Despite the successes of recent developments in visual AI, different shortcomings still exist; from missing exact logical reasoning, to abstract generalization abilities, to understanding complex and noisy scenes. Unfortunately, existing benchmarks, were not designed to capture more than a few of these aspects. Whereas deep learning datasets focus on visually complex data but simple visual reasoning tasks, inductive logic datasets involve complex logical learning tasks, however, lack the visual component. To address this, we propose the visual logical learning dataset, V-LoL, that seamlessly combines visual and logical challenges. Notably, we introduce the first instantiation of V-LoL, V-LoL-Trains, -- a visual rendition of a classic benchmark in symbolic AI, the Michalski train problem. By incorporating intricate visual scenes and flexible logical reasoning tasks within a versatile framework, V-LoL-Trains provides a platform for investigating a wide range of visual logical learning challenges. We evaluate a variety of AI systems including traditional symbolic AI, neural AI, as well as neuro-symbolic AI. Our evaluations demonstrate that even state-of-the-art AI faces difficulties in dealing with visual logical learning challenges, highlighting unique advantages and limitations specific to each methodology. Overall, V-LoL opens up new avenues for understanding and enhancing current abilities in visual logical learning for AI systems.

Aging societies, labor shortages and increasing wage costs call for assistance robots capable of autonomously performing a wide array of real-world tasks. Such open-ended robotic manipulation requires not only powerful knowledge representations and reasoning (KR&R) algorithms, but also methods for humans to instruct robots what tasks to perform and how to perform them. In this paper, we present a system for automatically generating executable robot control programs from human task demonstrations in virtual reality (VR). We leverage common-sense knowledge and game engine-based physics to semantically interpret human VR demonstrations, as well as an expressive and general task representation and automatic path planning and code generation, embedded into a state-of-the-art cognitive architecture. We demonstrate our approach in the context of force-sensitive fetch-and-place for Figure 1: We propose a knowledge-driven approach to convert human a robotic shopping assistant.

Tsetlin Machines (TsMs) are a promising and interpretable machine learning method which can be applied for various classification tasks. We present an exact encoding of TsMs into propositional logic and formally verify properties of TsMs using a SAT solver. In particular, we introduce in this work a notion of similarity of machine learning models and apply our notion to check for similarity of TsMs. We also consider notions of robustness and equivalence from the literature and adapt them for TsMs. Then, we show the correctness of our encoding and provide results for the properties: adversarial robustness, equivalence, and similarity of TsMs. In our experiments, we employ the MNIST and IMDB datasets for (respectively) image and sentiment classification. We discuss the results for verifying robustness obtained with TsMs with those in the literature obtained with Binarized Neural Networks on MNIST.

Studying the definability (expressibility) of logical connectives in terms of one another has a long history in logic. Proving the definability of one connective through another is usually done by providing an explicit formula that expresses one connective through others. Once such a formula is found, proving definability is usually a straightforward exercise. Proving undefinability is significantly harder and usually requires sophisticated techniques. Different domain-specific techniques have been proposed for various logical systems. Among them, the best-known is the bisimulation method for modal logics [19, 1, 2, 5, 15, 18, 4, 17, 16]. It is not clear how bisimulation can be applied to non-modal logics where completely different methods have been proposed [13, 20].

Statistical relational AI and probabilistic logic programming have so far mostly focused on discrete probabilistic models. The reasons for this is that one needs to provide constructs to succinctly model the independencies in such models, and also provide efficient inference. Three types of independencies are important to represent and exploit for scalable inference in hybrid models: conditional independencies elegantly modeled in Bayesian networks, context-specific independencies naturally represented by logical rules, and independencies amongst attributes of related objects in relational models succinctly expressed by combining rules. This paper introduces a hybrid probabilistic logic programming language, DC#, which integrates distributional clauses' syntax and semantics principles of Bayesian logic programs. It represents the three types of independencies qualitatively. More importantly, we also introduce the scalable inference algorithm FO-CS-LW for DC#. FO-CS-LW is a first-order extension of the context-specific likelihood weighting algorithm (CS-LW), a novel sampling method that exploits conditional independencies and context-specific independencies in ground models. The FO-CS-LW algorithm upgrades CS-LW with unification and combining rules to the first-order case.

Effective decision-making requires the use of knowledge. This has been a clear, and long-standing principle in AI research, as reflected, for example, in the seminal early work on knowledge and AI--summarized by Brachman and Levesque (1985)--and the thriving Knowledge Representation and Reasoning and the Uncertainty in AI communities. However, the message has been somewhat diluted as data-driven statistical learning has become increasingly pervasive across AI. Nevertheless, the idea that reasoning and learning need to work together (Khardon and Roth, 1996; Roth, 1996) and that knowledge representation is a crucial bridge between them has not been lost. One area where the link between learning, representation, and reasoning has been shown to be essential and has been studied extensively is Natural Language Processing (NLP), and in particular, the area of Structured Output Prediction within NLP. In structured problems, there is a need to assign values to multiple random variables that are interrelated. Examples include extracting multiple relations among entities in a document, where a the two arguments for a relation such as born-in cannot refer to people, or co-reference resolution, where gender agreement must be maintained when determining that a specific pronoun refers to a given entity. In these, and many other such problems, it is natural to represent knowledge as Boolean functions over propositional variables. These functions would express knowledge, for example, of the form "if the relation between two entities is born-in, then its arguments must be a person and a location" (formalized as functions such as x

This paper describes an evaluation of Automated Theorem Proving (ATP) systems on problems taken from the QMLTP library of first-order modal logic problems. Principally, the problems are translated to higher-order logic in the TPTP language using an embedding approach, and solved using higher-order logic ATP systems. Additionally, the results from native modal logic ATP systems are considered, and compared with those from the embedding approach. The findings are that the embedding process is reliable and successful, the choice of backend ATP system can significantly impact the performance of the embedding approach, native modal logic ATP systems outperform the embedding approach, and the embedding approach can cope with a wider range modal logics than the native modal systems considered.

This paper is a contribution to the research on dynamics in assumption-based argumentation (ABA). We investigate situations where a given knowledge base undergoes certain changes. We show that two frequently investigated problems, namely enforcement of a given target atom and deciding strong equivalence of two given ABA frameworks, are intractable in general. Notably, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semanticspreserving instances. Inspired by this observation, we search for tractable fragments for ABA frameworks by means of the instantiated AFs. We argue that the usual instantiation procedure is not suitable for the investigation of dynamic scenarios since too much information is lost when constructing the abstract framework. We thus consider an extension of AFs, called cvAFs, equipping arguments with conclusions and vulnerabilities in order to better anticipate their role after the underlying knowledge base is extended. We investigate enforcement and strong equivalence for cvAFs and present syntactic conditions to decide them. We show that the correspondence between cvAFs and ABA frameworks is close enough to capture dynamics in ABA. This yields the desired tractable fragment. We furthermore discuss consequences for the corresponding problems for logic programs.

In this paper, a modification of A* algorithm is considered for the shortest path problem. A weightage is introduced in the heuristic part of the A* algorithm to improve its efficiency. An application of the algorithm is considered for UAV path planning wherein velocity is taken as the weigtage to the heuristic. At the outset, calculus of variations based Lagrange's equation was used to identify velocity as the decisive factor for the dynamical system. This approach would be useful for other problems as well to improve the efficiency of algorithms in those areas.

We investigate a version of linear temporal logic whose propositional fragment is G\"odel-Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics: first a real-valued semantics, where statements have a degree of truth in the real unit interval and second a `bi-relational' semantics. We then show that these two semantics indeed define one and the same logic: the statements that are valid for the real-valued semantics are the same as those that are valid for the bi-relational semantics. This G\"odel temporal logic does not have any form of the finite model property for these two semantics: there are non-valid statements that can only be falsified on an infinite model. However, by using the technical notion of a quasimodel, we show that every falsifiable statement is falsifiable on a finite quasimodel, yielding an algorithm for deciding if a statement is valid or not. Later, we strengthen this decidability result by giving an algorithm that uses only a polynomial amount of memory, proving that G\"odel temporal logic is PSPACE-complete. We also provide a deductive calculus for G\"odel temporal logic, and show this calculus to be sound and complete for the above-mentioned semantics, so that all (and only) the valid statements can be proved with this calculus.