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We show how to translate a subset of RISC-V machine code compiled from a subset of C to quadratic unconstrained binary optimization (QUBO) models that can be solved by a quantum annealing machine: given a bound $n$, there is input $I$ to a program $P$ such that $P$ runs into a given program state $E$ executing no more than $n$ machine instructions if and only if the QUBO model of $P$ for $n$ evaluates to 0 on $I$. Thus, with more qubits on the machine than variables in the QUBO model, quantum annealing the model reaches 0 (ground) energy in constant time with high probability on some input $I$ that is part of the ground state if and only if $P$ runs into $E$ on $I$ executing no more than $n$ instructions. Translation takes $\mathcal{O}(n^2)$ time effectively turning a quantum annealer into a polynomial-time symbolic execution engine and bounded model checker, eliminating their path and state explosion problems. Here, we take advantage of the fact that any machine instruction may only increase the size of the program state by a constant amount of bits. Translation time comes down from $\mathcal{O}(n^2)$ to $\mathcal{O}(n\cdot|P|)$ if memory consumption of $P$ is bounded by a constant, establishing a linear (quadratic) upper bound on quantum space, in number of qubits on a quantum annealer, in terms of algorithmic time (space) in classical computing. Our prototypical open-source toolchain translates machine code that runs on real RISC-V hardware to models that can be solved by real quantum annealing hardware, as shown in our experiments.

We provide a mathematically and conceptually robust notion of quantum superpositions of graphs. We argue that, crucially, quantum superpositions of graphs require node names for their correct alignment, which we demonstrate through a no-signalling argument. Nevertheless, node names are a fiducial construct, serving a similar purpose to the labelling of points through a choice of coordinates in continuous space. Graph renamings are understood as a change of coordinates on the graph and correspond to a natively discrete analogue of diffeomorphisms. We postulate renaming invariance as a symmetry principle in discrete topology of similar weight to diffeomorphism invariance in the continuous. We show how to impose renaming invariance at the level of quantum superpositions of graphs.

We propose a general method for distributed Bayesian model choice, using the marginal likelihood, where a data set is split in non-overlapping subsets. These subsets are only accessed locally by individual workers and no data is shared between the workers. We approximate the model evidence for the full data set through Monte Carlo sampling from the posterior on every subset generating a model evidence per subset. The results are combined using a novel approach which corrects for the splitting using summary statistics of the generated samples. Our divide-and-conquer approach enables Bayesian model choice in the large data setting, exploiting all available information but limiting communication between workers. We derive theoretical error bounds that quantify the resulting trade-off between computational gain and loss in precision. The embarrassingly parallel nature yields important speed-ups when used on massive data sets as illustrated by our real world experiments. In addition, we show how the suggested approach can be extended to model choice within a reversible jump setting that explores multiple feature combinations within one run.

We present an overview on Temporal Logic Programming under the perspective of its application for Knowledge Representation and declarative problem solving. Such programs are the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). We focus on recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL, but performs a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). We obtain a proper extension of the stable models semantics for the general case of arbitrary temporal formulas. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between infinite and finite traces. We also provide other useful results, such as the translation into other formalisms like Quantified Equilibrium Logic or Second-order LTL, and some techniques for computing temporal stable models based on automata. In a second part, we focus on practical aspects, defining a syntactic fragment called temporal logic programs closer to ASP, and explain how this has been exploited in the construction of the solver TELINGO.

This paper makes a first step towards a logic of learning from experiments. For this, we investigate formal frameworks for modeling the interaction of causal and (qualitative) epistemic reasoning. Crucial for our approach is the idea that the notion of an intervention can be used as a formal expression of a (real or hypothetical) experiment. In a first step we extend the well-known causal models with a simple Hintikka-style representation of the epistemic state of an agent. In the resulting setting, one can talk not only about the knowledge of an agent about the values of variables and how interventions affect them, but also about knowledge update. The resulting logic can model reasoning about thought experiments. However, it is unable to account for learning from experiments, which is clearly brought out by the fact that it validates the no learning principle for interventions. Therefore, in a second step, we implement a more complex notion of knowledge that allows an agent to observe (measure) certain variables when an experiment is carried out. This extended system does allow for learning from experiments. For all the proposed logical systems, we provide a sound and complete axiomatization.

We study timed systems in which some timing features are unknown parameters. Parametric timed automata (PTAs) are a classical formalism for such systems but for which most interesting problems are undecidable. Notably, the parametric reachability emptiness problem, i.e., the emptiness of the parameter valuations set allowing to reach some given discrete state, is undecidable. Lower-bound/upper-bound parametric timed automata (L/U-PTAs) achieve decidability for reachability properties by enforcing a separation of parameters used as upper bounds in the automaton constraints, and those used as lower bounds. In this paper, we first study reachability. We exhibit a subclass of PTAs (namely integer-points PTAs) with bounded rational-valued parameters for which the parametric reachability emptiness problem is decidable. Using this class, we present further results improving the boundary between decidability and undecidability for PTAs and their subclasses such as L/U-PTAs. We then study liveness. We prove that: (1) the existence of at least one parameter valuation for which there exists an infinite run in an L/U-PTA is PSPACE-complete; (2) the existence of a parameter valuation such that the system has a deadlock is however undecidable; (3) the problem of the existence of a valuation for which a run remains in a given set of locations exhibits a very thin border between decidability and undecidability.

Analogy-making is at the core of human and artificial intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper introduces from first principles an abstract algebraic framework of analogical proportions of the form `$a$ is to $b$ what $c$ is to $d$' in the general setting of universal algebra. This enables us to compare mathematical objects possibly across different domains in a uniform way which is crucial for AI-systems. It turns out that our notion of analogical proportions has appealing mathematical properties. As we construct our model from first principles using only elementary concepts of universal algebra, and since our model questions some basic properties of analogical proportions presupposed in the literature, to convince the reader of the plausibility of our model we show that it can be naturally embedded into first-order logic via model-theoretic types and prove from that perspective that analogical proportions are compatible with structure-preserving mappings. This provides conceptual evidence for its applicability. In a broader sense, this paper is a first step towards a theory of analogical reasoning and learning systems with potential applications to fundamental AI-problems like commonsense reasoning and computational learning and creativity.

Strong invariance principles describe the error term of a Brownian approximation of the partial sums of a stochastic process. While these strong approximation results have many applications, the results for continuous-time settings have been limited. In this paper, we obtain strong invariance principles for a broad class of ergodic Markov processes. The main results rely on ergodicity requirements and an application of Nummelin splitting for continuous-time processes. Strong invariance principles provide a unified framework for analysing commonly used estimators of the asymptotic variance in settings with a dependence structure. We demonstrate how this can be used to analyse the batch means method for simulation output of Piecewise Deterministic Monte Carlo samplers. We also derive a fluctuation result for additive functionals of ergodic diffusions using our strong approximation results.

We take up an idea from the folklore of Answer Set Programming, namely that choices, integrity constraints along with a restricted rule format is sufficient for Answer Set Programming. We elaborate upon the foundations of this idea in the context of the logic of Here-and-There and show how it can be derived from the logical principle of extension by definition. We then provide an austere form of logic programs that may serve as a normalform for logic programs similar to conjunctive normalform in classical logic. Finally, we take the key ideas and propose a modeling methodology for ASP beginners and illustrate how it can be used.

Sources of commonsense knowledge aim to support applications in natural language understanding, computer vision, and knowledge graphs. These sources contain complementary knowledge to each other, which makes their integration desired. Yet, such integration is not trivial because of their different foci, modeling approaches, and sparse overlap. In this paper, we propose to consolidate commonsense knowledge by following five principles. We apply these principles to combine seven key sources into a first integrated CommonSense Knowledge Graph (CSKG). We perform analysis of CSKG and its various text and graph embeddings, showing that CSKG is a well-connected graph and that its embeddings provide a useful entry point to the graph. Moreover, we show the impact of CSKG as a source for reasoning evidence retrieval, and for pre-training language models for generalizable downstream reasoning. CSKG and all its embeddings are made publicly available to support further research on commonsense knowledge integration and reasoning.