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.

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 paradigm with various applications. Programs can easily have many answer sets that cannot be enumerated in practice, but counting still allows quantifying solution spaces. If one counts under assumptions on literals, one obtains a tool to comprehend parts of the solution space, so-called answer set navigation. However, navigating through parts of the solution space requires counting many times, which is expensive in theory. Knowledge compilation compiles instances into representations on which counting works in polynomial time. However, these techniques exist only for conjunctive normal form (CNF) formulas, and compiling ASP programs into CNF formulas can introduce an exponential overhead. This paper introduces a technique to iteratively count answer sets under assumptions on knowledge compilations of CNFs that encode supported models. Our anytime technique uses the inclusion–exclusion principle to improve bounds by over- and undercounting systematically. In a preliminary empirical analysis, we demonstrate promising results. After compiling the input (offline phase), our approach quickly (re)counts.

We present the Answer Set Programming (ASP)-based visualization tool clingraph, which aims at visualizing various concepts of ASP by means of ASP itself. This idea traces back to the aspviz tool and clingraph redevelops and extends it in the context of modern ASP systems. More precisely, clingraph takes graph specifications in terms of ASP facts and hands them over to the graph visualization system graphviz. The use of ASP provides a great interface between logic programs and/or answer sets and their visualization. Also, clingraph offers a Python application programming interface (API) that extends this ease of interfacing to clingo’s API and in turn to connect and monitor various aspects of the solving process.

As the popularity of adhesive joints in industry increases, so does the need for tools to support the process of selecting a suitable adhesive. While some such tools already exist, they are either too limited in scope or offer too little flexibility in use. This work presents a more advanced tool, that was developed together with a team of adhesive experts. We first extract the experts’ knowledge about this domain and formalize it in a Knowledge Base (KB). The IDP-Z3 reasoning system can then be used to derive the necessary functionality from this KB. Together with a user-friendly interactive interface, this creates an easy-to-use tool capable of assisting the adhesive experts. To validate our approach, we performed user testing in the form of qualitative interviews. The experts are very positive about the tool, stating that, among others, it will help save time and find more suitable adhesives.