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Following the fixpoint theory of Scott, the semantics of computer programs are defined in terms of the least fixpoints of recursive programs. This allows not only the justification of all existing verification techniques, but also their extension to the handling, in a uniform manner of various properties of computer programs, including correctness, termination, and equivalence. [ABSTRACT FROM AUTHOR]

A source of ideas for automata theory — the study of the brain — has been pushed aside in mathematical development of the theory. This paper suggests the ways in which automata theory might evolve over the next 25 years if it is to contribute to an understanding of how the brain processes information. [ABSTRACT FROM AUTHOR]

61 It is assumed that there is a similarity of function between the data names of a programming language and the file names of an operating system. The two functions are discussed in terms of the same basic concepts in order to identify the extent to which they overlap. It is suggested that there is some similarity between the idea of a file directory and a storable object of type context. Manipulations with contexts are then discussed at length. It is noted that there is a simple extension of Church's A notation that deals nicely with these ideas of context manipulation. Whereas a function can be regarded as the abstraction based upon the first two terms of the expression γ(namelist)(expression)(valuelist), it is found that a context can be viewed as an abstraction based upon the first two terms in the equivalent expression μ(namelist)(valuelist)(expression). [ABSTRACT FROM AUTHOR]

Discusses the development of a computational linguistic system based on pattern recognition and learning logic. Syntactic analysis of the structural relations among words within sentences; Use for parsing large quantities of English text with a maximum of accuracy and a minimum of ambiguity.

Focuses on the relation between the democracy and intellect. Existence of morality for the welfare of society; Necessity to suppress lying, theft and breach of contract to protect the society; Role of school and the church to teach the civic morality and conscience; Comments on the power of an individual person; Importance of logical education; Information on principles of logic; Role of logic in building faith in common sense; Description of relationship between the logic and morality.

Focuses on the logic of the process of testing, confirming and disconfirming hypotheses by observation and experimentation. Information on two famous logical puzzles which have been exercised by philosophers; Use of hypothesis by investigator to predict some phenomenon whose occurrence or nonoccurrence can be ascertained by observation; Possible best antidote for errors that arise from intuitions about confirmation.

Provides information on nonstandard analysis, a new branch of mathematics invented by the logician Abraham Robinson. Example of the use of infinitesimal arguments in geometry; Information on Archimedes' method of exhaustion; Critique of the infinitesimal method "The Analyst," which appeared in 1734; Link between logic and computing.

Focuses on the implications of the continuing failure of a person to solve some of the unsolved arithmetic problems. Reason of Aristotle for inventing logic; Geometric problems proposed by the ancient Greeks that they themselves could not solve; Importance of the development of non-Euclidean geometry to mathematical logic.

The article discusses how mathematical paradoxes can be solved. It cites that the paradox of incommensurables, Zeno's paradox of Achilles and the tortoise and other paradoxes in early history have produced major ideas in mathematics and science. Many philosophies and some systems of logic take contradiction as a basic principle. The prisoner's dilemma game is explained. The solution by Nigel Howard of the University of Pennsylvania for the game is provided.

The article looks at fundamental concepts in the area of overlap between computer theory and logic by means of games. The decision problem of logic must be considered because all mathematical theories can be formulated in the framework of elementary logic. Proving certain problems to be unsolvable by computer can be facilitated by reducing them to domino problems.

The article presents several mathematical problems. One ask whether it is possible for a man to remove his trousers if each end of a 10-foot length of rope is tied securely to his ankles. Another is how to identify each of the three men whom one always answers questions truthfully, one always responds with lies, and one randomizes his answer by asking three questions. Each question may be directed toward any of the them, and each must be a question that is only answerable by yes or no.

The article discusses the aspects of paradoxes. According to the author, there are several philosophers who disagree to resolve the paradox. W. V. Quine, a Harvard University logician, related paradoxes through his writing about the puzzle of a man who is condemned to be hanged. The first variation of the paradox taken from the article is the paradox of unexpected egg.

A dilemma is a problem involving a contradiction, an impasse or a conflict which cannot be resolved within the frame of reference in which the problem arose. One way of reacting to a dilemma is to interpret it as a struggle for power, to take sides and to see the meaning of life in the victory of one side over the other. Another way of dealing with, dilemmas is by compromise, an outlook congenial to the eclectics and to the empirically oriented. A third way of dealing with dilemmas is to ignore them. The dilemmas referred to are the paradoxes upon which man has stumbled from time to time in the effort to understand the world and his own thinking about the world.

The article presents a collection of puzzles and mathematical games which involves numbers, logic and probabilities. The collection includes a puzzle which asks how much area can cover a sheet of legal-sized paper 8½ by 12½ inches with seven file cards, each having sizes of three-by-five inches.

The article analyzes the decision-making process in businesses and presents seven mistakes in marketing logic. Common marketing fallacies include constant susceptibility, the presentation of the well-known, common motives, self-measuring image research, and an overestimation from tests. According to the article, in order to improve decision making, rational procedures must be used to decrease dependence on guesswork by critically examining assumptions and replacing them with knowledge derived from a good analysis.

The article discusses intellectual qualities that characterize the thinking of scientists, lawyers, and other professionals and examines the managerial mind. Empirical qualities in executives' thinking, or the factual and quantitative attitudes, can predict how they will approach a problem. Logical qualities of the deductive mind are theoretical attitude, predisposition for truth, and consistency--a modified version of the "validity" attitude in formal logic. Action-oriented qualities that characterize the managerial mind are the executive's desire to change things in the real world and a predisposition for timely action. Examples illustrate the nature of judgmental qualities that are identified as conceptual, quantity, weight, and whole problem.

This article presents information about the book "The Philosophy of Alfred North Whitehead," vol.3, edited by Paul Arthur Schilpp. When Alfred North Whitehead, one of the world's foremost logicians and philosophers proclaims that logic, conceived as an adequate analysis of the advance of thought, is a fake, it is certainly startling news in the realm of mind. His thought is so rich that it is possible to derive almost any variety of philosophic doctrine from it, as the essays in this book show. The concluding sentences of his essay on immortality are that the final outlook of philosophic thought cannot be based upon the exact statements which form the basis of the special sciences.

The article provides mathematical information regarding the concept of limits and infinite series. According to the author, limits of infinite series concept is an essential tool in a thorough understanding to the concept of calculus computation. Zeno of Elea, a Greek philosopher first demonstrated the logic of infinite series.

A mathematical game that tests logical reasoning is presented.

The article presents the author's views on critical intelligence as opposed to romanticism and pseudo-intellectualism. He contends that intellectualists possess a monopoly of soul. However, looking at the conventional types of intellectualism, the intellectualism of modern science and mathematical logic, it seems that the intellectualistic claim to a soul stands in need of argument.

The article presents comparison of English criticism with that of other countries, especially France. It has suffered from the superabundance of certain virtues: imaginative fervor, moral earnestness, geniality and humor. In the first place, they would seem, as compared with the French, to lack taste using the word in a somewhat literal sense. In this sense, taste, is a "prompt discernment like that of the tongue or palate, and which like it anticipates reflection. Mention has just been made of the French love of logic. Though this has not led them into an excess of aesthetic theorizing, it has given to their criticism method and coherency.