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Language, Proof and Logic

Dave Barker-Plummer and John Etchemendy

In this course you will be introduced to the concepts and techniques used in logic. We will start right from the beginning, assuming no prior exposure to this or similar material, and progress through discussions of the proof and model theories of propositional and first-order logic.

All learners receive a complete textbook and software package ($55.00 value).

We will proceed by giving a theory of truth, and of logical consequence, based on a formal language called FOL (the language of First-Order Logic). We adopt a formal language for making statements, since natural languages (like English, for example) are far too vague and ambiguous for us to analyze sufficiently. Armed with the formal language, we will be able to model the notions of truth, proof and consequence, among others.

What you'll learn

While logic is technical in nature, the key concepts in the course will be developed by considering natural English statements, and we will focus the relationships between such statements and their FOL counterparts. The goal of the course is to show how natural English statements and arguments can be formalized and analyzed.

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Examines logic, which is standard in computer science

Explores logic, which is foundational to most advanced math

Teaches logic, which is useful in semantic web understanding

Taught by Dave Barker-Plummer, who are recognized for their work in logic

Taught by John Etchemendy, who are recognized for their work in logic

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Reviews summary

Engaging, introductory logic and proofs course

Learners say Language, Proof and Logic is an introductory course that covers the foundations of formal logic, including its applications in computer science, philosophy, and linguistics. They note the course's overall engagement, especially due to its use of the Logic 2010 software which allows students to explore logical concepts hands-on through exercises and quizzes.

Course uses Logic 2010 for hands-on learning.

"The course makes use of the Logic 2010 software, which provides a user-friendly interface for exploring logical concepts and constructing proofs."

Engaging course with interactive elements.

"One of the strengths of the course is its use of interactive tools and software to engage students in the learning process."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Language, Proof and Logic with these activities:

Review your notes from previous logic courses

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Reviewing your notes from previous logic courses will help you to refresh your memory and to identify areas where you need additional support.

Browse courses on Logic

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Gather your notes from previous logic courses.
Review the notes and identify the key concepts and techniques.
Complete any practice exercises or problems that are included in your notes.

Review 'Introduction to Logic' by Irving Copi and Carl Cohen

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Review the textbook provided with the course to refresh your understanding of the basic concepts and techniques used in logic.

View Introduction to Logic on Amazon

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Read the first three chapters of the textbook.
Summarize the key concepts in each chapter.
Complete the practice exercises at the end of each chapter.

Practice writing proofs

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Practicing writing proofs will help you to develop your problem-solving skills and to improve your understanding of the logical principles that underlie the course material.

Browse courses on Logic

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Find a list of logic problems.
Write a proof for each problem.

Six other activities

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Watch video tutorials on logic

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Watching video tutorials can help you to learn the material more visually and to reinforce the concepts you learn in the course.

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Find a video tutorial series on logic.
Watch the videos and take notes.
Pause the videos and try to solve the problems on your own.

Solve logic puzzles

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Solving logic puzzles will help you to develop your problem-solving skills and apply the concepts you learn in the course.

Browse courses on Propositional Logic

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Find a collection of logic puzzles online or in a book.
Choose a puzzle and read it carefully.
Identify the key elements of the puzzle, such as the variables, the constraints, and the goal.
Apply the concepts you learn in the course to solve the puzzle.

Join a study group

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Working with other students in a study group can help you to learn the material more deeply and to identify areas where you need additional support.

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Find a study group that meets regularly.
Attend the study group meetings and participate actively.
Work with your group members to review the course material, solve problems, and prepare for exams.

Translate statements into FOL

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Translating statements into FOL will help you to develop your understanding of the syntax and semantics of FOL.

Browse courses on First-Order Logic

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Find a list of statements expressed in natural language.
Translate each statement into FOL using the appropriate syntax and vocabulary.

Write a logic paper

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Writing a logic paper will help you to demonstrate your understanding of the course material and to develop your critical thinking skills.

Browse courses on Propositional Logic

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Choose a topic for your paper.
Research your topic and gather evidence to support your argument.
Write a thesis statement that states your main argument.
Write the body of your paper, using evidence to support your argument.
Write a conclusion that summarizes your argument and restates your thesis.

Create a logic game

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Creating a logic game will help you to demonstrate your understanding of the course material and to develop your creativity.

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Design the game board.
Create the game rules.
Test the game and make any necessary adjustments.

Career center

Learners who complete Language, Proof and Logic will develop knowledge and skills that may be useful to these careers:

Formal Reasoning Instructor

Formal Reasoning Instructors work with students who are still developing their formal reasoning skills. The Logic, Proof and Language course offered by Stanford can help Formal Reasoning Instructors strengthen their understanding of logic and enhance their teaching abilities. The course provides clarity on formal languages, truth, and proof, enabling instructors to instill a deeper understanding of these concepts in their students.

See salaries and explore the career path for Formal Reasoning Instructor

Logic Programming Engineer

Logic Programming Engineers are responsible for the development, implementation and maintenance of logic-based software systems. The Logic, Proof and Language course offered by Stanford University provides a thorough grounding in the fundamental concepts of logic, including proof and model theories. Through the study of propositional and first-order logic, students gain valuable knowledge that can be applied to the design and construction of logic-based systems.

See salaries and explore the career path for Logic Programming Engineer

Artificial Intelligence Researcher

Artificial Intelligence Researchers develop and evaluate AI techniques and algorithms. The Logic, Proof and Language course from Stanford provides a solid theoretical foundation for understanding the principles of logic and its applications in AI. The course covers proof and model theories, as well as the use of formal languages to analyze arguments and reason about knowledge, equipping researchers with a valuable skill set for advancing AI research.

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Data Scientist

Data Scientists use scientific methods, processes, algorithms, and systems to extract knowledge and insights from data in various forms, both structured and unstructured. The Logic, Proof and Language course taught at Stanford provides a strong foundation in logical reasoning, proof construction, and model theory. This knowledge is essential for data scientists who need to analyze, interpret, and draw meaningful conclusions from complex datasets.

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Computer Scientist

Computer Scientists are responsible for designing, developing, and maintaining computer systems and applications. The Logic, Proof and Language course from Stanford University provides a strong theoretical foundation in logic and its applications to computer science. The course covers propositional and first-order logic, proof theory, and model theory, equipping computer scientists with essential knowledge for designing and analyzing complex systems.

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Cryptographer

Cryptographers develop and analyze techniques for secure communication and data protection. The Logic, Proof and Language course offered by Stanford University provides a strong foundation in logic, proof theory, and model theory. This knowledge is essential for cryptographers to understand the mathematical principles underlying cryptosystems and to design and analyze secure protocols.

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Software Engineer

Software Engineers design, develop, test, and maintain software systems. The Logic, Proof and Language course at Stanford University provides a solid foundation in logical reasoning and formal methods. The course covers propositional and first-order logic, proof theory, and model theory, equipping software engineers with valuable skills for designing and implementing robust and reliable software systems.

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Mathematician

Mathematicians explore the properties of numbers, space, and change. The Logic, Proof and Language course from Stanford provides a grounding in the fundamentals of logic, including proof and model theories. Through the study of propositional and first-order logic, students gain a deeper understanding of mathematical concepts and develop the ability to construct rigorous proofs.

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Philosopher

Philosophers study the fundamental nature of knowledge, reality, and existence. The Logic, Proof and Language course offered by Stanford University provides a strong foundation in logic and its applications to philosophy. The course covers propositional and first-order logic, proof theory, and model theory, equipping philosophers with valuable tools for analyzing arguments, constructing theories, and exploring philosophical problems.

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Systems Analyst

Systems Analysts are responsible for the analysis, design, and implementation of computer systems. The Logic, Proof and Language course offered by Stanford provides a strong foundation in formal methods and modeling techniques. The course covers propositional and first-order logic, proof theory, and model theory, equipping systems analysts with essential skills for designing and implementing complex, reliable systems.

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Economist

Economists study the production, distribution, and consumption of goods and services. Formal methods are increasingly used to study phenomena such as market equilibrium and decision-making under uncertainty. The Logic, Proof and Language course taught by Stanford provides a solid foundation in the principles of logic, proof theory, and model theory. This knowledge enables economists to develop rigorous theories and models that accurately capture the complexities of economic systems.

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Actuary

Actuaries evaluate the financial consequences of risk and uncertainty. The Logic, Proof and Language course from Stanford may be useful for Actuaries as it provides a foundation in logical reasoning and formal methods. The course covers propositional and first-order logic, proof theory, and model theory, equipping actuaries with valuable skills for analyzing risk, developing models, and making informed decisions.

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Quantitative Analyst

Quantitative Analysts develop and apply mathematical and statistical models to financial data. The Logic, Proof and Language course taught at Stanford may be useful for Quantitative Analysts as it provides a foundation in formal reasoning and proof construction. The course covers propositional and first-order logic, proof theory, and model theory, equipping analysts with valuable skills for developing and evaluating financial models.

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UX Researcher

UX Researchers study user behavior and feedback to improve the usability and effectiveness of products and services. The Logic, Proof and Language course at Stanford University may be useful for UX Researchers as it provides a foundation in formal reasoning and argument analysis. The course covers propositional and first-order logic, proof theory, and model theory, equipping researchers with valuable skills for analyzing user feedback, designing experiments, and developing user-centered designs.

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Policy Analyst

Policy Analysts research, analyze, and evaluate public policies. The Logic, Proof and Language course from Stanford may be useful for Policy Analysts as it provides a foundation in logical reasoning and argument analysis. The course covers propositional and first-order logic, proof theory, and model theory, equipping analysts with valuable skills for evaluating policy proposals, developing recommendations, and communicating policy implications.

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Reading list

We've selected 11 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Language, Proof and Logic.

The Development of Logic

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This classic work on logic great resource for students who want to learn more about the foundations of the subject. It covers a wide range of topics, from propositional logic to modal logic, and it is written in a clear and engaging style.

Language, Proof and Logic

What you'll learn

Good to know

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Reviews summary

Engaging, introductory logic and proofs course

Activities

Career center

Reading list

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