Decidability Results for the Boundedness Problem

We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the fixed-point recursion based on phi is spurious over the class of all trees in the sense that there is some uniform finite bound for the number of iterations phi takes to reach its least fixed point, uniformly across all trees. We also identify the exact complexity of this problem. The proof uses automata-theoretic techniques. This key result extends, by means of model-theoretic interpretations, to show decidability of the boundedness problem for MSO and guarded second-order logic (GSO) over the classes of structures of fixed finite tree-width. Further model-theoretic transfer arguments allow us to derive major known decidability results for boundedness for fragments of first-order logic as well as new ones

Grammars and Processors

The paper discusses the role of grammars in sentence processing, and explores some consequences of the Strong Competence Hypothesis of Bresnan and Kaplan for combinatory theories of grammar

Classes and theories of trees associated with a class of linear orders

Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms of the first-order theory of the generating class C, and indicate the problems obstructing such general results for the other classes. These problems arise from the possible existence of nondefinable paths in trees, that need not satisfy the first-order theory of C, so we have started analyzing first-order definable and undefinable paths in trees

CVPP: A Tool Set for Compositonal Verification of Control-Flow Safety Properties.

This paper describes CVPP, a tool set for compositional verification of control–flow safety properties for programs with procedures. The compositional verification principle that underlies CVPP is based on maximal models constructed from component specifications. Maximal models replace the actual components when verifying the whole program, either for the purposes of modularity of verification or due to unavailability of the component implementations at verification time. A characteristic feature of the principle and the tool set is the distinction between program structure and behaviour. While behavioural properties are more abstract and convenient for specification purposes, structural ones are easier to manipulate, in particular when it comes to verifica-tion or the construction of maximal models. Therefore, CVPP also contains the means to characterise a given behavioural formula by a set of structural formulae. The paper presents the underlying framework for compositional verification and the components of the tool set. Several verification scenarios are described, as well as wrapper tools that sup-port the automatic execution of such scenarios, providing appropriate pre – and post–processing to interface smoothly with the user and to encapsulate the inner workings of the tool set

On the modal aspects of causal sets

The possibility question concerns the status of possibilities: do they form an irreducible category of the external reality, or are they merely features of our cognitive framework? If fundamental physics is ever to shed light on this issue, it must be done by some future theory that unifies insights of general relativity and quantum mechanics. The paper investigates one programme of this kind, namely the causal sets programme, as it apparently considers alternative developments of a given system. To evaluate this claim, we prove some algebraic facts about the sequential growth of causal sets. These facts tell against alternative developments, given that causal sets are understood as particular events. We thus interpret causal sets as multi-realisable objects, like states. This interpretation, however, is undermined by an argument for the probabilistic constraint of General Covariance, as it says that multiple paths along which a causal set is produced are not physically different

Inquisitive bisimulation

Inquisitive modal logic InqML is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that they are interested in. Technically, InqML fits within the family of logics based on team semantics. From a model-theoretic perspective, it takes us a step in the direction of monadic second-order logic, as inquisitive modal operators involve quantification over sets of worlds. We introduce and investigate the natural notion of bisimulation equivalence in the setting of InqML. We compare the expressiveness of InqML and first-order logic in the context of relational structures with two sorts, one for worlds and one for information states. We characterise inquisitive modal logic, as well as its multi-agent epistemic S5-like variant, as the bisimulation invariant fragment of first-order logic over various natural classes of two-sorted structures. These results crucially require non-classical methods in studying bisimulation and first-order expressiveness over non-elementary classes of structures, irrespective of whether we aim for characterisations in the sense of classical or of finite model theory

An LFG approach to Modern Greek Relative Clauses

This thesis presents an account of the properties of Relative Clauses in Modern Greek, with particular focus on the distribution of the resumption and gap relativization strategies. For the most part relative clauses have been regarded in the literature as a type of Long Distance dependencies with unique properties.This thesis looks at the properties of three types of relative clauses in Modern Greek (restrictive, non-restrictive and free relative clauses). Working in the framework of Lexical Functional Grammar, we present an overview of the most important properties of Modern Greek Relative Clauses focusing on the distribution of the gap and resumption strategies in these constructions. We propose an analysis of Relative Clauses that brings forward the similarities of the three types of Relatives while at the same time manages to account for their dissimilarities, and it is shown that such constructions can be accommodated in LFG quite straightforwardly. The thesis also presents a computational implementation of the analysis using XLE (Xerox Linguistics Environment) a platform for testing and writing LFG grammars