Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification ([4], [5]) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference. Plural quantification will be then explained in terms of plural reference. As an app...

A topological duality for monadic n-valued Lukasiewicz algebras introduced by M. Abad (Abad, M.: Estructuras cíclica y monádica de un álgebra de Lukasiewicz nvalente. Notas de Lógica Matemática 36. Instituto de Matemática. Universidad Nacional del Sur, 1988) is determined. When restricted to the category of Q-distributive lattices and Q-homomorphims, it coincides with the duality obtained by R....

We consider an interpretation of monadic second-order logic of order in the continuous time structure of nitely variable signals and show the decidability of monadic logic in this structure. The expressive power of monadic logic is illustrated by providing a straightforward meaning preserving translation into monadic logic of three typical continuous time speciication formalism: Temporal Logic ...

In this paper, subclasses of monadic contextfree tree grammars (CFTGs) are compared. Since linear, nondeleting, monadic CFTGs generate the same class of string languages as tree adjoining grammars (TAGs), it is examined whether the restrictions of linearity and nondeletion on monadic CFTGs are necessary to generate the same class of languages. Epsilonfreeness on linear, nondeleting, monadic CFT...

It is a well-known result of Fagin that the complexity class NP coincides with the class of problems expressible in existential second-order logic (Z i), which allows sentences consisting of a string of existential second-order quantifiers followed by a first-order formula. Monadic NP is the class of problems expressible in monadic Z ; , i.e., Z ; with the restriction that the second-order quan...

We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the monadic second order theory of short chains (hence, in the monadic theory of the real line). We are intere...

We consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $X$, $(X, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $X$. We also show that, for a strong residuated lattice $X$, $bigcap {P_{lambda} ,|,P_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

Rationals and countable ordinals are important examples of structures with decidable monadic second-order theories. A chain is an expansion of a linear order by monadic predicates. We show that if the monadic second-order theory of a countable chain C is decidable then C has a non-trivial expansion with decidable monadic second-order theory.

Since the work of Rabin [9], it has been known that any monadic second order property of the (labeled) binary tree with successor functions (and not the prefix ordering) is a monadic ∆3 property. In this paper, we show this upper bound is optimal in the sense that there is a monadic Σ2 formula, stating the existence of a path where a given predicate holds infinitely often, which is not equivale...

Problems related to the complexity and to the decidability of several languages weaker than Prolog are studied in this paper. In particular, monadic logic programs, that is, programs containing only monadic functions and monadic predicates, are considered in detail. The functional complexity of a monadic logic program is the language of all words fi fk such that the literal p(fi(...(fk(a)). ..)...