We propose a method for generating rule sets as global and local explanations for tree-ensemble learning methods using answer set programming (ASP). To this end, we adopt a decompositional approach where the split structures of the base decision trees are exploited in the construction of rules, which in turn are assessed using pattern mining methods encoded in ASP to extract explanatory rules. For global explanations, candidate rules are chosen from the entire trained tree-ensemble models, whereas for local explanations, candidate rules are selected by only considering rules that are relevant to the particular predicted instance. We show how user-defined constraints and preferences can be represented declaratively in ASP to allow for transparent and flexible rule set generation, and how rules can be used as explanations to help the user better understand the models. Experimental evaluation with real-world datasets and popular tree-ensemble algorithms demonstrates that our approach is applicable to a wide range of classification tasks.

Answer set programming (ASP) has demonstrated its potential as an effective tool for concisely representing and reasoning about real-world problems. In this paper, we present an application in which ASP has been successfully used in the context of dynamic traffic distribution for urban networks, within a more general framework devised for solving such a real-world problem. In particular, ASP has been employed for the computation of the “optimal” routes for all the vehicles in the network. We also provide an empirical analysis of the performance of the whole framework, and of its part in which ASP is employed, on two European urban areas, which shows the viability of the framework and the contribution ASP can give.

This note presents a historical survey of informal semantics that are associated with logic programming under answer set semantics. We review these in uniform terms and align them with two paradigms: Answer Set Programming and ASP-Prolog — two prominent Knowledge Representation and Reasoning Paradigms in Artificial Intelligence.

In temporal extensions of answer set programming (ASP) based on linear time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic (MEL) provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in MEL and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.

Payroll management is a critical business task that is subject to a large number of rules, which vary widely between companies, sectors, and countries. Moreover, the rules are often complex and change regularly. Therefore, payroll management systems must be flexible in design. In this paper, we suggest an approach based on a flexible answer set programming (ASP) model and an easy-to-read tabular representation based on the decision model and notation standard. It allows HR consultants to represent complex rules without the need for a software engineer and to ultimately design payroll systems for a variety of different scenarios. We show how the multi-shot solving capabilities of the clingo ASP system can be used to reach the performance that is necessary to handle real-world instances.

Unit testing frameworks are nowadays considered a best practice, included in almost all modern software development processes, to achieve rapid development of correct specifications. Knowledge representation and reasoning paradigms such as Answer Set Programming (ASP), that have been used in industry-level applications, are not an exception. Indeed, the first unit testing specification language for ASP was proposed in 2011 as a feature of the ASPIDE development environment. Later, a more portable unit testing language was included in the LANA annotation language. In this paper we revisit both languages and tools for unit testing in ASP. We propose a new unit test specification language that allows one to inline tests within ASP programs, and we identify the computational complexity of the tasks associated with checking the various program-correctness assertions. Test-case specifications are transparent to the traditional evaluation, but can be interpreted by a specific testing tool. Thus, we present a novel environment supporting test-driven development of ASP programs.

In this note, we introduce the notion of support graph to define explanations for any model of a logic program. An explanation is an acyclic support graph that, for each true atom in the model, induces a proof in terms of program rules represented by labels. A classical model may have zero, one or several explanations: when it has at least one, it is called a justified model. We prove that all stable models are justified, whereas, for disjunctive programs, some justified models may not be stable. We also provide a meta-programming encoding in Answer Set Programming that generates the explanations for a given stable model of some program. We prove that the encoding is sound and complete, that is, there is a one-to-one correspondence between each answer set of the encoding and each explanation for the original stable model.

Epistemic logic programs (ELPs), extend answer set programming (ASP) with epistemic operators. The semantics of such programs is provided in terms of world views, which are sets of belief sets, that is, syntactically, sets of sets of atoms. Different semantic approaches propose different characterizations of world views. Recent work has introduced semantic properties that should be met by any semantics for ELPs, like the Epistemic Splitting Property, that, if satisfied, allows to modularly compute world views in a bottom-up fashion, analogously to “traditional” ASP. We analyze the possibility of changing the perspective, shifting from a bottom-up to a top-down approach to splitting. We propose a basic top-down approach, which we prove to be equivalent to the bottom-up one. We then propose an extended approach, where our new definition: (i) is provably applicable to many of the existing semantics; (ii) operates similarly to “traditional” ASP; (iii) provably coincides under any semantics with the bottom-up notion of splitting at least on the class of Epistemically Stratified Programs (which are, intuitively, those where the use of epistemic operators is stratified); (iv) better adheres to common ASP programming methodology.

Answer set programming (ASP) is a popular declarative programming language for solving hard combinatorial problems. Although ASP has gained widespread acceptance in academic and industrial contexts, there are certain user groups who may find it more advantageous to employ a higher-level language that closely resembles natural language when specifying ASP programs. In this paper, we propose a novel tool, called CNL2ASP, for translating English sentences expressed in a controlled natural language (CNL) form into ASP. In particular, we first provide a definition of the type of sentences allowed by our CNL and their translation as ASP rules and then exemplify the usage of the CNL for the specification of both synthetic and real-world combinatorial problems. Finally, we report the results of an experimental analysis conducted on the real-world problems to compare the performance of automatically generated encodings with the ones written by ASP practitioners, showing that our tool can obtain satisfactory performance on these benchmarks.

Given a conditional sentence “${\varphi}\Rightarrow \psi$" (if ${\varphi}$ then $\psi$) and respective facts, four different types of inferences are observed in human reasoning: Affirming the antecedent (AA) (or modus ponens) reasons $\psi$ from ${\varphi}$; affirming the consequent (AC) reasons ${\varphi}$ from $\psi$; denying the antecedent (DA) reasons $\neg\psi$ from $\neg{\varphi}$; and denying the consequent (DC) (or modus tollens) reasons $\neg{\varphi}$ from $\neg\psi$. Among them, AA and DC are logically valid, while AC and DA are logically invalid and often called logical fallacies. Nevertheless, humans often perform AC or DA as pragmatic inference in daily life. In this paper, we realize AC, DA and DC inferences in answer set programming. Eight different types of completion are introduced, and their semantics are given by answer sets. We investigate formal properties and characterize human reasoning tasks in cognitive psychology. Those completions are also applied to commonsense reasoning in AI.

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 presents a rich knowledge representation language aimed at formalizing causal knowledge. This language is used for accurately and directly formalizing common benchmark examples from the literature of actual causality. A definition of cause is presented and used to analyze the actual causes of changes with respect to sequences of actions representing those examples.

A plethora of approaches have been proposed for joint entity-relation (ER) extraction. Most of these methods largely depend on a large amount of manually annotated training data. However, manual data annotation is time-consuming, labor-intensive, and error-prone. Human beings learn using both data (through induction) and knowledge (through deduction). Answer Set Programming (ASP) has been a widely utilized approach for knowledge representation and reasoning that is elaboration tolerant and adept at reasoning with incomplete information. This paper proposes a new approach, ASP-enhanced Entity-Relation extraction (ASPER), to jointly recognize entities and relations by learning from both data and domain knowledge. In particular, ASPER takes advantage of the factual knowledge (represented as facts in ASP) and derived knowledge (represented as rules in ASP) in the learning process of neural network models. We have conducted experiments on two real datasets and compare our method with three baselines. The results show that our ASPER model consistently outperforms the baselines.

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.

We establish a novel relation between delete-free planning, an important task for the AI planning community also known as relaxed planning, and logic programming. We show that given a planning problem, all subsets of actions that could be ordered to produce relaxed plans for the problem can be bijectively captured with stable models of a logic program describing the corresponding relaxed planning problem. We also consider the supported model semantics of logic programs, and introduce one causal and one diagnostic encoding of the relaxed planning problem as logic programs, both capturing relaxed plans with their supported models. Our experimental results show that these new encodings can provide major performance gain when computing optimal relaxed plans, with our diagnostic encoding outperforming state-of-the-art approaches to relaxed planning regardless of the given time limit when measured on a wide collection of STRIPS planning benchmarks.

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.

This paper describes a generalization of Clark’s completion that is applicable to logic programs containing arithmetic operations and produces syntactically simple, natural looking formulas. If a set of first-order axioms is equivalent to the completion of a program, then we may be able to find standard models of these axioms by running an answer set solver. As an example, we apply this “reverse completion” procedure to the Sum and Product Puzzle.

Artificial Intelligence plays a main role in supporting and improving smart manufacturing and Industry 4.0, by enabling the automation of different types of tasks manually performed by domain experts. In particular, assessing the compliance of a product with the relative schematic is a time-consuming and prone-to-error process. In this paper, we address this problem in a specific industrial scenario. In particular, we define a Neuro-Symbolic approach for automating the compliance verification of the electrical control panels. Our approach is based on the combination of Deep Learning techniques with Answer Set Programming (ASP), and allows for identifying possible anomalies and errors in the final product even when a very limited amount of training data is available. The experiments conducted on a real test case provided by an Italian Company operating in electrical control panel production demonstrate the effectiveness of the proposed approach.

Answer set programming is a declarative logic programming paradigm geared towards solving difficult combinatorial search problems. While different logic programs can encode the same problem, their performance may vary significantly. It is not always easy to identify which version of the program performs the best. We present the system predictor (and its algorithmic backend) for estimating the grounding size of programs, a metric that can influence a performance of a system processing a program. We evaluate the impact of predictor when used as a guide for rewritings produced by the answer set programming rewriting tools projector and lpopt. The results demonstrate potential to this approach.

Detecting sets of relevant patterns from a given dataset is an important challenge in data mining. The relevance of a pattern, also called utility in the literature, is a subjective measure and can be actually assessed from very different points of view. Rule-based languages like Answer Set Programming (ASP) seem well suited for specifying user-provided criteria to assess pattern utility in a form of constraints; moreover, declarativity of ASP allows for a very easy switch between several criteria in order to analyze the dataset from different points of view. In this paper, we make steps toward extending the notion of High-Utility Pattern Mining; in particular, we introduce a new framework that allows for new classes of utility criteria not considered in the previous literature. We also show how recent extensions of ASP with external functions can support a fast and effective encoding and testing of the new framework. To demonstrate the potential of the proposed framework, we exploit it as a building block for the definition of an innovative method for predicting ICU admission for COVID-19 patients. Finally, an extensive experimental activity demonstrates both from a quantitative and a qualitative point of view the effectiveness of the proposed approach.