Knowledge representation and reasoning (KRR) systems describe and reason with complex concepts and relations in the form of facts and rules. Unfortunately, wide deployment of KRR systems runs into the problem that domain experts have great difficulty constructing correct logical representations of their domain knowledge. Knowledge engineers can help with this construction process, but there is a deficit of such specialists. The earlier Knowledge Authoring Logic Machine (KALM) based on Controlled Natural Language (CNL) was shown to have very high accuracy for authoring facts and questions. More recently, KALMFL, a successor of KALM, replaced CNL with factual English, which is much less restrictive and requires very little training from users. However, KALMFL has limitations in representing certain types of knowledge, such as authoring rules for multi-step reasoning or understanding actions with timestamps. To address these limitations, we propose KALMRA to enable authoring of rules and actions. Our evaluation using the UTI guidelines benchmark shows that KALMRA achieves a high level of correctness (100%) on rule authoring. When used for authoring and reasoning with actions, KALMRA achieves more than 99.3% correctness on the bAbI benchmark, demonstrating its effectiveness in more sophisticated KRR jobs. Finally, we illustrate the logical reasoning capabilities of KALMRA by drawing attention to the problems faced by the recently made famous AI, ChatGPT.

We present Locksynth, a tool that automatically derives synchronization needed for destructive updates to concurrent data structures that involve a constant number of shared heap memory write operations. Locksynth serves as the implementation of our prior work on deriving abstract synchronization code. Designing concurrent data structures involves inferring correct synchronization code starting with a prior understanding of the sequential data structure’s operations. Further, an understanding of shared memory model and the synchronization primitives is also required. The reasoning involved transforming a sequential data structure into its concurrent version can be performed using Answer Set Programming, and we mechanized our approach in previous work. The reasoning involves deduction and abduction that can be succinctly modeled in ASP. We assume that the abstract sequential code of the data structure’s operations is provided, alongside axioms that describe concurrent behavior. This information is used to automatically derive concurrent code for that data structure, such as dictionary operations for linked lists and binary search trees that involve a constant number of destructive update operations. We also are able to infer the correct set of locks (but not code synthesis) for external height-balanced binary search trees that involve left/right tree rotations. Locksynth performs the analyses required to infer correct sets of locks and as a final step, also derives the C++ synchronization code for the synthesized data structures. We also provide a performance analysis of the C++ code synthesized by Locksynth with the hand-crafted versions available from the Synchrobench microbenchmark suite. To the best of our knowledge, our tool is the first to employ ASP as a backend reasoner to perform concurrent data structure synthesis.

This paper introduces a framework for assisting policy authors in refining and improving their policies. In particular, we focus on authorization and obligation policies that can be encoded in Gelfond and Lobo’s $\mathscr{AOPL}$ language for policy specification. We propose a framework that detects the statements that make a policy inconsistent, underspecified, or ambiguous with respect to an action being executed in a given state. We also give attention to issues that arise at the intersection of authorization and obligation policies, for instance when the policy requires an unauthorized action to be executed. The framework is encoded in Answer Set Programming.

In answer set programming (ASP), the user can define declaratively a problem and solve it with efficient solvers; practical applications of ASP are countless and several constraint problems have been successfully solved with ASP. On the other hand, solution time usually grows in a superlinear way (often, exponential) with respect to the size of the instance, which is impractical for large instances. A widely used approach is to split the optimization problem into subproblems (SPs) that are solved in sequence, some committing to the values assigned by others, and reconstructing a valid assignment for the whole problem by juxtaposing the solutions of the single SPs. On the one hand, this approach is much faster due to the superlinear behavior; on the other hand, it does not provide any guarantee of optimality: committing to the assignment of one SP can rule out the optimal solution from the search space. In other research areas, logic-Based Benders decomposition (LBBD) proved effective; in LBBD, the problem is decomposed into a master problem (MP) and one or several SPs. The solution of the MP is passed to the SPs that can possibly fail. In case of failure, a no-good is returned to the MP that is solved again with the addition of the new constraint. The solution process is iterated until a valid solution is obtained for all the SPs or the MP is proven infeasible. The obtained solution is provably optimal under very mild conditions. In this paper, we apply for the first time LBBD to ASP, exploiting an application in health care as case study. Experimental results show the effectiveness of the approach. We believe that the availability of LBBD can further increase the practical applicability of ASP technologies.

Fairness in machine learning is of considerable interest in recent years owing to the propensity of algorithms trained on historical data to amplify and perpetuate historical biases. In this paper, we argue for a formal reconstruction of fairness definitions, not so much to replace existing definitions but to ground their application in an epistemic setting and allow for rich environmental modeling. Consequently we look into three notions: fairness through unawareness, demographic parity and counterfactual fairness, and formalize these in the epistemic situation calculus.

A ProbLog program is a logic program with facts that only hold with a specified probability. In this contribution, we extend this ProbLog language by the ability to answer “What if” queries. Intuitively, a ProbLog program defines a distribution by solving a system of equations in terms of mutually independent predefined Boolean random variables. In the theory of causality, Judea Pearl proposes a counterfactual reasoning for such systems of equations. Based on Pearl’s calculus, we provide a procedure for processing these counterfactual queries on ProbLog programs, together with a proof of correctness and a full implementation. Using the latter, we provide insights into the influence of different parameters on the scalability of inference. Finally, we also show that our approach is consistent with CP-logic, that is with the causal semantics for logic programs with annotated with disjunctions.

Automatic differentiation (AD) is a range of algorithms to compute the numeric value of a function’s (partial) derivative, where the function is typically given as a computer program or abstract syntax tree. AD has become immensely popular as part of many learning algorithms, notably for neural networks. This paper uses Prolog to systematically derive gradient-based forward- and reverse-mode AD variants from a simple executable specification: evaluation of the symbolic derivative. Along the way we demonstrate that several Prolog features (DCGs, co-routines) contribute to the succinct formulation of the algorithm. We also discuss two applications in probabilistic programming that are enabled by our Prolog algorithms. The first is parameter learning for the Sum-Product Loop Language and the second consists of both parameter learning and variational inference for probabilistic logic programming.

We discuss how to implement backjumping (or intelligent backtracking) in Prolog by using the built-ins throw/1 and catch/3. We show that it is impossible in a general case, contrary to a claim that “backjumping is exception handling." We provide two solutions. One works for binary programs; in a general case it imposes a restriction on where backjumping may originate. The other restricts the class of backjump targets. We also discuss implementing backjumping by using backtracking and the Prolog database. Additionally, we explain the semantics of Prolog exception handling in the presence of coroutining.

Refactoring is modifying a program without changing its external behavior. In this paper, we make the concept of external behavior precise for a simple answer set programming language. Then we describe a proof assistant for the task of verifying that refactoring a program in that language is performed correctly.

Answer Set Programming with Quantifiers ASP(Q) extends Answer Set Programming (ASP) to allow for declarative and modular modeling of problems from the entire polynomial hierarchy. The first implementation of ASP(Q), called QASP, was based on a translation to Quantified Boolean Formulae (QBF) with the aim of exploiting the well-developed and mature QBF-solving technology. However, the implementation of the QBF encoding employed in qasp is very general and might produce formulas that are hard to evaluate for existing QBF solvers because of the large number of symbols and subclauses. In this paper, we present a new implementation that builds on the ideas of QASP and features both a more efficient encoding procedure and new optimized encodings of ASP(Q) programs in QBF. The new encodings produce smaller formulas (in terms of the number of quantifiers, variables, and clauses) and result in a more efficient evaluation process. An algorithm selection strategy automatically combines several QBF-solving back-ends to further increase performance. An experimental analysis, conducted on known benchmarks, shows that the new system outperforms QASP.