We study an extension of monadic second-order logic of order with the uncountability quantifier “there exist uncountably many sets”. We prove that, over the class of finitely branching trees, this extension is equally expressive to plain monadic second-order logic of order. Additionally we find that the continuum hypothesis holds for classes of sets definable in monadic second-order logic over ...

Coquidt, J.-L., M. Dauchet, R. Gilleron and S. VBgviilgyi, Bottom-up tree pushdown automata: classification and connection with rewrite systems, Theoretical Computer Science 127 (1994) 69-98. We define different types of bottom-up tree pushdown automata and study their connections with rewrite systems. Along this line of research we complete and generalize the results of Gallier, Book and Salom...

The purpose of this paper is to explain how the theory of Gröbner bases can be used for automated proving in Monadic Logic. The paper is organized as follows: in Section 1 we recall the syntax and semantics of Monadic Logic, and we describe the aim of this paper: the resolution by an algebraic algorithm of the deduction problem in Monadic Logic. Successively, we reduce the deduction problem in ...

This is the first part of a two part work on the monadic theory of short orders (embedding neither w1 nor w1*). This part provides the technical groundwork for decidability results. Other applications are possible. ?0. Introduction. A chain is a linearly ordered set. A chain is short iff it embeds neither o)1 nor Oj1. A chain is Specker iff it does not embed any uncountable subchain of the real...

We define a class of finite state automata acting on transfinite sequences, and use these automata to prove that no singular cardinal can be defined by a monadic second order formula over the ordinals. A formula φ is monadic second order (monadic for short) if each of its variables is assigned a type, either the type “first order” or the type “second order.” When interpreting the formula over a...

We introduce the branching transitive closure operator on weighted monadic second-order logic formulas where the branching corresponds in a natural way to the branching inherent in trees. For arbitrary commutative semirings, we prove that weighted monadic second order logics on trees is equivalent to the definability by formulas which start with one of the following operators: (i) a branching t...

Modularity in programming language semantics derives from abstracting over the structure of underlying denotations, yielding semantic descriptions that are more abstract and reusable. One such semantic framework is Liang’s modular monadic semantics in which the underlying semantic structure is encapsulated with a monad. Such abstraction can be at odds with program verification, however, because...

Abstract The aim of my article is to present the critique by Brentanians – more precisely, Brentano himself and his students Stumpf Marty thesis that colours are properties relational a perceiver. For Brentanians, monadic physical properties. I will show, think do not exhibit relationality perception when we experience them, concepts them contain any mark representing relation perception; this ...

In the analysis of the structure of totally categorical first order theories, the second author showed that certain combinatorial counting functions play an important role. Those functions are invariants of the structures and are always polynomials in one or many variables, depending on the number of independent dimensions of the theory in question. The first author introduced the notion of gra...

The tree languages of tree-adjoining grammars are precisely those of linear monadic context-free tree grammars. Unlike the original proof, we present a direct transformation of a tree-adjoining grammar into an equivalent linear monadic context-free tree grammar.