few results are known about the proof-theoretic aspects of their use. We propose a sound and complete sequent calculus for preferred model entailment in QCL, where a formula F is entailed by a QCL-theory T if F is true in all preferred models of T. The calculus is based on labeled sequent and refutation calculi, and can be easily adapted for different purposes. For instance, using the calculus as a cornerstone, calculi for other choice logics such as conjunctive choice logic (CCL) and lexicographic choice logic (LCL) can be obtained in a straightforward way.

Choice logics and their computational properties

Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case basis, albeit they share several common features. This calls for a more general choice logic framework, with QCL and CCL as well as some of their derivatives being particular instantiations. We provide such a framework, which allows us, on the one hand, to easily define new choice logics and, on the other hand, to examine properties of different choice logics in a uniform setting. In particular, we investigate strong equivalence, a core concept in non-classical logics for understanding formula simplification, and computational complexity. Our analysis also yields new results for QCL and CCL. For example, we show that the main reasoning task regarding preferred models of choice logic formulas is Θ2P-complete for QCL and CCL, while being Δ2P-complete for a newly introduced choice logic. The complexity of preferred model entailment for choice logic theories ranges from coNP to Π2P.

Qualitative Choice Logic For Modeling Experts Recommendations of Antibiotics

Qualitative Choice Logic (QCL) is a logic-based formalism for preference handling. The logic adds to classical propositional logic a new connective called ordered disjunction (~).x~y intuitively means: if possible x, but if x is not possible then at least y. The aim of this paper is to explore QCL in healthcare domain, particularly for modeling experts reasoning for providing recommendations of antibiotics. We show that QCL is fully adapted for modeling this problem.

Value-based argumentation framework built from prioritized qualitative choice logic

Abstract The notion of preference is crucial in many fields. This justifies the development of many formalisms for preferences representation such as CP-nets, qualitative choice logic and its extensions. Preferences help to choose the best option in decision making, to compare between arguments in argumentation theory, etc. In this paper, we establish a link between a preference formalism, called Prioritized Qualitative Choice Logic (PQCL) and argumentation theory. We show that for any set of preferences expressed using PQCL (called PQCL theory), a Value-based Argumentation Framework (VAF) can be built. However, we point out some problems related to the evaluation of arguments which does not guarantee the correspondence between elements of PQCL theory and those of its associated VAF. We show that the major problem is due to the evaluation of arguments defined in existing argumentation frameworks, where an absolute status is assigned to each argument: objectively (or skeptically) accepted if it belongs to every extension, subjectively (or credulously) accepted if it is in some extensions and not in others and rejected if it does not belong to any extension. To deal with this problem, we propose to revise the evaluation of arguments in the corresponding VAF. As a result, there is a direct relationship between preferred extensions of the corresponding VAF and preferred models of a set of preferences expressed using PQCL. In addition, rank ordering the set of arguments is possible. The relationship between the two formalisms is interesting since on the one hand, it points out that one should be careful in using argumentation theory for decision making purposes or in formalizing a given problem as an argumentation framework and on the other hand, it makes it possible to use an argumentation framework for preference elicitation.

Instantiated First Order Qualitative Choice Logic for an efficient handling of alerts correlation

Intrusion Detection Systems (IDS) are necessary and important tools for monitoring information systems. However they produce a huge quantity of alerts. Alerts correlation is a process that reduces the number of alerts reported by intrusion detection systems. In this paper, we propose a new algorithm for a logical-based alerts correlation approach that integrates: security operator's knowledge and preferences. The representation and the reasoning on these knowledge and preferences are done using a new logic called Instantiated First Order Qualitative Choice Logic (IFO-QCL). Our modeling views an alert as an interpretation which allows us to have an efficient algorithm that performs the correlation process in a polynomial time. This paper also provides experimental results which are achieved on datasets issued from a real monitoring system.

An alert correlation approach based on security operator's knowledge and preferences

One of the major problems of intrusion detection concerns the large amount of alerts that intrusion detection systems (IDS) produce. Security operator who analyzes alerts and takes decisions, is often submerged by the high number of alerts to analyze. In this paper, we present a new alert correlation approach based on knowledge and preferences of security operators. This approach, which is complementary to existing ones, allows to rank-order produced alerts on the basis of a security operator knowledge about the system, used IDS and his preferences about alerts that he wants to analyze or to ignore. Our approach is based on the development of a new non-classical logic for representing preferences, called FO-MQCL (First Order - Minimal Qualitative Choice Logic). Our logic extends a fragment of the first order logic by adding a new logical connective. The general idea is to present only alerts that fully fit security operator's preferences and knowledge. And if needed, less preferred alerts can also be presented.

Logical formalisms for representing bipolar preferences

Bipolar preferences distinguish between negative preferences inducing what is acceptable by complementation and positive preferences representing what is really satisfactory. This article provides a review of the main logics for preference representation. Representing preferences in a bipolar logical way has the advantage of enabling us to reason about them, while increasing their expressive power in a cognitively meaningful way. In the article, we first focus on the possibilistic logic setting and then discuss two other logics: qualitative choice logic and penalty logic. Finally, an application of bipolar preferences querying systems is outlined. © 2008 Wiley Periodicals, Inc.

Two alternatives for handling preferences in qualitative choice logic

Reasoning about preferences is a major issue in many decision making problems. Recently, a new logic for handling preferences, called qualitative choice logic ( QCL), was presented. This logic adds to classical propositional logic a new connective, called ordered disjunction symbolized by × ⇒ . That new connective is used to express preferences between alternatives. Intuitively, if A and B are propositional formulas then A × ⇒ B means: “if possible A, but if A is impossible then at least B”. One of the important limitations of QCL is that it does not correctly deal with negated and conditional preferences. Conditional rules that involve preferences are expressed using propositional implication. However, using QCL semantics, there is no difference between such material implication “( KLM × ⇒ Air France ) ⇒ Hotel Package ” and the purely propositional formula “ ( Air France ∨ KLM ) ⇒ Hotel Package ”. Moreover, the negation in QCL misses some desirable properties from propositional calculus. This paper first proposes an extension of QCL language to universally quantified first-order logic framework. Then, we propose two new logics that correctly address QCL’ s limitations. Both of them are based on the same QCL language, but define new non-monotonic consequence relations. The first logic, called PQCL (prioritized qualitative choice logic), is particularly adapted for handling prioritized preferences, while the second one, called QCL + (positive qualitative choice logic), is appropriate for handling positive preferences. In both cases, we show that any set of preferences, can equivalently be transformed into a set of basic preferences from which efficient inferences can be applied. Lastly, we show how our logics can be applied to alert correlation.

Qualitative choice logic

Qualitative choice logic ( QCL) is a propositional logic for representing alternative, ranked options for problem solutions. The logic adds to classical propositional logic a new connective called ordered disjunction: A × → B intuitively means: if possible A, but if A is not possible then at least B. The semantics of qualitative choice logic is based on a preference relation among models. Consequences of QCL theories can be computed through a compilation to stratified knowledge bases which in turn can be compiled to classical propositional theories. We also discuss potential applications of the logic, several variants of QCL based on alternative inference relations, and their relation to existing nonmonotonic formalisms. 1 1 This is a revised and extended version of the paper that appeared in Proc. 8th Internat. Conference on Principles of Knowledge Representation and Reasoning (KR 2002), Toulouse, France, 2002, pp. 158–169.