We present JudgeD, a probabilistic datalog. A JudgeD program defines a distribution over a set of traditional datalog programs by attaching logical sentences to clauses to implicitly specify traditional data programs. Through the logical sentences, JudgeD provides a novel method for the expression of complex dependencies between both rules and facts. JudgeD is implemented as a proof-of-concept in the language Python. The implementation allows connection to external data sources, and features both a Monte Carlo probability approximation as well as an exact solver supported by BDDs. Several directions for future work are discussed and the implementation is released under the MIT license.

While there exist several approaches in the constraint programming community to learn a constraint theory, few of them have considered the learning of constraint optimization problems.To alleviate this situation, we introduce an initial approach to learning first-order weighted MAX-SAT theories. It employs inductive logic programming techniques to learn a set of first-order clauses and then uses preference learning techniques to learn the weights of the clauses.In order to learn these weighted clauses, the clausal optimization system uses examples of possible worlds and a set of preferences that state which examples are preferred over other ones.The technique is also empirically evaluated on a number of examples.These experiments show that the system is capable of learning clauses and weights that accurately capture underlying models.

Recent work by Janhunen, Tasharrofi, and Ternovska (2016) started from the following observation: "if SAT From the result of this oracle call, a learned clause is generated and added to ϕ. Now that formalism; (2) It can be immediately combined with other these highly-performant SATsolvers exist, research often SAT extensions (such as integer variables, acyclicity, or any stretches beyond SAT, either because of trying to tackle other theory propagator); (3) No dedicated propagators need problems of a complexity higher than NP or because the input to be developed for the new extension because the nested format of SAT solvers (propositional logic) is too limited solver is (automatically) used as a propagator for its internal to concisely and naturally express certain domain specific theory; for example, it was shown by Janhunen, Tasharrofi, constraints, such as graph properties.

We investigate two QBF resolution systems that use extension variables: weak extended Q-resolution, where the extension variables are quantified at the innermost level, and extended Q-resolution, where the extension variables can be placed inside the quantifier prefix. These systems have been considered previously by Wintersteiger et al, who give experimental evidence that extended Q-resolution is stronger than weak extended Q-resolution. Here we prove an exponential separation between the two systems, thereby confirming the conjecture of Wintersteiger et al. Conceptually, this separation relies on showing strategy extraction for weak extended Q-resolution by bounded-depth circuits. In contrast, we show that this strong strategy extraction result fails in extended Q-resolution.

2QBF is a special case of general quantified Boolean formulae (QBF). It is limited to just two quantification levels, i.e., to a form forall-exists. Despite this limitation it applies to a wide range of applications, e.g., to artificial intelligence, graph theory, synthesis, etc.. Recent research showed that CEGAR-based methods give a performance boost to QBF solving (e.g, compared to QDPLL). Conjunctive normal form (CNF) is a commonly accepted representation for both SAT and QBF problems; however, it does not reflect the circuit structure that might be present in the problem. Existing attempts of extracting this structure from CNF and using it in 2QBF context do not show advantages over CNF based 2QBF solvers. In this work we introduce a new workflow for 2QBF, containing a new semantic circuit extraction algorithm and a CEGAR-based 2QBF solver that uses circuit structure and is improved by a so-called "cofactor sharing'' heuristics. We evaluate the proposed methodology on a range of benchmarks and show the practicality of the new approach.

We present RELOOP, a domain-specific language for relational optimization embedded in Python. It allows the user to express relational optimization problems in a natural syntax that follows logic and linear algebra, rather than in the restrictive standard form required by solvers, and can automatically compile the model to a lower-order but equivalent model. Moreover, RELOOP makes it easy to combine relational optimization with high-level features of Python such as loops, parallelism and interfaces to relational databases.

Over the last decade, building on advances in the areas of knowledge compilation and weighted model counting has drastically increased the scalability of inference in probabilistic logic programs. In this paper, we provide an overview of how this has been possible and point out some open challenges.

While it is empirically confirmed folklore that conjunctive normal form (CNF) is not the ideal input format for QBF solvers, most tool developers and therefore also the users focus on formulas in this restricted structure. One important factor for establishing non-CNF solving is the input format. To overcome drawbacks of available formats, the QCIR format has recently been presented. The QCIR format is a circuit-based input format for quantified Boolean formulas which supports structure sharing. In contrast to previous formats, the representation is very compact, yet still easy to parse and to read for the human user. In this paper, we analyze the QCIR format in detail and provide tools and benchmarks which, we hope, will make its usage attractive and motivate tool developers to support this format as well as users to formulate their encodings in this format.

SAT and #SAT are at the heart of many important problem formulations in AI, the most prominent being reasoning and learning in first-order and probabilistic knowledge bases. In practice, all contemporary systems resort to domain closure: objects in the universe are all and only the ones mentioned in the knowledge base. This is in stark contrast to the natural ability of human beings to infer things about sensory inputs and unforeseen data: they infer the existence of objects from their observations; no predefined list of objects is given or known in advance. In this paper, we introduce the formal foundations for reasoning in open universes in a general way, purely based on SAT and #SAT technology.

A new computational paradigm has emerged in computer both Renault and Toyota have deployed online configuration science over the past few decades, which is exemplified by systems based on knowledge compilation). QBF solvers the use of SAT solvers to tackle problems in the complexity have been used in model checking, verification, debugging, class NP. Finally, function problem solvers have and engineering investment is made towards developing been used in model-based diagnosis, design debugging, highly efficient solvers for a prototypical problem CAD and bioinformatics. The cost of this investment is then on a variety of topics, including algorithms; descriptions amortized as these solvers are applied to a broader class of of implementations and/or evaluations of beyond NP problems via reductions (in contrast to developing dedicated solvers; their applications (including encodings); the complexity algorithms for each encountered problem). SAT solvers, classes they reach; and their connections to one for example, are now routinely used to solve problems in another.