Recursive Online Enumeration of All Minimal Unsatisfiable Subsets

In various areas of computer science, we deal with a set of constraints to be satisfied. If the constraints cannot be satisfied simultaneously, it is desirable to identify the core problems among them. Such cores are called minimal unsatisfiable subsets (MUSes). The more MUSes are identified, the more information about the conflicts among the constraints is obtained. However, a full enumeration of all MUSes is in general intractable due to the large number (even exponential) of possible conflicts. Moreover, to identify MUSes algorithms must test sets of constraints for their simultaneous satisfiabilty. The type of the test depends on the application domains. The complexity of tests can be extremely high especially for domains like temporal logics, model checking, or SMT. In this paper, we propose a recursive algorithm that identifies MUSes in an online manner (i.e., one by one) and can be terminated at any time. The key feature of our algorithm is that it minimizes the number of satisfiability tests and thus speeds up the computation. The algorithm is applicable to an arbitrary constraint domain and its effectiveness demonstrates itself especially in domains with expensive satisfiability checks. We benchmark our algorithm against state of the art algorithm on Boolean and SMT constraint domains and demonstrate that our algorithm really requires less satisfiability tests and consequently finds more MUSes in given time limits

A Max-Term Counting Based Knowledge Inconsistency Checking Strategy and Inconsistency Measure Calculation of Fuzzy Knowledge Based Systems

The task of finding all the minimal inconsistent subsets plays a vital role in many theoretical works especially in large knowledge bases and it has been proved to be a NP-complete problem. In this work, at first we propose a max-term counting based knowledge inconsistency checking strategy. And, then, we put forward an algorithm for finding all minimal inconsistent subsets, in which we establish a Boolean lattice to organize the subsets of the given knowledge base and use leaf pruning to optimize the algorithm efficiency. Comparative experiments and analysis also show the algorithm’s improvement over past approaches. Finally, we give an application for inconsistency measure calculation of fuzzy knowledge based systems

Computing explanations for unlively queries in databases

A query is lively in a database schema if it returns a non-empty answer for some database satisfying the schema. Debugging a database schema requires not only determining queries (as well as views or tables) that are not lively, but also fixing them. To make that task easier it is required to provide the designer with some explanation of why a query is not lively. To the best of our knowledge, the existing methods for liveliness checking in databases do not provide such explanations. An explanation is understood as the minimal set of constraints that are responsible for the non-liveliness of the tested query. In this paper we propose a method for computing such explanations which is independent of the particular method used to determine liveliness of a given query. Our method provides three levels of search: one explanation, a maximal set of non-overlapping explanations, and all explanations. The first two levels require only a linear number of callings to the underlying method. In addition, we propose a filter to reduce the number of callings to the underlying liveliness method. We also experimentally compare our method with a more naive method for query liveliness and with the best known method for finding unsatisfiable subsets of constraints.Postprint (published version

Improving MCS Enumeration via Caching

Enumeration of minimal correction sets (MCSes) of conjunctive normal form formulas is a central and highly intractable problem in infeasibility analysis of constraint systems. Often complete enumeration of MCSes is impossible due to both high computational cost and worst-case exponential number of MCSes. In such cases partial enumeration is sought for, finding applications in various domains, including axiom pinpointing in description logics among others. In this work we propose caching as a means of further improving the practical efficiency of current MCS enumeration approaches, and show the potential of caching via an empirical evaluation.Peer reviewe