Piecewise-affine (PWA) systems are widely used for modeling and control of robotics problems including modeling contact dynamics. A common approach is to encode the control problem of the PWA system as a Mixed-Integer Convex Program (MICP), which can be solved by general-purpose off-the-shelf MICP solvers. To mitigate the scalability challenge of solving these MICP problems, existing work focuses on devising efficient and strong formulations of the problems, while less effort has been spent on exploiting their specific structure to develop specialized solvers. The latter is the theme of our work. We focus on efficiently handling one-hot constraints, which are particularly relevant when encoding PWA dynamics. We have implemented our techniques in a tool, Soy, which organically integrates logical reasoning, arithmetic reasoning, and stochastic local search. For a set of PWA control benchmarks, Soy solves more problems, faster, than two state-of-the-art MICP solvers.

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking is easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes cardinality and parity (XOR) reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

To date, we know only a few handcrafted quantified Boolean formulas (QBFs) that are hard for central QBF resolution systems such as Q-Res and QU-Res, and only one specific QBF family to separate Q-Res and QU-Res. Here we provide a general method to construct hard formulas for Q-Res and QU-Res. The construction uses simple propositional formulas (e.g. minimally unsatisfiable formulas) in combination with easy QBF gadgets (Σb2 formulas without constant winning strategies). This leads to a host of new hard formulas, including new classes of hard random QBFs. We further present generic constructions for formulas separating Q-Res and QU-Res, and for separating Q-Res and LD-Q-Res.

We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of width measures (with treewidth and cliquewidth as popular examples). As an important special case of our framework, we identify logics exhibiting width-finite finitely universal model sets, warranting decidable entailment for a wide range of homomorphism-closed queries, subsuming a diverse set of practically relevant query languages. As a particularly powerful width measure, we propose Blumensath's partitionwidth, which subsumes various other commonly considered width measures and exhibits highly favorable computational and structural properties. Focusing on the formalism of existential rules as a popular showcase, we explain how finite-partitionwidth sets of rules subsume other known abstract decidable classes but - leveraging existing notions of stratification - also cover a wide range of new rulesets. We expose natural limitations for fitting the class of finite-unification sets into our picture and provide several options for remedy.

This paper introduces a novel approach to detour management in Urban Air Traffic Management (UATM) using knowledge representation and reasoning. It aims to understand the complexities and requirements of UAM detours, enabling a method that quickly identifies safe and efficient routes in a carefully sampled environment. This method implemented in Answer Set Programming uses non-monotonic reasoning and a two-phase conversation between a human manager and the UATM system, considering factors like safety and potential impacts. The robustness and efficacy of the proposed method were validated through several queries from two simulation scenarios, contributing to the symbiosis of human knowledge and advanced AI techniques. The paper provides an introduction, citing relevant studies, problem formulation, solution, discussions, and concluding comments.

We study challenges using reinforcement learning in controlling energy systems, where apart from performance requirements, one has additional safety requirements such as avoiding blackouts. We detail how these safety requirements in real-time temporal logic can be strengthened via discretization into linear temporal logic (LTL), such that the satisfaction of the LTL formulae implies the satisfaction of the original safety requirements. The discretization enables advanced engineering methods such as synthesizing shields for safe reinforcement learning as well as formal verification, where for statistical model checking, the probabilistic guarantee acquired by LTL model checking forms a lower bound for the satisfaction of the original real-time safety requirements.

Modeling and verification of dynamic systems operating over a relational representation of states are increasingly investigated problems in AI, Business Process Management, and Database Theory. To make these systems amenable to verification, the amount of information stored in each relational state needs to be bounded, or restrictions are imposed on the preconditions and effects of actions. We introduce the general framework of relational action bases (RABs), which generalizes existing models by lifting both these restrictions: unbounded relational states can be evolved through actions that can quantify both existentially and universally over the data, and that can exploit numerical datatypes with arithmetic predicates. We then study parameterized safety of RABs via (approximated) SMT-based backward search, singling out essential meta-properties of the resulting procedure, and showing how it can be realized by an off-the-shelf combination of existing verification modules of the state-of-the-art MCMT model checker. We demonstrate the effectiveness of this approach on a benchmark of data-aware business processes. Finally, we show how universal invariants can be exploited to make this procedure fully correct.

In various service-oriented applications such as distributed autonomous delivery, healthcare, tourism, transportation, and many others, where service agents need to perform serial and time-bounded tasks to achieve their goals, quality of service must constantly be assured. In addition to safety requirements, such agents also need to fulfill performance requirements in order to satisfy their quality of service. This paper proposes the novel quality-aware time window temporal logic (QTWTL) by extending the traditional time window temporal logic (TWTL) with two operators for counting and aggregation operations. We also propose offline runtime monitoring algorithms for the performance monitoring of QTWTL specifications. To analyze the feasibility and efficiency of our proposed approach, we generate a large number of traces using the New York City Taxi and Limousine Commission Trip Record data, formalize their performance requirements using QTWTL, and monitor them using the proposed algorithms. The obtained results show that the monitoring algorithm has a linear space and time complexity with respect to the number of traces monitored.

Motivated by the expressiveness of hyperproperties, Hyperproperties extend trace properties to express properties of several hyper-temporal logics, such as HyperLTL [20], sets of traces, and they are increasingly popular in specifying various HyperSTL [38], and HyperMTL [11], were recently proposed by extending security and performance-related properties in domains such the conventional temporal logics such as Linear Temporal as cyber-physical systems, smart grids, and automotive. This paper Logic (LTL) [41], Signal Temporal Logic (STL) [37], and Metric Temporal introduces HyperTWTL, which extends Time Window Temporal Logic (MTL) [33], respectively. Consequently, various model Logic (TWTL)-a domain-specific formal specification language for checking techniques have been proposed for verifying HyperLTL robotics, by allowing explicit and simultaneous quantification over [20, 22, 25, 27], HyperMTL [11, 30], HyperMITL [31], HyperSTL multiple execution traces. We propose two different semantics for [38] specifications employing alternating automata, model checking, HyperTWTL, synchronous and asynchronous, based on the alignment strategy synthesis, and several other methods [32]. of the timestamps in the traces. Consequently, we demonstrate Time bounded specifications are common in many applications, the application of HyperTWTL in formalizing important such as robotics.

We introduce a formal framework (called NCDC-ASP) for representing and reasoning about cardinal directions between extended spatial objects on a plane, using Answer Set Programming (ASP). NCDC-ASP preserves the meaning of cardinal directional relations as in Cardinal Directional Calculus (CDC), and provides solutions to all consistency checking problems in CDC under various conditions (i.e., for a complete/incomplete set of basic/disjunctive CDC constraints over connected/disconnected spatial objects). In particular, NCDC-ASP models a discretized version of the consistency checking problem in ASP, over a finite grid (rather than a plane), where we provide new lower bounds on the grid size to guarantee that it correctly characterizes solutions for the consistency checking in CDC. In addition, NCDC-ASP has the following two novelties important for applications. NCDC-ASP introduces default CDC constraints to represent and reason about background or commonsense knowledge that involves default qualitative directional relations (e.g., "the ice cream truck is by default to the north of the playground" or "the keyboard is normally placed in front of the monitor"). NCDC-ASP introduces inferred CDC constraints to allow inference of missing CDC relations and to provide them as explanations. We illustrate the uses and usefulness of NCDC-ASP with interesting scenarios from the real-world. We design and develop a variety of benchmark instances, and comprehensively evaluate NCDC-ASP from the perspectives of computational efficiency.