A century ago, discoveries of a serious kind of logical error made separately by several leading mathematicians led to acceptance of a sharply enhanced standard for rigor within what ultimately became the foundation for Computer Science. By 1931, Godel had obtained a definitive and remarkable result: an inherent limitation to that foundation. The resulting limitation is not applicable to actual human cognition, to even the smallest extent, unless both of these extremely brittle assumptions hold: humans are infallible reasoners and reason solely via formal inference rules. Both assumptions are contradicted by empirical data from well-known Cognitive Science experiments. This article investigates how a novel multi-part methodology recasts computability theory within Computer Science to obtain a definitive limitation whose application to human cognition avoids assumptions contradicting empirical data. The limitation applies to individual humans, to finite sets of humans, and more generally to any real-world entity.

We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). FLoP focuses on generalizing from short proofs to longer ones of similar structure. To achieve that, FLoP uses state-of-the-art RL approaches that were previously not applied in theorem proving. In particular, we show that curriculum learning significantly outperforms previous learning-based proof guidance on a synthetic dataset of increasingly difficult arithmetic problems.

We propose a set of compositional design patterns to describe a large variety of systems that combine statistical techniques from machine learning with symbolic techniques from knowledge representation. As in other areas of computer science (knowledge engineering, software engineering, ontology engineering, process mining and others), such design patterns help to systematize the literature, clarify which combinations of techniques serve which purposes, and encourage re-use of software components. We have validated our set of compositional design patterns against a large body of recent literature.

We present a fast and scalable algorithm to induce non-monotonic logic programs from statistical learning models. We reduce the problem of search for best clauses to instances of the High-Utility Itemset Mining (HUIM) problem. In the HUIM problem, feature values and their importance are treated as transactions and utilities respectively. We make use of TreeExplainer, a fast and scalable implementation of the Explainable AI tool SHAP, to extract locally important features and their weights from ensemble tree models. Our experiments with UCI standard benchmarks suggest a significant improvement in terms of classification evaluation metrics and running time of the training algorithm compared to ALEPH, a state-of-the-art Inductive Logic Programming (ILP) system.

The process of identifying changes or transformations in a scene along with the ability of reasoning about their causes and effects, is a key aspect of intelligence. In this work we go beyond recent advances in computational perception, and introduce a more challenging task, Image-based Event-Sequencing (IES). In IES, the task is to predict a sequence of actions required to rearrange objects from the configuration in an input source image to the one in the target image. IES also requires systems to possess inductive generalizability. Motivated from evidence in cognitive development, we compile the first IES dataset, the Blocksworld Image Reasoning Dataset (BIRD) which contains images of wooden blocks in different configurations, and the sequence of moves to rearrange one configuration to the other. We first explore the use of existing deep learning architectures and show that these end-to-end methods under-perform in inferring temporal event-sequences and fail at inductive generalization. We then propose a modular two-step approach: Visual Perception followed by Event-Sequencing, and demonstrate improved performance by combining learning and reasoning. Finally, by showing an extension of our approach on natural images, we seek to pave the way for future research on event sequencing for real world scenes.

Dynamic Epistemic Logic (DEL) is a family of multimodal logics that has proved to be very successful for epistemic reasoning in planning tasks. In this logic, the agent's knowledge is captured by modal epistemic operators whereas the system evolution is described in terms of (some subset of) dynamic logic modalities in which actions are usually represented as semantic objects called event models. In this paper, we study a variant of DEL, that wecall DEL[ASP], where actions are syntactically described by using an Answer Set Programming (ASP) representation instead of event models. This representation directly inherits high level expressive features like indirect effects, qualifications, state constraints, defaults, or recursive fluents that are common in ASP descriptions of action domains. Besides, we illustrate how this approach can be applied for obtaining conditional plans in single-agent, partially observable domains where knowledge acquisition may be represented as indirect effects of actions.

We introduce a new operation which can be used to compositionally construct second-order multi-hop templates in a neural model, and evaluate a number of alternative implementations, with different time and memory trade offs. These techniques scale to KBs with millions of entities and tens of millions of triples, and lead to simple models with competitive performance on several learning tasks requiring multi-hop reasoning.

Automated theorem proving in large theories can be learned via reinforcement learning over an indefinitely growing action space. In order to select actions, one performs nearest neighbor lookups in the knowledge base to find premises to be applied. Here we address the exploration for reinforcement learning in this space. Approaches (like epsilon-greedy strategy) that sample actions uniformly do not scale to this scenario as most actions lead to dead ends and unsuccessful proofs which are not useful for training our models. In this paper, we compare approaches that select premises using randomly initialized similarity measures and mixing them with the proposals of the learned model. We evaluate these on the HOList benchmark for tactics based higher order theorem proving. We implement an automated theorem prover named DeepHOL-Zero that does not use any of the human proofs and show that our improved exploration method manages to expand the training set continuously. DeepHOL-Zero outperforms the best theorem prover trained by imitation learning alone.

Artificial Intelligence has come a long way from being the stuff of science fiction movies and books to becoming an integral part of our daily lives. Today, AI is one of the fastest growing global industries. Investments and experiments in AI have been taking place all around the world. Given its unimaginably wide range of uses; AI is a field of expertise that is set to grow in a very huge way over the coming years. AI professionals are among the highest paid in the field of IT. Ans: Artificial Intelligence is a part of computer science that aims to create machine that are intelligent and seek to work and react the way humans do. Q2)What to you understand by an artificial intelligence Neural Network?

Continuous queries over data streams may suffer from blocking operations and/or unbound wait, which may delay answers until some relevant input arrives through the data stream. These delays may turn answers, when they arrive, obsolete to users who sometimes have to make decisions with no help whatsoever. Therefore, it can be useful to provide hypothetical answers - "given the current information, it is possible that X will become true at time t" - instead of no information at all. In this paper we present a semantics for queries and corresponding answers that covers such hypothetical answers, together with an online algorithm for updating the set of facts that are consistent with the currently available information.