Aiding an Introduction to Formal Reasoning Within a First-Year Logic Course for CS Majors Using a Mobile Self-Study App

Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a sequent calculus for first-order logic, formalized in the interactive proof assistant Isabelle/HOL. Our formalization is based on work by Stefan Berghofer, which we have since updated to use Isabelle's declarative proof style Isar (Archive of Formal Proofs, Entry FOL-Fitting, August 2007 / July 2018). We represent variables with de Bruijn indices; this makes substitution under quantifiers less intuitive for a human reader. However, the nature of natural numbers yields an elegant solution when compared to implementations of substitution using variables represented by strings. The sequent calculus considered has the special property of an always empty antecedent and a list of formulas in the succedent. We obtain the proofs of soundness and completeness for the sequent calculus as a derived result of the inverse duality of its tableau counterpart. We strive to not only present the results of the proofs of soundness and completeness, but also to provide a deep dive into a programming-like approach to the formalization of first-order logic syntax, semantics and the sequent calculus. We use the formalization in a bachelor course on logic for computer science and discuss our experiences.

The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.

The role of games in computing science has been given some consideration in the literature. We aim to design games that can be used for teaching logic. Specifically, we build on the Minefield game used in the Stanford Intro to Logic course, and present a version, which we call MineFOL, that incorporates time constraints. We also move beyond the Stanford examples in that we provide a formalisation of the game, with a view to eventually generating game instances automatically as well as from user input, and show how MineFOL can be used as a learning tool. We also developed an online platform supporting learners in at least three ways. First, the learners can practice reasoning in First Order Logic (FOL) and proving strategies such as resolution through various MineFOL games. Second, the learners can practice formalisation in FOL, by allowing learners to build their own games. Third, the learners become aware of the need of interleaving various technologies to solve a logicbased task. In this line, MineFOL is formalised in such way to allow augmenting reasoning in FOL with search strategies.

This is a textbook based on an interdisciplinary (advanced undergraduate level) course that was originally taught by the three authors at Duke. It is intended for many different disciplines. Even though it covers mathematical and philosophical topics, it occasionally still feels like a textbook whose origins lie more in computer science than in the other disciplines. This isn’t even surprising, for an interdisciplinary focus on logic easily draws one towards computer science and artificial intelligence. In three parts, each written by one of the authors, a three-chapter overview is given of the topics of proof-theory, computability-theory and philosophical logic. Yet, rather than a juxtaposition of logical, mathematical, computational, and philosophical subjects, this textbook isn’t merely intended as an illustration of how logic is relevant for many different disciplines, but forms the basis for a different kind of introduction to logic. This reviewer surely applauds the intent to teach logic to philosophers more like we would teach it to computer scientists—with an emphasis on what it allows us to achieve, but also to teach it to computer scientists more like we would (or ought to) teach it to philosophers—with more attention to the diversity in logic than to the dominant background role of classical logic. While Part 1 is concerned with proof-theory, with chapters on classical propositional logic, first-order logic, and Prolog, it also double-tasks as an introduction to formal logic. Thus, chapter 1 reviews the language and semantics of propositional logic, and even goes on to prove two basic meta-theoretical results by

Many researchers regarded that problem solving skill is one of the most important learning outcomes to help students adapt to the learning and working environment (Xiao et al, 2019). Through reading a large number of articles and experimental research, this study finds that currently the development of and research on problem-solving skill in university students who are major in computer science in digital logic course in Inner Mongolia is limited, especially in the context of STEM education. STEM education is currently widely valued in the K12 stage, but the STEM literacy of college students also needs to be paid attention to. There is an important need for developing university students’ problem-solving skill systematically and effectively, revealing the importance of this research. In the research field, process of engineering design was designed to developing students’ problem-solving skill. In order to have an in-depth understanding of the research questions, mixed methods were adopted. Students were divided into 2 groups: Experimental Group and the Control Group. The participants were 1 teacher and 140 students at university second-year at a university in Inner Mongolia. To collect reliable and valid data, standardized test of problem-solving skill, teacher interview form was designed. Independent T-test was used to analyze the quantitative data.

Density elimination by substitutions is introduced as a uniform method for removing applications of the Takeuti-Titani density rule from proofs in first-order hypersequent calculi. For a large class of calculi, density elimination by this method is guaranteed by known sufficient conditions for cut-elimination. Moreover, adding the density rule to any axiomatic extension of a simple first-order logic gives a logic that is rational complete; i.e., complete with respect to linearly and densely ordered algebras: a precursor to showing that it is a fuzzy logic (complete for algebras with a real unit interval lattice reduct). Hence the sufficient conditions for cut-elimination guarantee rational completeness for a large class of first-order substructural logics.

It is well-known that almost all nonmonotonic formalisms have a higher worst-case complexity than classical reasoning. In some sense, this observation denies one of the original motivations of nonmonotonic systems, which was the expectation taht nonmonotonic rules should help to speed-up the reasoning process, and not make it more difficult. In this paper, we look at this issue from a proof-theoretical perspective. We consider analytic calculi for certain nonmonotonic logis and analyze to what extent the presence of nonmonotonic rules can simplify the search for proofs. In particular, we show that there are classes of first-order formulae which have only extremely long “classical” proofs, i.e., proofs without applications of nonmonotonic rules, but there are short proofs using nonmonotonic inferences. Hence,despite the increase of complexity in the worst case, there are instances where nonmonotonic reasoning can be much simpler than classical (cut-free) reasoning.

We formalize in Isabelle/HOL soundness and completeness of a one-sided sequent calculus for first-order logic. The completeness is shown via a translation from a semantic tableau calculus, whose completeness proof we base on the theory entry ‘First-Order Logic According to Fitting’ by Berghofer in the Archive of Formal Proofs. The calculi and proof techniques are taken from Ben-Ari’s textbook Mathematical Logic for Computer Science (Springer, 2012). We thereby demonstrate that Berghofer’s approach works not only for natural deduction but also constitutes a framework for mechanically checked completeness proofs for a range of proof systems.

First-order temporal logic is a concise and powerful notation, with many potential applications in both Computer Science and Artificial Intelligence. While the full logic is highly complex, recent work on monodic first-order temporal logics has identified important enumerable and even decidable fragments. In this paper, we develop a clausal resolution method for the monodic fragment of first-order temporal logic over expanding domains. We first define a normal form for monodic formulae and then introduce novel resolution calculi that can be applied to formulae in this normal form. We state correctness and completeness results for the method. We illustrate the method on a comprehensive example. The method is based on classical first-order resolution and can, thus, be efficiently implemented.

Our theorem proving system named TTP (which is short for Teaching Theorem Proving) can construct the natural deduction proofs of the first-order logic formulas with quantifiers. It is written in CLISP. It has 4 learning models. Students can use the system to do their logic homework step by step and learn the skills of proving logic theorems. If they don't know how to prove the theorems, they can ask for hints. In our university about 300 students used the system to learn logic and do homework during 3 years, they did 2000 problems in logic.

In latest paper “Commonsense visual sensemaking for autonomous driving: on generalized neuro-symbolic online abduction integrating vision and semantics”, which appeared in journal “Artificial intelligence’’(Vol.299,2021), the authors claimed that It incorporates the latest technologies in visual computing and has been developed as a modular framework that can be generally used in hybrid architectures for real-time perception and control. It has been developed as a modular framework that can be generally used in hybrid architectures for real-time perception and control. This advancement represents a useful side of symbolism.Research on the visual computation has received a great deal of attention The demands on human-based cognitive computing are very high. for example, the implementation of autonomous driving functions depends on the effective cooperation of three components: perception, decision making and execution. The perception layer identifies people, objects, and signs on the road by simulating the human eye through multi-dimensional sensors; the decision layer evaluates and makes decisions through pre-processing such as algorithm fusion and feature extraction; the data is fused and output to each control unit in the execution layer; and finally, the hardware mechanism in the execution layer makes feedback actions to realize the full set of autonomous driving operations.In this work, we try to show that this kind of symbolism framework will encounter the so-called “the framing problem” as earlier attempts to formalize the changes of knowledge in event flows. The framing problem is the problem of finding a sufficient set of axioms for a feasible description for environments of the robot or automatic driving. The framing problem is naturally not a problem for connectionism, because the mathematical basis behind it is not formal logic. But among old-school AI, formal logic is still dominant, and implicit in the framing problem is also the flaw in old-school AI's use of symbolic computation as a model of the mind and perception. While end-to-end vision and control based on deep learning has (arguably) been successful for self-driving cars, integrating hybrid vision and semantic solutions at each step, there are clear needs in fulfilling the fundamental legal and ethical responsibilities involving interpretable, human-centered AI and industrialization. However, other paradigms may be worth adopting, for example, the abstract neuro-symbolic approach to online visual perception using answer set programming (ASP) is systematically formalized and fully implemented.In fact, the framing problem describes the problem of expressing facts about the world using first-order logic (FOL). Representing the state of a robot or an automatic driving in traditional FOL requires the use of several axioms that simply imply that things in the environment do not change arbitrarily. For example, we describe a 'block world' in terms of rules about stacking blocks on top of each other. In the FOL system, other axioms need to be used to infer the environment (for example, blocks cannot change position unless they are moved).

In this paper, we investigate an extended first-order Belnap-Dunn logic with classical negation. We introduce a Gentzen-type sequent calculus FBD+ for this logic and prove theorems for syntactically and semantically embedding FBD+ into a Gentzen-type sequent calculus for first-order classical logic. Moreover, we show the cut-elimination theorem for FBD+ and prove the completeness theorems with respect to both valuation and many-valued semantics for FBD+.

Human-computer interaction for virtual-real fusion

Introduction: The paper explores the trends in the field of artificial intelligence, especially analyzing the improvements in deep learning and machine learning that are revolutionizing the computer science discipline. The study gives details of the current trends and new approaches, possible uses, and other possible advancements. The author discusses a literature review incorporating trends identified in the prior year to discuss what these trends mean for academia and industry as well as the future of AI in computer science. Artificial intelligence has developed quite fast to be one of the key factors in the progress of computer science. Out of all the subfields of AI, DL and ML are receiving substantial attention from academicians as well as industrialists owing to the game-changing effects that these two fields have brought in data processing, decision-making, and automation zones. These technologies have not only helped transform conventional solution-seeking procedures in computer science but have also facilitated various new courses for research. Methodology: This work employs the literature review and analysis from 2015 to 2024 approach for the analysis of current advancements and emerging trends in deep learning and machine learning in computer science. The analysis of the research papers published in recent years, the industry reports, and case studies in the paper presents the views seeking to understand the state of AI in computer science. The examination is built based on categories, which are algorithmic improvement, real-world uses, and artificial intelligence implementation across industries. This approach means a systematic assessment of how deep learning and machine learning affect the field for better. Conclusion: An analysis of the trends in inventiveness of AI shows that the future of AI, especially in areas such as deep learning as well as machine learning, indicates increased inventiveness at a very impressive pace. It is one thing to use these technologies to progress computer sciences to the limits of what is possible today. It is clearly seen that the future of AI heavily relies on the future advancement of deep learning and machine learning, where it is anticipated to increase in its importance within artificial intelligence. The findings of this paper affirm the necessity to advance the studies of the specific areas of artificial intelligence proposed and call for interdisciplinarity to harness the potential of artificial intelligence for computer science.

Artificial intelligence (AI) technologies are advancing swiftly, both in terms of quantity and quality. Students must possess a solid understanding, abilities, and skills to successfully employ them. Therefore, the purpose of this quantitative study is to examine students’ AI literacy, including AI technological understanding, its practical application, critical appraisal, and its effects on students’ AI output quality, self-efficacy, and academic performance. Moreover, this research examines the effects of students’ AI self-efficacy and output quality on their academic achievement. An online survey was used to gather responses from 286 Austrian university students. Structural equation modeling was performed to test the research model. The findings indicate that AI technical understanding and the practical application significantly and positively influenced AI self-efficacy, while AI practical application had a significant and positive influence on both, AI self-efficacy and AI output quality. AI critical appraisal significantly and negatively impacted AI self-efficacy and AI output quality, whereas AI technical understanding, critical appraisal, practical application, self-efficacy, and output quality had an insignificant effect on students’ academic performance. The findings of this study may deepen the understanding of students’ AI literacy, contribute to the literature in this relatively new academic field, and help clarify the contradictory findings on the effects of AI-powered technology use on students’ learning outcomes. This research can also help integrate AI-powered tools into education effectively and improve students’ AI literacy so they can use them ethically and effectively. The results may also help revise and create new AI policies, curricula, and educational initiatives.