Related papers: Monadic Second-Order Logic with Arbitrary Monadic …

A celebrated 1969 theorem of Michael Rabin is that the MSO theory of the real order where the monadic quantifier is allowed only to range over the sets of rational numbers, is decidable. In 1975 Saharon Shelah proved that if the monadic…

This paper investigates acceptance conditions for finite automata recognizing omega-regular languages. As a first result, we show that, under any acceptance condition that can be defined in the MSO logic, a finite automaton can recognize at…

We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the…

Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…

It is shown that order-invariance of two-variable first-logic is decidable in the finite. This is an immediate consequence of a decision procedure obtained for the finite satisfiability problem for existential second-order logic with two…

In this paper we study finite higher-dimensional automata (HDAs) from the logical point of view. Languages of HDAs are sets of finite bounded-width interval pomsets with interfaces (iiPoms<=k) closed under order extension. We prove that…

We present a systematic approach to logical predicates based on universal coalgebra and higher-order abstract GSOS, thus making a first step towards a unifying theory of logical relations. We first observe that logical predicates are…

We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…

We present a new proof that $O_2$ is a multiple context-free language. It contrasts with a recent proof by Salvati (2015) in its avoidance of concepts that seem specific to two-dimensional geometry, such as the complex exponential function.…

Research on information extraction from Web pages (wrapping) has seen much activity recently (particularly systems implementations), but little work has been done on formally studying the expressiveness of the formalisms proposed or on the…

We show that a special case of the Feferman-Vaught composition theorem gives rise to a natural notion of automata for finite words over an infinite alphabet, with good closure and decidability properties, as well as several logical…

Weighted automata are non-deterministic automata where the transitions are equipped with weights. They can model quantitative aspects of systems like costs or energy consumption. The value of a run can be computed, for example, as the…

We introduce a restricted second-order logic $\mathrm{SO}^{\mathit{plog}}$ for finite structures where second-order quantification ranges over relations of size at most poly-logarithmic in the size of the structure. We demonstrate the…

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

The use of monoids in the study of word languages recognized by finite-state automata has been quite fruitful. In this work, we look at the same idea of "recognizability by finite monoids" for other monoids. In particular, we attempt to…

This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to the foreground the logical, linguistic and philosophical…

We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…

Generalizing standard monadic second-order logic for Kripke models, we introduce monadic second-order logic interpreted over coalgebras for an arbitrary set functor. Similar to well-known results for monadic second-order logic over trees,…

A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…

We consider ideals and Boolean combinations of ideals. For the regular languages within these classes we give expressively complete automaton models. In addition, we consider general properties of regular ideals and their Boolean…