Trail-And-Error machines have been proposed by Hintikka and Mutanen as an alternative formulation of the notion of computation. These machines extend the capabilities of the Turing machine and widen the theory of computation.

Ideograms have great communicative value. They refer to concepts in a simple manner, easing the understanding of related ideas. Moreover, ideograms can simplify the often cumbersome notation used in the fields of Physics and physical Chemistry. Nonetheless only a few ideograms—like \ and Å—have been defined to date. In this work we propose that the scientific community follows the example of Mathematics—as well as that of oriental languages—and bestows a more important role upon ideograms. To support this thesis we propose (...) ideograms for essential concepts in Physics and Chemistry. They are designed to be intuitive, and their goal is to make equations easier to read and understand. Our symbols are included in a publicly available package. (shrink)

Vagueness is a linguistic phenomenon as well as a property of physical objects. Fuzzy set theory is a mathematical model of vagueness that has been used to define vague models of computation. The prominent model of vague computation is the fuzzy Turing machine. This conceptual computing device gives an idea of what computing under vagueness means, nevertheless, it is not the most natural model. Based on the properties of this and other models of vague computing, an attempt is made to (...) formulate a basis for a philosophy of a theory of fuzzy computation. (shrink)

Trail-And-Error machines have been proposed by Hintikka and Mutanen as an alternative formulation of the notion of computation. These machines extend the capabilities of the Turing machine and widen the theory of computation.

Generally, an object is vague when its properties cannot precisely defined. The ontic view of vagueness is the idea that vagueness is a fundamental property of Nature. This simply means that everything is vague: animals, plants, molecules, atoms, etc. Furthermore, if atoms and molecules are vague, then the subject matter of chemistry is vague. However, we first need to understand why molecules and atoms are vague.

The book provides the first full length exploration of fuzzy computability. It describes the notion of fuzziness and present the foundation of computability theory. It then presents the various approaches to fuzzy computability. This text provides a glimpse into the different approaches in this area, which is important for researchers in order to have a clear view of the field. It contains a detailed literature review and the author includes all proofs to make the presentation accessible. Ideas for future research (...) and explorations are also provided. Students and researchers in computer science and mathematics will benefit from this work. (shrink)

The book starts with the assumption that vagueness is a fundamental property of this world. From a philosophical account of vagueness via the presentation of alternative mathematics of vagueness, the subsequent chapters explore how vagueness manifests itself in the various exact sciences: physics, chemistry, biology, medicine, computer science, and engineering.