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1 Alonzo Church, Ann. Math., 2nd ser., 33, 346-366 (1932), and 34, 839-864 (1933). S. C. Kleene, Ann. Math., 2nd ser., 35, 529-544 (1934). We shall refer to the latter paper as Kleene 1934. 2 Alonzo Church and J. B. Rosser, "Some Properties of Conversion." 3 Explicit formal definitions are given by S. C. Kleene, Amer. Jour. Math., 57, 153173 (1935). This paper, and a second part of it, forthcom...

Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra p...

From the start, Kurt Godel observed that computer and brain paradigms were considered on a par by researchers and that researchers had misunderstood his theorems. He hailed with displeasure that the brain transcends computers. In this brief article, we point out that Artificial Intelligence (AI) comprises multitudes of human-made methodologies, systems, and languages, and implemented with compu...

To study the behaviour of silver eels (Anguilla anguilla L.) during their downstream migration, particularly near a hydroelectric power dam, we tagged nine eels with ultrasonic transmitters and tracked their paths in the River Mosel, Germany. The onset of migration coincided with the first flood event that followed the full moon but was independent of daytime, because migration and turbine pass...

In information security, ignorance is not bliss. It is always stated that hiding the protocols (let the other be ignorant about it) does not increase the security of organizations. However, there are cases that ignorance creates protocols. In this paper, we propose distributed contingency logic, a proper extension of contingency (ignorance) logic. Intuitively, a formula is distributed contingen...

in this paper, we introduce the notion of multiplier in -algebra and study relationships between multipliers and some special mappings, likeness closure operators, homomorphisms and ( -derivations in -algebras. we introduce the concept of idempotent multipliers in bl-algebra and weak congruence and obtain an interconnection between idempotent multipliers and weak congruences. also, we introduce...

We determine when a model 90? of ZF can be expanded to a model <SW, %y of a weak extension of Godel Bernays: GB + the A] comprehension axiom. For nonstandard W, the ordinal of the standard part of ÜR must equal the inductive closure ordinal of SK, and 2J? must satisfy the axioms of ZF with replacement and separation for formulas involving predicates for all hyperelementary relations on SK. We a...

New trends and the effect of key factors influence the quality of the holes produced by ECM processes. Researchers developed a fuzzy logic controller by adding intelligence to the ECM process. Maintaining optimum ECM process conditions ensures higher machining efficiency and performance. This paper presents the development of a fuzzy logic controller to add intelligence to the ECM process. An e...