Computer Science

Over the last years, there has been increasing research on the scaling behaviour of statistical relational representations with the size of the domain, and on the connections between domain size dependence and lifted inference. In particular, the asymptotic behaviour of statistical relational representations has come under scrutiny, and projectivity was isolated as the strongest form of domain size independence. In this contribution we show that every probabilistic logic program under the distribution semantics is asymptotically equivalent to a probabilistic logic program consisting only of determinate clauses over probabilistic facts. To facilitate the application of classical results from finite model theory, we introduce the abstract distribution semantics, defined as an arbitrary logical theory over probabilistic facts to bridge the gap to the distribution semantics underlying probabilistic logic programming. In this representation, determinate logic programs correspond to quantifier-free theories, making asymptotic quantifier results avilable for use. We can conclude that every probabilistic logic program inducing a projective family of distributions is in fact captured by this class, and we can infer interesting consequences for the expressivity of probabilistic logic programs as well as for the asymptotic behaviour of probabilistic rules.

Monitors are a key tool in the field of runtime verification, where they are used to check for system properties by analysing execution traces generated by processes. Work on runtime monitoring carried out in a series of papers by Aceto et al. has specified monitors using a variation on the regular fragment of Milner's CCS and studied two trace-based notions of equivalence over monitors, namely verdict and ω -verdict equivalence. This article is devoted to the study of the equational logic of monitors modulo those two notions of equivalence. It presents complete equational axiomatizations of verdict and ω -verdict equivalence for closed and open terms over recursion-free monitors.

This is an informal survey of progress in Weihrauch complexity (cf arXiv:1707.03202) in the period 2018-2020. Open questions are emphasised.

Analogy-making is at the core of human intelligence and creativity with applications to such diverse tasks as commonsense reasoning, learning, language acquisition, and story telling. This paper contributes to the foundations of artificial general intelligence by introducing 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. The main idea is to define solutions to analogical equations in terms of maximal sets of algebraic justifications, which amounts to deriving abstract terms of concrete elements from a `known' source domain which can then be instantiated in an `unknown' target domain to obtain analogous elements. It turns out that our notion of analogical proportions has appealing mathematical properties. For example, we show that analogical proportions preserve functional dependencies across different domains, which is desirable. We study Lepage's axioms of analogical proportions and argue why we disagree with his symmetry, central permutation, strong reflexivity, and strong determinism axioms. We compare our framework with two prominent and recently introduced frameworks of analogical proportions from the literature in the concrete domains of sets and numbers, and we show that in each case we either disagree with the notion from the literature justified by some plausible counter-example or we can show that our model yields strictly more reasonable solutions. This provides 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.

We present a bisimulation relation for neighbourhood spaces, a generalisation of topological spaces. We show that this notion, path preserving bisimulation, preserves formulas of the spatial logic SLCS. We then use this preservation result to show that SLCS cannot express standard topological properties such as separation and connectedness. Furthermore, we compare the bisimulation relation with standard modal bisimulation and modal bisimulation with converse on graphs and prove it coincides with the latter.

The timed position of documents retrieved by learning to rank models can be seen as signals. Signals carry useful information such as drop or rise of documents over time or user behaviors. In this work, we propose to use the logic formalism called Signal Temporal Logic (STL) to characterize document behaviors in ranking accordingly to the specified formulas. Our analysis shows that interesting document behaviors can be easily formalized and detected thanks to STL formulas. We validate our idea on a dataset of 100K product signals. Through the presented framework, we uncover interesting patterns, such as cold start, warm start, spikes, and inspect how they affect our learning to ranks models.

Ontology-mediated query answering (OMQA) is a promising approach to data access and integration that has been actively studied in the knowledge representation and database communities for more than a decade. The vast majority of work on OMQA focuses on conjunctive queries, whereas more expressive queries that feature counting or other forms of aggregation remain largely unex-plored. In this paper, we introduce a general form of counting query, relate it to previous proposals, and study the complexity of answering such queries in the presence of DL-Lite ontologies. As it follows from existing work that query answering is intractable and often of high complexity, we consider some practically relevant restrictions, for which we establish improved complexity bounds.

This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming P≠NP and the Unique Games Conjecture, the best polynomial time approximation algorithm for any CSP is given by solving and rounding a specific semidefinite programming relaxation. We prove an analogue of this result for algorithms that are definable as FPC-interpretations, which holds without the assumption that P≠NP . While we are not able to drop (an FPC-version of) the Unique Games Conjecture as an assumption, we do present some partial results toward proving it. Specifically, we give a novel construction which shows that, for all α>0 , there exists a positive integer q=poly( 1 α ) such that no there is no FPC-interpretation giving an α -approximation of Unique Games on a label set of size q .

We introduce arboreal categories, which have an intrinsic process structure, allowing dynamic notions such as bisimulation and back-and-forth games, and resource notions such as number of rounds of a game, to be defined. These are related to extensional or "static" structures via arboreal covers, which are resource-indexed comonadic adjunctions. These ideas are developed in a very general, axiomatic setting, and applied to relational structures, where the recently introduced comonadic constructions for pebbling, Ehrenfeucht-Fraïssé and modal bisimulation games are recovered, showing that many of the fundamental notions of finite model theory and descriptive complexity arise from instances of arboreal covers.

We present a new approach to conformance testing of black-box reactive systems. We consider system specifications written as linear temporal logic formulas to generate tests as sequences of input/output pairs: inputs are extracted from the Buchi automata corresponding to the specifications, and outputs are obtained by feeding the inputs to the systems. Conformance is checked by comparing input/output sequences with automata traces to detect violations of the specifications. We consider several criteria for extracting tests and for stopping generation, and we compare them experimentally using both indicators of coverage and error-detection. The results show that our methodology can generate test suites with good system coverage and error-detection capability.