Possibilistic logic is the most popular approach to represent and reason with uncertain and partially inconsistent knowledge. Regarding normal forms, the encoding of real-world problems does usually not result in a clausal formula and although a possibility nonclausal formula is theoretically equivalent to some possibilistic clausal formula [26, 22], approaches needing clausal form transformations are practically infeasible or have experimentally shown to be highly inefficient as discussed below. Two kinds of clausal form transformation are known: (1) one is based on the repetitive application of the distributive laws to the input non-clausal formula until a logically equivalent clausal formula is obtained; and (2) the other transformation, Tsetin-transformation [59], is based on recursively substituting sub-formulas in the input non-clausal formula by fresh literals until obtaining an equi-satisfiable, but not equivalent, clausal formula.

This course is being covered by a Semiconductor Industry Professional with about 4 years of industrial experience with Masters Degree in Embedded Systems and will have elements of practical application throughout the course for better understanding. Digital Electronics course is essential for many graduate courses and forms the basis for many other courses. It's important to get these basics right to build strong foundation. You can quickly go through introductory lectures which are available for preview and signup for the rest of the course! Check out the initial few lectures for dis counts on the course!

Boolean matching is significant to digital integrated circuits design. An exhaustive method for Boolean matching is computationally expensive even for functions with only a few variables, because the time complexity of such an algorithm for an n-variable Boolean function is $O(2^{n+1}n!)$. Sensitivity is an important characteristic and a measure of the complexity of Boolean functions. It has been used in analysis of the complexity of algorithms in different fields. This measure could be regarded as a signature of Boolean functions and has great potential to help reduce the search space of Boolean matching. In this paper, we introduce Boolean sensitivity into Boolean matching and design several sensitivity-related signatures to enhance fast Boolean matching. First, we propose some new signatures that relate sensitivity to Boolean equivalence. Then, we prove that these signatures are prerequisites for Boolean matching, which we can use to reduce the search space of the matching problem. Besides, we develop a fast sensitivity calculation method to compute and compare these signatures of two Boolean functions. Compared with the traditional cofactor and symmetric detection methods, sensitivity is a series of signatures of another dimension. We also show that sensitivity can be easily integrated into traditional methods and distinguish the mismatched Boolean functions faster. To the best of our knowledge, this is the first work that introduces sensitivity to Boolean matching. The experimental results show that sensitivity-related signatures we proposed in this paper can reduce the search space to a very large extent, and perform up to 3x speedup over the state-of-the-art Boolean matching methods.

This paper presents a comprehensive framework for run-time self-checking of logical agents, by means of temporal axioms to be dynamically checked. These axioms are specified by using an agent-oriented interval temporal logic defined to this purpose. We define syntax, semantics and pragmatics for this new logic, specifically tailored for application to agents. In the resulting framework, we encompass and extend our past work.

Visual question answering (VQA) has been gaining a lot of traction in the machine learning community in the recent years due to the challenges posed in understanding information coming from multiple modalities (i.e., images, language). In VQA, a series of questions are posed based on a set of images and the task at hand is to arrive at the answer. To achieve this, we take a symbolic reasoning based approach using the framework of formal logic. The image and the questions are converted into symbolic representations on which explicit reasoning is performed. We propose a formal logic framework where (i) images are converted to logical background facts with the help of scene graphs, (ii) the questions are translated to first-order predicate logic clauses using a transformer based deep learning model, and (iii) perform satisfiability checks, by using the background knowledge and the grounding of predicate clauses, to obtain the answer. Our proposed method is highly interpretable and each step in the pipeline can be easily analyzed by a human. We validate our approach on the CLEVR and the GQA dataset. We achieve near perfect accuracy of 99.6% on the CLEVR dataset comparable to the state of art models, showcasing that formal logic is a viable tool to tackle visual question answering. Our model is also data efficient, achieving 99.1% accuracy on CLEVR dataset when trained on just 10% of the training data.

We propose two new doxastic extensions of fuzzy \L ukasiewicz logic in which their semantics are Kripke-based with both fuzzy atomic propositions and fuzzy accessibility relations. A class of these extensions is equipped with uninformed belief operator, and the other class is based on a new notion of skeptical belief. We model a fuzzy version of muddy children problem and a CPA-security experiment using uniformed belief and skeptical belief, respectively. Moreover, we prove soundness and completeness for both of these belief extensions.

A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic. It is demonstrated (i) how meta-theoretical studies can be automated this way, and (ii) how non-trivial reasoning in the target logic (public announcement logic), required e.g. to obtain a convincing encoding and automation of the wise men puzzle, can be realized. Key to the presented semantical embedding is that evaluation domains are modeled explicitly and treated as an additional parameter in the encodings of the constituents of the embedded target logic; in previous related works, e.g. on the embedding of normal modal logics, evaluation domains were implicitly shared between meta-logic and target logic. The work presented in this article constitutes an important addition to the pluralist LogiKEy knowledge engineering methodology, which enables experimentation with logics and their combinations, with general and domain knowledge, and with concrete use cases -- all at the same time.

The goal of program synthesis from examples is to find a computer program that is consistent with a given set of input-output examples. Most learning-based approaches try to find a program that satisfies all examples at once. Our work, by contrast, considers an approach that breaks the problem into two stages: (a) find programs that satisfy only one example, and (b) leverage these per-example solutions to yield a program that satisfies all examples. We introduce the Cross Aggregator neural network module based on a multi-head attention mechanism that learns to combine the cues present in these per-example solutions to synthesize a global solution. Evaluation across programs of different lengths and under two different experimental settings reveal that when given the same time budget, our technique significantly improves the success rate over PCCoder [32] and other ablation baselines.

Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL formulas for classifying traces; despite a growing interest of the research community, existing solutions suffer from two limitations: they do not scale beyond small formulas, and they may exhaust computational resources without returning any result. We introduce a new algorithm addressing both issues: our algorithm is able to construct formulas an order of magnitude larger than previous methods, and it is anytime, meaning that it in most cases successfully outputs a formula, albeit possibly not of minimal size. We evaluate the performances of our algorithm using an open source implementation against publicly available benchmarks.

The OSSU curriculum is a complete education in computer science using online materials. It's for those who want a proper, well-rounded grounding in concepts fundamental to all computing disciplines, and for those who have the discipline, will, and (most importantly!) good habits to obtain this education largely on their own, but with support from a worldwide community of fellow learners. It is designed according to the degree requirements of undergraduate computer science majors, minus general education (non-CS) requirements, as it is assumed most of the people following this curriculum are already educated outside the field of CS. The courses themselves are among the very best in the world, often coming from Harvard, Princeton, MIT, etc., but specifically chosen to meet the following criteria. When no course meets the above criteria, the coursework is supplemented with a book.