Éric Grégoire

Boosting complete techniques thanks to local search methods

In this paper, an efficient heuristic allowing one to localize inconsistent kernels in propositional knowledge‐bases is described. Then, it is shown that local search techniques can boost the performance of logically complete methods for SAT. More precisely, local search techniques can be used to guide the branching strategy of logically complete techniques like Davis and Putnams one, giving rise to significant performance improvements, in particular when addressing locally inconsistent problems. Moreover, this approach appears very competitive in the context of consistent SAT instances, too.

Logic-based approaches to information fusion

This survey covers recent contributions from the artificial intelligence research literature about logic-based information fusion. First, the main current approaches dealing with the standard propositional logic formalism are presented and compared. Then, techniques for fusing weighted belief bases are discussed. Finally, relationships between propositional information fusion and related areas such as belief revision and multi-agent negotiation are mentioned. d.

Local-search Extraction of MUSes

SAT is probably one of the most-studied constraint satisfaction problems. In this paper, a new hybrid technique based on local search is introduced in order to approximate and extract minimally unsatisfiable subformulas (in short, MUSes) of unsatisfiable SAT instances. It is based on an original counting heuristic grafted to a local search algorithm, which explores the neighborhood of the current interpretation in an original manner, making use of a critical clause concept. Intuitively, a critical clause is a falsified clause that becomes true thanks to a local search flip only when some other clauses become false at the same time. In the paper, the critical clause concept is investigated. It is shown to be the cornerstone of the efficiency of our approach, which outperforms competing ones to compute MUSes, inconsistent covers and sets of MUSes, most of the time.

Automatic extraction of functional dependencies

In this paper, a new polynomial time technique for extracting functional dependencies in Boolean formulas is proposed. It makes an original use of the well-known Boolean constraint propagation technique (BCP) in a new preprocessing approach that extracts more hidden Boolean functions and dependent variables than previously published approaches on many classes of instances.

On Approaches to Explaining Infeasibility of Sets of Boolean Clauses

These last years, the issue of locating and explaining contradictions inside sets of propositional clauses has received a renewed attention due to the emergence of very efficient SAT solvers. In case of inconsistency, many such solvers merely conclude that no solution exists or provide an upper approximation of the subset of clauses that are contradictory. However, in most application domains, only knowing that a problem does not admit any solution is not enough informative, and it is important to know which clauses are actually conflicting. In this paper, the focus is on the concept of minimally unsatisfiable subformulas (MUSes), which explain logical inconsistency in terms of minimal sets of contradictory clauses. Specifically, various recent results and computational approaches about MUSes and related concepts are discussed.

Using local search to find MSSes and MUSes

In this paper, a new complete technique to compute Maximal Satisfiable Subsets (MSSes) and Minimally Unsatisfiable Subformulas (MUSes) of sets of Boolean clauses is introduced. The approach improves the currently most efficient complete technique in several ways. It makes use of the powerful concept of critical clause and of a computationally inexpensive local search oracle to boost an exhaustive algorithm proposed by Liffiton and Sakallah. These features can allow exponential efficiency gains to be obtained. Accordingly, experimental studies show that this new approach outperforms the best current existing exhaustive ones.

Recovering and Exploiting Structural Knowledge from CNF Formulas

In this paper, a new pre-processing step is proposed in the resolution of SAT instances, that recovers and exploits structural knowledge that is hidden in the CNF. It delivers an hybrid formula made of clauses together with a set of equations of the form y = f(x1, ..., xn) where f is a standard connective operator among (?, ?, ?) and where y and xi are boolean variables of the initial SAT instance. This set of equations is then exploited to eliminate clauses and variables, while preserving satisfiability. These extraction and simplification techniques allowed us to implement a new SAT solver that proves to be the most efficient current one w.r.t. several important classes of instances.

THE LANDSCAPE OF INCONSISTENCY: A PERSPECTIVE

The focus of this introduction to this special issue is to draw a picture as comprehensive as possible about various dimensions of inconsistency. In particular, we consider: (1) levels of knowledge at which inconsistency occurs; (2) categories and morphologies of inconsistency; (3) causes of inconsistency; (4) circumstances of inconsistency; (5) persistency of inconsistency; (6) consequences of inconsistency; (7) metrics for inconsistency; (8) theories for handling inconsistency; (9) dependencies among occurrences of inconsistency; and (10) problem domains where inconsistency has been studied. The take-home message is that inconsistency is ubiquitous and handling inconsistency is consequential in our endeavors. How to manage and reason in the presence of inconsistency presents a very important issue in semantic computing, cloud computing, social computing, and many other data-rich or knowledge-rich computing systems.

MUS-based generation of arguments and counter-arguments

Most of the approaches of computational argumentation define an argument as a pair consisting of premises and a conclusion, where the latter is entailed by the former. However, the matter of computing arguments and counter-arguments remains largely unsettled. We propose here a method to compute arguments and counter-arguments in the context of propositional logic, by using the concept of a MUS (Minimally Unsatisfiable Subset). The idea relies on the fact that reduction ad absurdum is valid in propositional logic: 〈Φ,α〉 is an argument induced from a knowledge base Δ iff Φ ⋃ {¬α} is inconsistent. Therefore, if Φ ⋃ {¬α} is a MUS of Δ ⋃ {¬α} that contains ¬α then 〈Φ,α〉 is an argument from Δ. Not only do we present an algorithm that generates arguments, we also present an algorithm generating the complete argumentation tree induced by a given argument. We include a report on computational experimentations with both algorithms.

Eliminating Redundant Clauses in SAT Instances

In this paper, we investigate to which extent the elimination of a class of redundant clauses in SAT instances could improve the efficiency of modern satisfiability provers. Since testing whether a SAT instance does not contain any redundant clause is NP-complete, a logically incomplete but polynomial-time procedure to remove redundant clauses is proposed as a pre-treatment of SAT solvers. It relies on the use of the linear-time unit propagation technique and often allows for significant performance improvements of the subsequent satisfiability checking procedure for really difficult real-world instances.