Humans can generate reasonable answers to novel queries (Schulz, 2012): if I asked you what kind of food you want to eat for lunch, you would respond with a food, not a time. The thought that one would respond "After 4pm" to "What would you like to eat" is either a joke or a mistake, and seriously entertaining it as a lunch option would likely never happen in the first place. While understanding how people come up with new ideas, thoughts, explanations, and hypotheses that obey the basic constraints of a novel search space is of central importance to cognitive science, there is no agreed-on formal model for this kind of reasoning. We propose that a core component of any such reasoning system is a type theory: a formal imposition of structure on the kinds of computations an agent can perform, and how they're performed. We motivate this proposal with three empirical observations: adaptive constraints on learning and inference (i.e. generating reasonable hypotheses), how people draw distinctions between improbability and impossibility, and people's ability to reason about things at varying levels of abstraction.

In this paper we investigate how to estimate the hardness of Boolean satisfiability (SAT) encodings for the Logical Equivalence Checking problem (LEC). Meaningful estimates of hardness are important in cases when a conventional SAT solver cannot solve a SAT instance in a reasonable time. We show that the hardness of SAT encodings for LEC instances can be estimated \textit{w.r.t.} some SAT partitioning. We also demonstrate the dependence of the accuracy of the resulting estimates on the probabilistic characteristics of a specially defined random variable associated with the considered partitioning. The paper proposes several methods for constructing partitionings, which, when used in practice, allow one to estimate the hardness of SAT encodings for LEC with good accuracy. In the experimental part we propose a class of scalable LEC tests that give extremely complex instances with a relatively small input size $n$ of the considered circuits. For example, for $n = 40$, none of the state-of-the-art SAT solvers can cope with the considered tests in a reasonable time. However, these tests can be solved in parallel using the proposed partitioning methods.

Program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values over multiple examples, such as intervals. To overcome this limitation, we introduce an inductive logic programming approach which combines relational learning with numerical reasoning. Our approach, which we call NUMSYNTH, uses satisfiability modulo theories solvers to efficiently learn programs with numerical values. Our approach can identify numerical values in linear arithmetic fragments, such as real difference logic, and from infinite domains, such as real numbers or integers. Our experiments on four diverse domains, including game playing and program synthesis, show that our approach can (i) learn programs with numerical values from linear arithmetical reasoning, and (ii) outperform existing approaches in terms of predictive accuracies and learning times.

Data-driven decision making is becoming an integral part of manufacturing companies. Data is collected and commonly used to improve efficiency and produce high quality items for the customers. IoT-based and other forms of object tracking are an emerging tool for collecting movement data of objects/entities (e.g. human workers, moving vehicles, trolleys etc.) over space and time. Movement data can provide valuable insights like process bottlenecks, resource utilization, effective working time etc. that can be used for decision making and improving efficiency. Turning movement data into valuable information for industrial management and decision making requires analysis methods. We refer to this process as movement analytics. The purpose of this document is to review the current state of work for movement analytics both in manufacturing and more broadly. We survey relevant work from both a theoretical perspective and an application perspective. From the theoretical perspective, we put an emphasis on useful methods from two research areas: machine learning, and logic-based knowledge representation. We also review their combinations in view of movement analytics, and we discuss promising areas for future development and application. Furthermore, we touch on constraint optimization. From an application perspective, we review applications of these methods to movement analytics in a general sense and across various industries. We also describe currently available commercial off-the-shelf products for tracking in manufacturing, and we overview main concepts of digital twins and their applications.

A magic value in a program is a constant symbol that is essential for the execution of the program but has no clear explanation for its choice. Learning programs with magic values is difficult for existing program synthesis approaches. To overcome this limitation, we introduce an inductive logic programming approach to efficiently learn programs with magic values. Our experiments on diverse domains, including program synthesis, drug design, and game playing, show that our approach can (i) outperform existing approaches in terms of predictive accuracies and learning times, (ii) learn magic values from infinite domains, such as the value of pi, and (iii) scale to domains with millions of constant symbols.

We provide a framework for probabilistic reasoning in Vadalog-based Knowledge Graphs (KGs), satisfying the requirements of ontological reasoning: full recursion, powerful existential quantification, expression of inductive definitions. Vadalog is a Knowledge Representation and Reasoning (KRR) language based on Warded Datalog+/-, a logical core language of existential rules, with a good balance between computational complexity and expressive power. Handling uncertainty is essential for reasoning with KGs. Yet Vadalog and Warded Datalog+/- are not covered by the existing probabilistic logic programming and statistical relational learning approaches for several reasons, including insufficient support for recursion with existential quantification, and the impossibility to express inductive definitions. In this work, we introduce Soft Vadalog, a probabilistic extension to Vadalog, satisfying these desiderata. A Soft Vadalog program induces what we call a Probabilistic Knowledge Graph (PKG), which consists of a probability distribution on a network of chase instances, structures obtained by grounding the rules over a database using the chase procedure. We exploit PKGs for probabilistic marginal inference. We discuss the theory and present MCMC-chase, a Monte Carlo method to use Soft Vadalog in practice. We apply our framework to solve data management and industrial problems, and experimentally evaluate it in the Vadalog system.

TML (Tau Meta-Language) is a variant of Datalog. It is intended to serve as a translator between formal languages (and more uses, see under the Philosophy section). The main difference between TML and common Datalog implementations is that TML works under the Partial Fixed-Point (PFP) semantics, unlike common implementations that follow the Well-Founded Semantics (WFS) or stratified Datalog. By that TML (like with WFS) imposes no syntactic restrictions on negation, however unlike WFS or stratified Datalog it is PSPACE complete rather than P complete. TML's implementation heavily relies on BDDs (Binary Decision Diagrams) in its internals. This gives it extraordinary performance in time and space terms, and allowing negation to be feasible even over large universes. In fact negated bodies, as below, do not consume more time or space than positive bodies by any means, thanks to the BDD mechanism. TML follows the PFP semantics in the following sense. On each step, all rules are executed once and only once, causing a set of insertions and deletions of terms.

Reasoning about complex networks has in recent years become an important topic of study due to its many applications: the adoption of commercial products, spread of disease, the diffusion of an idea, etc. In this paper, we present the MANCaLog language, a formalism based on logic programming that satisfies a set of desiderata proposed in previous work as recommendations for the development of approaches to reasoning in complex networks. To the best of our knowledge, this is the first formalism that satisfies all such criteria. We first focus on algorithms for finding minimal models (on which multi-attribute analysis can be done), and then on how this formalism can be applied in certain real world scenarios. Towards this end, we study the problem of deciding group membership in social networks: given a social network and a set of groups where group membership of only some of the individuals in the network is known, we wish to determine a degree of membership for the remaining group-individual pairs. We develop a prototype implementation that we use to obtain experimental results on two real world datasets, including a current social network of criminal gangs in a major U.S.\ city. We then show how the assignment of degree of membership to nodes in this case allows for a better understanding of the criminal gang problem when combined with other social network mining techniques -- including detection of sub-groups and identification of core group members -- which would not be possible without further identification of additional group members.

We present a formal tasK AllocatioN and scheduling apprOAch for multi-robot missions (KANOA). KANOA supports two important types of task constraints: task ordering, which requires the execution of several tasks in a specified order; and joint tasks, which indicates tasks that must be performed by more than one robot. To mitigate the complexity of robotic mission planning, KANOA handles the allocation of the mission tasks to robots, and the scheduling of the allocated tasks separately. To that end, the task allocation problem is formalised in first-order logic and resolved using the Alloy model analyzer, and the task scheduling problem is encoded as a Markov decision process and resolved using the PRISM probabilistic model checker. We illustrate the application of KANOA through a case study in which a heterogeneous robotic team is assigned a hospital maintenance mission.

This EPTCS volume contains the joint proceedings for the fourth international workshop on Formal Methods for Autonomous Systems (FMAS 2022) and the fourth international workshop on Automated and verifiable Software sYstem DEvelopment (ASYDE 2022), which were held on the 26th and 27th of September 2022. FMAS 2022 and ASYDE 2022 were held in conjunction with 20th International Conference on Software Engineering and Formal Methods (SEFM'22), at Humboldt University in Berlin. For FMAS, this year's workshop was our return to having in-person attendance after two editions of FMAS that were entirely online because of the restrictions necessitated by COVID-19. We were also keen to ensure that FMAS 2022 remained easily accessible to people who were unable to travel, so the workshop facilitated remote presentation and attendance. The goal of FMAS is to bring together leading researchers who are using formal methods to tackle the unique challenges presented by autonomous systems, to share their recent and ongoing work. Autonomous systems are highly complex and present unique challenges for the application of formal methods. Autonomous systems act without human intervention, and are often embedded in a robotic system, so that they can interact with the real world. As such, they exhibit the properties of safety-critical, cyber-physical, hybrid, and real-time systems. We are interested in work that uses formal methods to specify, model, or verify autonomous and/or robotic systems; in whole or in part. We are also interested in successful industrial applications and potential directions for this emerging application of formal methods.