A description of finitely generated free monadic MV -algebras and a characterization of projective monadic MV -algebras in locally finite varieties is given. It is shown that unification type of locally finite varieties is unitary.

A word rewriting system is called monadic if each of its right hand sides is either a single letter or the empty word. We study the images of higher order indexed languages (defined by Maslov) under inverse derivations of infinite monadic systems. We show that the inverse derivations of deterministic level n indexed languages by confluent regular monadic systems are deterministic level n+1 lang...

We investigate the expressive power of existential monadic second-order logic (monadic Σ1) on finite transition systems. In particular, we look at its power to express properties that are invariant under forms of bisimulation and compare these to properties expressible in corresponding fixed-point modal calculi. We show that on finite unary transition systems the bisimulation invariant fragment...

The paper deals with logically definable families of sets (or point-sets) of rational numbers. In particular we are interested whether the families definable over the real line with a unary predicate for the rationals are definable over the rational order alone. Let φ(X,Y ) and ψ(Y ) range over formulas in the first-order monadic language of order. Let Q be the set of rationals and F be the fam...

The application of ideas from universal algebra to computer science has long been a major theme of Joseph Goguen’s research, perhaps even the major theme. One strand of this work concerns algebraic datatypes. Recently there has been some interest in what one may call algebraic computation types. As we will show, these are also given by equational theories, if one only understands the notion of ...

Linear diagrams have recently been shown to be more effective than Euler diagrams when used for set-based reasoning. However, unlike the growing corpus of knowledge about formal aspects of Euler and Venn diagrams, there has been no formalisation of linear diagrams. To fill this knowledge gap, we present and formalise Point and Line (PaL) diagrams, an extension of simple linear diagrams containi...

CPS transformation is an important tool in the compilation of functional programming languages. For strict languages, such as our web programming language “Rinso” or Microsoft’s F#, monadic expressions can help with structuring and composing computations. To apply a CPS transformation in the compilation process of such a language, we integrate explicit monadic abstraction in a call-by-value sou...