A hallmark of human cognition is the ability to continually acquire and distill observations of the world into meaningful, predictive theories. In this paper we present a new mechanism for logical theory acquisition which takes a set of observed facts and learns to extract from them a set of logical rules and a small set of core facts which together entail the observations. Our approach is neuro-symbolic in the sense that the rule pred- icates and core facts are given dense vector representations. The rules are applied to the core facts using a soft unification procedure to infer additional facts. After k steps of forward inference, the consequences are compared to the initial observations and the rules and core facts are then encouraged towards representations that more faithfully generate the observations through inference. Our approach is based on a novel neural forward-chaining differentiable rule induction network. The rules are interpretable and learned compositionally from their predicates, which may be invented. We demonstrate the efficacy of our approach on a variety of ILP rule induction and domain theory learning datasets.

We study dynamic changes of agents' observational power in logics of knowledge and time. We consider CTL*K, the extension of CTL* with knowledge operators, and enrich it with a new operator that models a change in an agent's way of observing the system. We extend the classic semantics of knowledge for perfect-recall agents to account for changes of observation, and we show that this new operator strictly increases the expressivity of CTL*K. We reduce the model-checking problem for our logic to that for CTL*K, which is known to be decidable. This provides a solution to the model-checking problem for our logic, but its complexity is not optimal. Indeed we provide a direct decision procedure with better complexity.

In this paper, we investigate the problem of synthesizing strategies for linear temporal logic (LTL) specifications that are interpreted over finite traces -- a problem that is central to the automated construction of controllers, robot programs, and business processes. We study a natural variant of the finite LTL synthesis problem in which strategy guarantees are predicated on specified environment behavior. We further explore a quantitative extension of LTL that supports specification of quality measures, utilizing it to synthesize high-quality strategies. We propose new notions of optimality and associated algorithms that yield strategies that best satisfy specified quality measures. Our algorithms utilize an automata-game approach, positioning them well for future implementation via existing state-of-the-art techniques.

It has been argued that it is much easier to convey logical statements using rules rather than OWL (or description logic (DL)) axioms. Based on recent theoretical developments on transformations between rules and DLs, we have developed ROWLTab, a Protege plugin that allows users to enter OWL axioms by way of rules; the plugin then automatically converts these rules into OWL 2 DL axioms if possible, and prompts the user in case such a conversion is not possible without weakening the semantics of the rule. In this paper, we present ROWLTab, together with a user evaluation of its effectiveness compared to entering axioms using the standard Protege interface. Our evaluation shows that modeling with ROWLTab is much quicker than the standard interface, while at the same time, also less prone to errors for hard modeling tasks.

Comprehending procedural text, e.g., a paragraph describing photosynthesis, requires modeling actions and the state changes they produce, so that questions about entities at different timepoints can be answered. Although several recent systems have shown impressive progress in this task, their predictions can be globally inconsistent or highly improbable. In this paper, we show how the predicted effects of actions in the context of a paragraph can be improved in two ways: (1) by incorporating global, commonsense constraints (e.g., a non-existent entity cannot be destroyed), and (2) by biasing reading with preferences from large-scale corpora (e.g., trees rarely move). Unlike earlier methods, we treat the problem as a neural structured prediction task, allowing hard and soft constraints to steer the model away from unlikely predictions. We show that the new model significantly outperforms earlier systems on a benchmark dataset for procedural text comprehension (+8% relative gain), and that it also avoids some of the nonsensical predictions that earlier systems make.

In recent years, non-monotonic Inductive Logic Programming has received growing interest. Specifically, several new learning frameworks and algorithms have been introduced for learning under the answer set semantics, allowing the learning of common-sense knowledge involving defaults and exceptions, which are essential aspects of human reasoning. In this paper, we present a noise-tolerant generalisation of the learning from answer sets framework. We evaluate our ILASP3 system, both on synthetic and on real datasets, represented in the new framework. In particular, we show that on many of the datasets ILASP3 achieves a higher accuracy than other ILP systems that have previously been applied to the datasets, including a recently proposed differentiable learning framework.

Probabilistic Logic Programming extends Logic Programming by enabling the representation of uncertain information. Probabilistic Logic Programming is at the intersection of two wider research fields: the integration of logic and probability and Probabilistic Programming. Logic enables the representation of complex relations among entities while probability theory is useful for model uncertainty over attributes and relations. Combining the two is a very active field of study. Probabilistic Programming extends programming languages with probabilistic primitives that can be used to write complex probabilistic models.

Detecting small sets of relevant patterns from a given dataset is a central challenge in data mining. The relevance of a pattern is based on user-provided criteria; typically, all patterns that satisfy certain criteria are considered relevant. Rule-based languages like Answer Set Programming (ASP) seem well-suited for specifying such criteria in a form of constraints. Although progress has been made, on the one hand, on solving individual mining problems and, on the other hand, developing generic mining systems, the existing methods either focus on scalability or on generality. In this paper we make steps towards combining local (frequency, size, cost) and global (various condensed representations like maximal, closed, skyline) constraints in a generic and efficient way. We present a hybrid approach for itemset, sequence and graph mining which exploits dedicated highly optimized mining systems to detect frequent patterns and then filters the results using declarative ASP. To further demonstrate the generic nature of our hybrid framework we apply it to a problem of approximately tiling a database. Experiments on real-world datasets show the effectiveness of the proposed method and computational gains for itemset, sequence and graph mining, as well as approximate tiling.

Answer Set Programming (ASP) is a powerful modeling formalism for combinatorial problems. However, writing ASP models is not trivial. We propose a novel method, called Sketched Answer Set Programming (SkASP), aiming at supporting the user in resolving this issue. The user writes an ASP program while marking uncertain parts open with question marks. In addition, the user provides a number of positive and negative examples of the desired program behaviour. The sketched model is rewritten into another ASP program, which is solved by traditional methods. As a result, the user obtains a functional and reusable ASP program modelling her problem. We evaluate our approach on 21 well known puzzles and combinatorial problems inspired by Karp's 21 NP-complete problems and demonstrate a use-case for a database application based on ASP.

The increasing incorporation of Artificial Intelligence in the form of automated systems into decision-making procedures highlights not only the importance of decision theory for automated systems but also the need for these decision procedures to be explainable to the people involved in them. Traditional realist accounts of explanation, wherein explanation is a relation that holds (or does not hold) eternally between an explanans and an explanandum, are not adequate to account for the notion of explanation required for artificial decision procedures. We offer an alternative account of explanation as used in the context of automated decision-making that makes explanation an epistemic phenomenon, and one that is dependent on context. This account of explanation better accounts for the way that we talk about, and use, explanations and derived concepts, such as `explanatory power', and also allows us to differentiate between reasons or causes on the one hand, which do not need to have an epistemic aspect, and explanations on the other, which do have such an aspect. Against this theoretical backdrop we then review existing approaches to explanation in Artificial Intelligence and Machine Learning, and suggest desiderata which truly explainable decision systems should fulfill.