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The representation of free variables is crucial for the efficiency of the implementation of various kinds of rewrite systems. We give an innovative, although very natural, representation of variables abstract enough to fit in many different frameworks and more satisfactory from an operational perspective than usual representations. This work also provides a generalisation of director strings fo...

Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements. This paper consists of three parts. In the first part we consider some options for labels: simple constant labels vs labels with free variables, logic depended inference rules vs labels manipulation based on a label algebra. ...

In this paper we have a closer look at one of the rules of the tableau calculus presented in [3], called the δ–rule, and the modification of this rule, that has been proved to be sound and complete in [6], called the δ–rule, which uses fewer free variables. We show that an even more liberalized version, the δ + –rule, that in addition reduces the number of different Skolem–function symbols that...

theory of wide-scope indefinites which is similar, though not identical, to that proposed by Kratzer (1998). I show that a subset of St’át’imcets indefinites takes obligatory wide scope with respect to if-clauses, negation, and modals, and is unable to be distributed over by quantificational phrases. These wide-scope effects cannot be accounted for by movement, but require an analysis involving...

We identify a subproblem of the model-checking problem for the epistemic μ-calculus which is decidable. Formulas in the instances of this subproblem allow free variables within the scope of epistemic modalities in a restricted form that avoids embodying any form of common knowledge. Our subproblem subsumes known decidable fragments of epistemic CTL/LTL, may express winning strategies in two-pla...

In this paper, the notion of equivalence models for quantified Boolean formulas with free variables is introduced. The computational complexity of the equivalence model checking problem is investigated in the general case and some restricted cases. We also establish a connection between the structure of some quantified Boolean formulas and the structure of models.

We introduce a first-order language for semantic underspecification that we call Constraint Language for Lambda-Structures (CLLS). A A-structure can be considered as a A-term up to consistent renaming of bound variables (a-equality); a constraint of CLLS is an underspec-ified description of a A-structure. CLLS solves a capturing problem omnipresent in underspec-ified scope representations. CLLS...

If P is a hereditary property then we show that, for the existence of a perfect f -factor, P is a sufficient condition for countable graphs and yields a sufficient condition for graphs of size א1. Further we give two examples of a hereditary property which is even necessary for the existence of a perfect f -factor. We also discuss the א2-case. We consider graphs G = (V,E), where V = V (G) is a ...

Several authors have recently argued that semantic interpretation is subject to economy constraints. In particular, Fox (1999) argued that the interpretation of pronouns is subject to binding economy, which favors local binding over non-local binding. The present paper points out a problem for binding economy. The aim, then, is to see if this problem can be resolved in a conservative way, that ...