Operators in functional languages such as APL and FFP are a useful programming concept. However, this concept cannot be fully exploited in these languages because of certain constraints. It is proposed that an operator should be associated with a structure having the algebraic properties on which the operator's behavior depends. This is illustrated by introducing a language that provides mechan...

Algebraic structures sometimes need to be typed. For example, matrices over a ring form a ring, but the product is a only a partial operation: dimensions have to agree. Therefore, an easy way to look at matrices algebraically is to consider “typed rings”. We prove some “untyping” theorems: in some algebras (semirings, Kleene algebras, residuated monoids), types can be reconstructed from valid u...

Einstein product and Einstein sum are good alternatives to the algebraic product and algebraic sum, respectively. Nevertheless, it seems that in the literature there is little investigation on aggregation techniques using the Einstein operations on IFS for aggregating a collection of intuitionistic fuzzy value (IFV). The induced ordered weighted averaging operator is more suitable for aggregati...

A brief survey of real algebraic structures on topological spaces is given.

We define a new notion of an algebraic model structure, in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads, and prove “algebraic” analogs of classical results. Using a modified version of Quillen’s small object argument, we show that every cofibrantly generated model structure in the usual sense underlies a cofibrantly generated algebraic mo...

Extending previous work, we define monoidal algebraic model structures and give examples. The main structural component is what we call an algebraic Quillen two-variable adjunction; the principal technical work is to develop the category theory necessary to characterize them. Our investigations reveal an important role played by “cellularity”—loosely, the property of a cofibration being a relat...

If we view fuzzy logic as a logic, i.e., as a particular case of a multivalued logic, then one of the most natural questions to ask is whether the corresponding propositional logic is decidable, i.e., does there exist an algorithm that, given two propositional formulas F and G, decides whether these two formulas always have the same truth value. It is known that the simplest fuzzy logic, in whi...