Quantified Integer Programming (QIP) bridges multiple domains by extending Quantified Boolean Formulas (QBF) to incorporate general integer variables and linear constraints while also generalizing Integer Programming through variable quantification. As a special case of Quantified Constraint Satisfaction Problems (QCSP), QIP provides a versatile framework for addressing complex decision-making scenarios. Additionally, the inclusion of a linear objective function enables QIP to effectively model multistage robust discrete linear optimization problems, making it a powerful tool for tackling uncertainty in optimization. While two primary solution paradigms exist for QBF -- search-based and expansion-based approaches -- only search-based methods have been explored for QIP and QCSP. We introduce an expansion-based approach for QIP using Counterexample-Guided Abstraction Refinement (CEGAR), adapting techniques from QBF. We extend this methodology to tackle multistage robust discrete optimization problems with linear constraints and further embed it in an optimization framework, enhancing its applicability. Our experimental results highlight the advantages of this approach, demonstrating superior performance over existing search-based solvers for QIP in specific instances. Furthermore, the ability to model problems using linear constraints enables notable performance gains over state-of-the-art expansion-based solvers for QBF.

In the age of highly automated systems and the development of autonomous systems, a possible application scenario for ANNs is to use them as controllers for safety-critical cyber-physical systems (CPSes) [9]. Such CPSes capture the often complex environment, analyse the data and make control decisions about the future system behaviour. Guarantees on compliance with safety requirements, e.g., that human lives are not endangered, are of utmost importance. Whenever such guarantees are obtained via formal verification of the system behaviour, an ANN being a component of the system under analysis has also to be subject to verification [23]. The underlying weighted summation of the input neurons before application of the activation function can be represented by simple linear combinations and is therefore very appealing for classical verification methods dealing with linear arithmetic. However, this observation is deceptive when nonlinear activation functions are part of the ANN as such nonlinear functions are often hard to analyse in themselves [23]. Apart from restricted decidability results for reachability problems as in [9], the runtime of algorithms for automatic verification suffers from the multiple occurrence of nonlinear activation functions in complex ANNs such that only relatively small networks could be tackled. Depending on the class of activation functions and the underlying possibly necessary abstractions thereof, recent approaches were able to deal with ANNs comprising 20 to 300 nodes [10, 18, 19]. So-called satisfiability modulo theory (SMT) solvers implement algorithms that search for solutions to Boolean combinations of arithmetic constraints or prove the absence thereof.

Abstract: Compiling commonsense knowledge is traditionally an AI topic approached by manual labor. Recent advances in web data processing have enabled automated approaches. In this demonstration we will showcase three systems for automated commonsense knowledge base construction, highlighting each time one aspect of specific interest to the data management community. The demos are available online at https://quasimodo.r2.enst.fr, Knowledge and reasoning about general-world concepts are major challenges in AI. In recent years, these tasks are supported by a growing number of knowledge repositories, so-called commonsense knowledge bases (CSKBs), that store statements like lions live in groups, or painters use pencils.

Constraint Programming (CP) is a powerful declarative programming paradigm combining inference and search in order to find solutions to various type of constraint systems. Dealing with highly disjunctive constraint systems is notoriously difficult in CP. Apart from trying to solve each disjunct independently from each other, there is little hope and effort to succeed in constructing intermediate results combining the knowledge originating from several disjuncts. In this paper, we propose If Then Else (ITE), a lightweight approach for implementing stratified constructive disjunction and negation on top of an existing CP solver, namely SICStus Prolog clp(FD). Although constructive disjunction is known for more than three decades, it does not have straightforward implementations in most CP solvers. ITE is a freely available library proposing stratified and constructive reasoning for various operators, including disjunction and negation, implication and conditional. Our preliminary experimental results show that ITE is competitive with existing approaches that handle disjunctive constraint systems.

Decomposition is a technique to obtain complete solutions by assembling independently obtained partial solutions. In particular, constraint decomposition plays an important role in distributed databases, distributed scheduling and violation detection: It enables conflict-free local decision making, while avoiding communication overloading. One of the main issues in decomposition is the loss of flexibility due to decomposition. Here, flexibility roughly refers to the freedom in choosing suitable values for the variables in order to satisfy the constraints. In this paper, we concentrate on linear constraint systems and efficient decomposition techniques for them. Using a generalization of a flexibility metric developed for Simple Temporal Networks, we show how an efficient decomposition technique for linear constraint systems can be derived that minimizes the loss of flexibility. As a by-product of this decomposition technique, we propose an intuitively attractive flexibility metric for linear constraint systems where decomposition does not incur any loss of flexibility.

We propose a timed and soft extension of Concurrent Constraint Programming. The time extension is based on the hypothesis of bounded asynchrony: the computation takes a bounded period of time and is measured by a discrete global clock. Action prefixing is then considered as the syntactic marker which distinguishes a time instant from the next one. Supported by soft constraints instead of crisp ones, tell and ask agents are now equipped with a preference (or consistency) threshold which is used to determine their success or suspension. In the paper we provide a language to describe the agents behavior, together with its operational and denotational semantics, for which we also prove the compositionality and correctness properties. After presenting a semantics using maximal parallelism of actions, we also describe a version for their interleaving on a single processor (with maximal parallelism for time elapsing). Coordinating agents that need to take decisions both on preference values and time events may benefit from this language. To appear in Theory and Practice of Logic Programming (TPLP).

In probabilistic logic entailments, even moderate size problems can yield linear constraint systems with so many variables that exact methods are impractical. This difficulty can be remedied in many cases of interest by introducing a threevalued logic (true, false, and "don't care"). The three-valued approach allows the construction of "compressed" constraint systems which have the same solution sets as their two-valued counterparts, but which may involve dramatically fewer variables. PROLIFERATION OF WORLDS An entailment problem in Nilsson's (1986) probabilistic logic derives an estimate for the prior probability of one sentence (hereafter, the "target") from the priors for a set of other ("source") sentences. V is a matrix derived from an inventory of all consistent patterns of truth assignments (1 true, 0 false) for the source and target sentences.

Department of Computer Science Brown University Providence, RI 02912 Abstract In general, the best explanation for a given observation makes no promises on how good it is with respect to other alternative explanations. A major deficiency of message-passing schemes for belief revision in Bayesian networks is their inability to generate alternatives beyond the second best. In this paper, we present a general approach based on linear constraint systems that naturally generates alternative explanations in an orderly and highly efficient manner. This approach is then applied to cost-based abduction problems as well as belief revision in Bayesian networks. INTRODUCTION We are constantly faced with the problem of explaining the observations we have gathered with our senses. Our explanations are constructed by assuming certain facts or hypotheses which support our observations. For example, suppose I decide to phone my friend Tony at the office.

Combining a set of existing constraint solvers into an integ rated system of cooperating solvers is a useful and economic principle to solve hybrid constraint problems. In this paper we show that this approach can also be used to integrate differ ent language paradigms into a unified framework. Furthermore, we study the syntacti c, semantic and operational impacts of this idea for the amalgamation of declarative and constraint programming. To appear in Theory and Practice of Logic Programming (TPLP).