Timothy Williamson (1999) presents, without endorsing, an argument that for any n > 1, any sentence that is nth order vague is (n + 1)th order vague. The setting for the argument is a standard Kripke-style model theory for a propositional language enriched with an operator ∆ for ‘Definitely’. A model is a triple 〈W,≺, [[]]〉, where W is a domain of “points”, ≺ is an “accessibility” relation on W...

A leftist grammar is a rewrite system in which the only kind of production rules allowed are “create left-context” via a −→ ba, and “erase left-context” via ba −→ a. There is a special start symbol, S, which cannot be created or erased, but which can create context. A string w is said to be in L(G) if wS can be transformed through a sequence of rewrite rules to S. To the best of our knowledge, ...

This paper addresses the problem of determining the distance between two regular languages. It will show how to expand Jaccard distance, which works on finite sets, to potentially-infinite regular languages. The entropy of a regular language plays a large role in the extension. Much of the paper is spent investigating the entropy of a regular language. This includes addressing issues that have ...

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

Omega-regular algebras axiomatise the equational theory of omega-regular expressions as induced by omega-regular language identity. Wagner presented an omega-regular algebra which requires recursively defined side conditions in some of its axioms. We introduce a first-order Horn axiomatisation for which such conditions can be avoided because additive and multiplicative units are absent. We prov...

In this paper, we introduce a variant of the Ehrenfeucht-Fräıssé game from logic which is useful for analyzing the expressive power of classes of generalized regular expressions. An extension of the game to generalized ω-regular expressions is also established. To gain insight into how the game can be applied to attack the long-standing generalized star height 2 problem, we propose and solve a ...

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language – the input of the problem – and fixed language called filter is non-empty. We consider two kind of problems depending on representation of regular language. If a regular language on input is represented by a DFA, then we obtain (deterministic) regular realizability...

This paper describes the INEX 2003 participation of the Language & Inference Technology group of the University of Amsterdam. We participated in all three of the tasks, content-only, strict contentand-structure and vague content-and-structure.

Vague predicates such as heap, tall, bald, near to, nicer than, etc. are characterized by their Sorites susceptibility and the existence of borderline cases. In attempting to develop a general theory, diverse vague predicates are often analyzed in rather broad natural language settings. Because this has proven to be rather difficult, the phenomenon of vagueness is studied here in a narrower and...

Why is ordinary language vague? We argue that in contexts which a cooperative speaker not perfectly informed about the world, use of vague expressions can offer an optimal tradeoff between truthfulness (Gricean Quality) and informativeness Quantity). Focusing on approximation such as “around”, are semantically vague, we show they allow to convey indirect probabilistic information, way give list...