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Distinguishing non-standard natural numbers in a set theory within ?ukasiewicz logic: Archive for Mathematical Logic, Vol. 46, No. 3. (23 April 2007), pp. 281-287.Abstra ct In $$\mathbfH$$, a set theory with the comprehension principle within ?ukasiewicz infinite-value d predicate logic, we prove that a statement which can be interpreted as ?there is an infinite descending sequence of initial segments of ?? is truth value 1 in any model of $$\mathbfH$$, and we prove an analogy of Hjek?s theorem with a very simple procedure.

Source: Archive for Mathematical Logic, Vol. 46, No. 3. (23 April 2007), pp. 281-287.
On Evans's Vague Object from Set Theoretic Viewpoint: Journal of Philosophical Logic, Vol. 35, No. 4. (2006), pp. 423-434.Abstra ct Gareth Evans proved that if two objects are indeterminatel y equal then they are different in reality. He insisted that this contradicts the assumption that there can be vague objects. However we show the consistency between Evans's proof and the existence of vague objects within classical logic. We formalize Evans's proof in a set theory without the axiom of extensionality , and we define a set to be vague if it violates extensionality with respect to some other set. There exist models of set theory where the axiom of extensionality does not hold, so this shows that there can be vague objects.

Source: Journal of Philosophical Logic, Vol. 35, No. 4. (2006), pp. 423-434.
Bounded Arithmetic, Proof Complexity and TwoPapers of Parikh: This article surveys R. Parikh's work on feasibility, bounded arithmetic and the complexity of proofs. We discuss in depth two of Parikh's papers on these subjects and some of the subsequent progress in the areas of feasible arithmetic and lengths of proofs. 1
An incremental formal semantics for promela: (1997)An approach to a formal semantics for PROMELA is presented. The approach uses SOS rules to define a labeled transition system model for a PROMELA program. The approach is a bottom-up, incremental approach with three basic steps (declarations, single processes, parallel processes). PROMELA before version 2.0 is treated nearly entirely. Especially assertions, never claims and correctness conditions are discussed.

Source: (1997)
Forcing in Proof Theory: The Bulletin of Symbolic Logic, Vol. 10, No. 3. (2004), pp. 305-333.Paul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizi ng model-theoreti c arguments.

Source: The Bulletin of Symbolic Logic, Vol. 10, No. 3. (2004), pp. 305-333.
Forcing on Bounded Arithmetic II: The Journal of Symbolic Logic, Vol. 63, No. 3. (1998), pp. 860-868.

Source: The Journal of Symbolic Logic, Vol. 63, No. 3. (1998), pp. 860-868.
Routing Information Protocol in HOL/SPIN: (2000), pp. 53-72.

Source: (2000), pp. 53-72.
Writing Space: Computers, Hypertext, and the Remediation of Print: (01 March 2001)

Source: (01 March 2001)
Die Bibliothek der Zukunft. Text und Schrift in Zeiten des Internet.: (01 August 2001)

Source: (01 August 2001)
The Gutenberg Galaxy: The Making of Typographic Man: (01 June 1962)Nearly every decade has its own claim to a revolution that is the biggest since the invention of the printing press. Well, what was that original revolution, still the defending champion of cultural upheavals, actually like? In The Gutenberg Galaxy, University of Toronto theorist Marshall McLuhan described the shift from an oral to a print culture and in the process set off a bit of a revolution of his own. The Gutenberg Galaxy, the first of McLuhan's major books, is also the most accessible, but, as you would expect from the man who told us that "the medium is the message," it's innovative in style as well as content, structured as a mosaic of short essays, quotes, and aphorisms, one of which introduced the idea of the "global village" to a world that would soon fulfill McLuhan's prophecy. Movable type, as much if not more than any meaningful arrangement of that type, transformed Renaissance consciousness- -just as electronic circuitry is transforming us now. That is the basic premise of Marshall McLuhan's The Gutenberg Galaxy. New technologies create new human environments, and "technological environments are not merely passive containers … but are active processes that reshape people and other technologies alike." McLuhan's second book, The Gutenberg Galaxy was published in 1962, won the Canadian Governor General's Medal that same year, and pushed McLuhan toward international prominence. Like most of McLuhans's other work--Understa nding Media or The Global Village, for example--The Gutenberg Galaxy is a rich, dense text that draws freely, almost frantically, from works of philosophy, economics, political theory, history, and especially literature. There are liberal doses of Shakespeare--t ext and commentary--sp rinkled throughout, as well as trenchant appropriations from Rabelais, Cervantes, Leibnitz, Blake, Joyce, and many others. Attempting to match his medium to his metaphors, McLuhan structures his book using what he calls "a mosaic or field approach" and ends up producing more than 100 short sections separated by pithy glosses in large bold type, such as "Schizophrenia may be a necessary consequence of literacy," or " Nobody ever made a grammatical error in a non-literate society." Today's reader might find the "mosaic of perpetually interacting forms" into which the author organizes his data and quotations distinctly Web-like. Indeed, one could say of McLuhan and his complex rhetorical circuitry what McLuhan himself says about Shakespeare: "His insights appear so richly in his lines that it is very difficult to select among them." --Russell Prather

Source: (01 June 1962)

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