A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered structures, and another form to define them on unordered non-Aristotelian structures. Using the canonical forms, logics are developed for complete problems in various ...

The mediaeval logic of Aristotelian privation, represented by Ockham’sexposition of All A is non-P as All S is of a type T that is naturally P and no S isP, is critically evaluated as an account of privative negation. It is argued thatthere are two senses of privative negation: (1) an intensifier (as in subhuman),the inverse of Neoplatonic hypernegation (superhuman), which is st...

Aristotelian diagrams, such as the square of opposition, are well-known in context normal modal logics (i.e., systems logic which can be given a relational semantics terms Kripke models). This paper studies diagrams for non-normal (based on neighborhood semantics, topologically inspired generalization semantics). In particular, we investigate phenomenon logic-sensitivity diagrams. We distinguis...

Logic as a philosophical discipline originated in ancient Greece, at about the same time as mathematics was constituted as a deductive science. From ancient times two logical systems have survived – the Aristotelian syllogistic logic and the Stoic propositional logic. It took almost two thousand years, until in the works of Boole, Frege and Peano logic was turned into a formal discipline. The r...

By developing F. Smarandache thema on paradoxes in mathematics it is stated, firstly, ifin measurement (natural science) experiments the best solutions are found by using methods of modem data analysis theory, then some difficulties with the interpretation of the computation results are liable to occur; secondly, one is not capable to overcome these difficulties without a data analysis theory m...

To organize information, librarians create structures. These structures grow from a logic that goes back at least as far as Aristotle. It is the basis of classification as we practice it, and thesauri and subject headings have developed from it. Feminist critiques of logic suggest that logic is gendered in nature. This article will explore how these critiques play out in contemporary standards ...

Aristo mantığı-Arap grameri ilişkisine dair tartışmalar erken dönem dilcileri arasında yaşandığı gibi modern dilbilimcileri tarafından da sürdürülmüştür. Bu mantık ve nahiv ilimlerinin amaç işlevleri etrafında şekillenebildiği mantığın nahvin doğuşunda gelişmesinde etkili olup olmadığı konusuna yoğunlaşmıştır. Sözü edilen etkiye ilminin özgünlüğü kavramını gündeme getirmiştir. çalışma mantığını...

In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve objective, argue in favor of two statements: (i) is not classical and (ii) programming emanating from programming.