Note on paraconsistency and reasoning about fractions

We apply a paraconsistent logic to reason about fractions.Comment: 6 page

Poly-infix operators and operator families

Poly-infix operators and operator families are introduced as an alternative for working modulo associativity and the corresponding bracket deletion convention. Poly-infix operators represent the basic intuition of repetitively connecting an ordered sequence of entities with the same connecting primitive.Comment: 8 page

Architectural Adequacy and Evolutionary Adequacy as Characteristics of a Candidate Informational Money

For money-like informational commodities the notions of architectural adequacy and evolutionary adequacy are proposed as the first two stages of a moneyness maturity hierarchy. Then three classes of informational commodities are distinguished: exclusively informational commodities, strictly informational commodities, and ownable informational commodities. For each class money-like instances of that commodity class, as well as monies of that class may exist. With the help of these classifications and making use of previous assessments of Bitcoin, it is argued that at this stage Bitcoin is unlikely ever to evolve into a money. Assessing the evolutionary adequacy of Bitcoin is perceived in terms of a search through its design hull for superior design alternatives. An extensive comparison is made between the search for superior design alternatives to Bitcoin and the search for design alternatives to a specific and unconventional view on the definition of fractions.Comment: 25 page

Transreal arithmetic as a consistent basis for paraconsistent logics

Paraconsistent logics are non-classical logics which allow non-trivial and consistent reasoning about inconsistent axioms. They have been pro- posed as a formal basis for handling inconsistent data, as commonly arise in human enterprises, and as methods for fuzzy reasoning, with applica- tions in Artificial Intelligence and the control of complex systems. Formalisations of paraconsistent logics usually require heroic mathe- matical efforts to provide a consistent axiomatisation of an inconsistent system. Here we use transreal arithmetic, which is known to be consis- tent, to arithmetise a paraconsistent logic. This is theoretically simple and should lead to efficient computer implementations. We introduce the metalogical principle of monotonicity which is a very simple way of making logics paraconsistent. Our logic has dialetheaic truth values which are both False and True. It allows contradictory propositions, allows variable contradictions, but blocks literal contradictions. Thus literal reasoning, in this logic, forms an on-the- y, syntactic partition of the propositions into internally consistent sets. We show how the set of all paraconsistent, possible worlds can be represented in a transreal space. During the development of our logic we discuss how other paraconsistent logics could be arithmetised in transreal arithmetic

Dialectical Multivalued Logic and Probabilistic Theory

There are two probabilistic algebras: one for classical probability and the other for quantum mechanics. Naturally, it is the relation to the object that decides, as in the case of logic, which algebra is to be used. From a paraconsistent multivalued logic therefore, one can derive a probability theory, adding the correspondence between truth value and fortuity