Growing a Domain Specific Language with Split Extensions

In this paper we consider simple language extensions given by a pair of transducers. When these transducers are viewed as trees transformers, one of this transducer provides an embedding of the original language into its extension while the other, a left-inverse to the embedding, allows every expression of the extended language to be expanded into an expression of the original language. This is of course the easy case and the work presented here should be considered as a work in progress where we have reach only a very preliminary stage. The purpose of this report is to introduce our approach to the extension of domain specific languages, fix the notations and definitions and illustrate the case, of what might be termed the class of the split extensions, where the embedding of the language into its extension has a left-inverse. We shall, in the next future, investigate the general case of language extensions where the embedding doesn't necessarily have a left-inverse

A notion of functional completeness for first-order structure

Using ☆-congruences and implications, Weaver (1993) introduced the concepts of prevariety and quasivariety of first-order structures as generalizations of the corresponding concepts for algebras. The notion of functional completeness on algebras has been defined and characterized by Burris and Sankappanavar (1981), Kaarli and Pixley (2001), Pixley (1996), and Quackenbush (1981). We study the notion of functional completeness with respect to ☆-congruences. We extend some results on functionally complete algebras to first-order structures A=(A;FA;RA) and find conditions for these structures to have a compatible Pixley function which is interpolated by term functions on suitable subsets of the base set A

Fuzzy n-Fold Filters of Pseudoresiduated Lattices

Given a pseudoresiduated lattice M and a lattice L, we introduce and characterize the fuzzy versions of different n-fold implicative (resp., obstinate, Boolean, normal, and extended involutive) filters of M. Moreover, we study some relationships between these different types of fuzzy n-fold filters

Folding Theory Applied to Residuated Lattices

Residuated lattices play an important role in the study of fuzzy logic based on t-norms. In this paper, we introduce some notions of n-fold filters in residuated lattices, study the relations among them, and compare them with prime, maximal and primary, filters. This work generalizes existing results in BL-algebras and residuated lattices, most notably the works of Lele et al., Motamed et al., Haveski et al., Borzooei et al., Van Gasse et al., Kondo et al., Turunen et al., and Borumand Saeid et al., we draw diagrams summarizing the relations between different types of n-fold filters and n-fold residuated lattices