In 1974 an article appeared in Science magazine with the dry-sounding title “Judgment Under Uncertainty: Heuristics and Biases” by a pair of psychologists who were not well known outside their discipline of decision theory. In it Amos Tversky and Daniel Kahneman introduced the world to Prospect Theory, which mapped out how humans actually behave when faced with decisions about gains and losses, in contrast to how economists assumed that people behave. Prospect Theory turned Economics on its head by demonstrating through a series of ingenious experiments that people are much more concerned with losses than they are with gains, and that framing a choice from one perspective or the other will result in decisions that are exactly the opposite of each other, even if the outcomes are monetarily the same. Prospect Theory led cognitive psychology in a new direction that began to uncover other human biases in thinking that are probably not learned but are part of our brain’s wiring.

Thinking fast and slow.

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The Uses Of Argument

A machine equivalent to Turing machine, that is more intuitive in its working is defined. Three derivation rules are added to Elementary Arithmetic of Godel and his incompleteness theorems are proved without using any metalanguage. Two axioms are added to Zermelo-Fraenkel theory to derive the Continuum Hypothesis and to split the unit interval into infinitesimals.

Foundations of Computer Science

The Logic Of Real Arguments

Description: The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for both reading and writing proofs. The second chapter of the book discusses the techniques in proving if/then statements by contrapositive and proofing by contradiction. It also includes the negation statement, and/or. It examines various theorems, such as the if and only-if, or equivalence theorems, the existence theorems, and the uniqueness theorems. In addition, use of counter examples, mathematical induction, composite statements including multiple hypothesis and multiple conclusions, and equality of numbers are covered in this chapter. The book also provides mathematical topics for practicing proof techniques. Included here are the Cartesian products, indexed families, functions, and relations. The last chapter of the book provides review exercises on various topics. Undergraduate students in engineering and physical science will find this book invaluable.-Jumps right in with the needed vocabulary-gets students thinking like mathematicians from the beginning-Offers a large variety of examples and problems with solutions for students to work through on their own-Includes a collection of exercises without solutions to help instructors prepare assignments-Contains an extensive list of basic mathematical definitions and concepts needed in abstract mathematics Contents: Chapter 1: Getting Started Introduction and Basic Terminology General Suggestions

The Nuts and Bolts of Proofs

In contrast to Computer Science and Software Engineering, where it’s fundamental role is widely recognized, logic plays a practically non-existent role in information systems (IS) curricula. In this paper we argue that instead of logic’s exclusion from the IS curriculum, a significant adaptation of the contents, as well as teaching methodologies, is required for an alignment with the needs of IS practitioners. We present a vision for such adaptation and report on concrete steps towards its implementation in the design and teaching of a course for graduate IS students at the University of Haifa. We discuss the course plan and present a qualitative analysis of feedback provided by students of the course.

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An Old Discipline with a New Twist: The Course “Logic in Action”

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An Old Discipline with a New Twist: The Course “Logic in Action”